Prompt:
<|im_start|>user
Calculate the "Bohr radius" in angstroms to 3 decimal places for ${He}^{+}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Calculate the "Bohr radius" in angstroms to 3 decimal places for ${He}^{+}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Calculate the "Bohr radius" in angstroms to 3 decimal places for ${He}^{+}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For red light of wavelength $(\lambda) 6.7102 \times 10^{-5} cm$, emitted by excited lithium atoms, calculate:

the frequency $(v)$ in Hz, to 4 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For red light of wavelength $(\lambda) 6.7102 \times 10^{-5} cm$, emitted by excited lithium atoms, calculate:

the frequency $(v)$ in Hz, to 4 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For red light of wavelength $(\lambda) 6.7102 \times 10^{-5} cm$, emitted by excited lithium atoms, calculate:

the frequency $(v)$ in Hz, to 4 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For red light of wavelength $(\lambda) 6.7102 \times 10^{-5} cm$, emitted by excited lithium atoms, calculate:

the frequency $(v)$ in Hz, to 4 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Electromagnetic radiation of frequency $3.091 \times 10^{14} \mathrm{~Hz}$ illuminates a crystal of germanium (Ge). Calculate the wavelength of photoemission in meters generated by this interaction. Germanium is an elemental semiconductor with a band gap, $E_{g}$, of $0.7 \mathrm{eV}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Electromagnetic radiation of frequency $3.091 \times 10^{14} \mathrm{~Hz}$ illuminates a crystal of germanium (Ge). Calculate the wavelength of photoemission in meters generated by this interaction. Germanium is an elemental semiconductor with a band gap, $E_{g}$, of $0.7 \mathrm{eV}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Electromagnetic radiation of frequency $3.091 \times 10^{14} \mathrm{~Hz}$ illuminates a crystal of germanium (Ge). Calculate the wavelength of photoemission in meters generated by this interaction. Germanium is an elemental semiconductor with a band gap, $E_{g}$, of $0.7 \mathrm{eV}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Electromagnetic radiation of frequency $3.091 \times 10^{14} \mathrm{~Hz}$ illuminates a crystal of germanium (Ge). Calculate the wavelength of photoemission in meters generated by this interaction. Germanium is an elemental semiconductor with a band gap, $E_{g}$, of $0.7 \mathrm{eV}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the energy gap (in eV, to 1 decimal place) between the electronic states $n=3$ and $n=8$ in a hydrogen atom?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the energy gap (in eV, to 1 decimal place) between the electronic states $n=3$ and $n=8$ in a hydrogen atom?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the energy gap (in eV, to 1 decimal place) between the electronic states $n=3$ and $n=8$ in a hydrogen atom?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the energy gap (in eV, to 1 decimal place) between the electronic states $n=3$ and $n=8$ in a hydrogen atom?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine for hydrogen the velocity in m/s of an electron in an ${n}=4$ state. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine for hydrogen the velocity in m/s of an electron in an ${n}=4$ state. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine for hydrogen the velocity in m/s of an electron in an ${n}=4$ state. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine for hydrogen the velocity in m/s of an electron in an ${n}=4$ state. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A pure crystalline material (no impurities or dopants are present) appears red in transmitted light.

Subproblem 0: Is this material a conductor, semiconductor or insulator? Give the reasons for your answer.

Solution: If the material is pure (no impurity states present), then it must be classified as a \boxed{semiconductor} since it exhibits a finite "band gap" - i.e. to activate charge carriers, photons with energies in excess of "red" radiation are required.

Final answer: The final answer is semiconductor. I hope it is correct.

Subproblem 1: What is the approximate band gap $\left(\mathrm{E}_{g}\right)$ for this material in eV? Please round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A pure crystalline material (no impurities or dopants are present) appears red in transmitted light.

Subproblem 0: Is this material a conductor, semiconductor or insulator? Give the reasons for your answer.

Solution: If the material is pure (no impurity states present), then it must be classified as a \boxed{semiconductor} since it exhibits a finite "band gap" - i.e. to activate charge carriers, photons with energies in excess of "red" radiation are required.

Final answer: The final answer is semiconductor. I hope it is correct.

Subproblem 1: What is the approximate band gap $\left(\mathrm{E}_{g}\right)$ for this material in eV? Please round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A pure crystalline material (no impurities or dopants are present) appears red in transmitted light.

Subproblem 0: Is this material a conductor, semiconductor or insulator? Give the reasons for your answer.

Solution: If the material is pure (no impurity states present), then it must be classified as a \boxed{semiconductor} since it exhibits a finite "band gap" - i.e. to activate charge carriers, photons with energies in excess of "red" radiation are required.

Final answer: The final answer is semiconductor. I hope it is correct.

Subproblem 1: What is the approximate band gap $\left(\mathrm{E}_{g}\right)$ for this material in eV? Please round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: A pure crystalline material (no impurities or dopants are present) appears red in transmitted light.

Subproblem 0: Is this material a conductor, semiconductor or insulator? Give the reasons for your answer.

Solution: If the material is pure (no impurity states present), then it must be classified as a \boxed{semiconductor} since it exhibits a finite "band gap" - i.e. to activate charge carriers, photons with energies in excess of "red" radiation are required.

Final answer: The final answer is semiconductor. I hope it is correct.

Subproblem 1: What is the approximate band gap $\left(\mathrm{E}_{g}\right)$ for this material in eV? Please round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Calculate the minimum potential $(V)$ in volts (to 1 decimal place) which must be applied to a free electron so that it has enough energy to excite, upon impact, the electron in a hydrogen atom from its ground state to a state of $n=5$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Calculate the minimum potential $(V)$ in volts (to 1 decimal place) which must be applied to a free electron so that it has enough energy to excite, upon impact, the electron in a hydrogen atom from its ground state to a state of $n=5$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Calculate the minimum potential $(V)$ in volts (to 1 decimal place) which must be applied to a free electron so that it has enough energy to excite, upon impact, the electron in a hydrogen atom from its ground state to a state of $n=5$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Calculate the minimum potential $(V)$ in volts (to 1 decimal place) which must be applied to a free electron so that it has enough energy to excite, upon impact, the electron in a hydrogen atom from its ground state to a state of $n=5$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

Subproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
v \lambda &=c
\end{aligned}
\]
$v$ (frequency) $=\frac{c}{\lambda}=\frac{3 \times 10^{8} m / s}{408 \times 10^{-9} m}= \boxed{7.353e14} s^{-1}$

Final answer: The final answer is 7.353e14. I hope it is correct.

Subproblem 1: the wave number in $m^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
1 / \lambda=\bar{v}
\end{aligned}
\]
$\bar{v}$ (wavenumber) $=\frac{1}{\lambda}=\frac{1}{408 \times 10^{-9} m}=\boxed{2.45e6} m^{-1}$

Final answer: The final answer is 2.45e6. I hope it is correct.

Subproblem 2: the wavelength in angstroms.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

Subproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
v \lambda &=c
\end{aligned}
\]
$v$ (frequency) $=\frac{c}{\lambda}=\frac{3 \times 10^{8} m / s}{408 \times 10^{-9} m}= \boxed{7.353e14} s^{-1}$

Final answer: The final answer is 7.353e14. I hope it is correct.

Subproblem 1: the wave number in $m^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
1 / \lambda=\bar{v}
\end{aligned}
\]
$\bar{v}$ (wavenumber) $=\frac{1}{\lambda}=\frac{1}{408 \times 10^{-9} m}=\boxed{2.45e6} m^{-1}$

Final answer: The final answer is 2.45e6. I hope it is correct.

Subproblem 2: the wavelength in angstroms.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

Subproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
v \lambda &=c
\end{aligned}
\]
$v$ (frequency) $=\frac{c}{\lambda}=\frac{3 \times 10^{8} m / s}{408 \times 10^{-9} m}= \boxed{7.353e14} s^{-1}$

Final answer: The final answer is 7.353e14. I hope it is correct.

Subproblem 1: the wave number in $m^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
1 / \lambda=\bar{v}
\end{aligned}
\]
$\bar{v}$ (wavenumber) $=\frac{1}{\lambda}=\frac{1}{408 \times 10^{-9} m}=\boxed{2.45e6} m^{-1}$

Final answer: The final answer is 2.45e6. I hope it is correct.

Subproblem 2: the wavelength in angstroms.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

Subproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
v \lambda &=c
\end{aligned}
\]
$v$ (frequency) $=\frac{c}{\lambda}=\frac{3 \times 10^{8} m / s}{408 \times 10^{-9} m}= \boxed{7.353e14} s^{-1}$

Final answer: The final answer is 7.353e14. I hope it is correct.

Subproblem 1: the wave number in $m^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.

Solution: To solve this problem we must know the following relationships:
\[
\begin{aligned}
1 / \lambda=\bar{v}
\end{aligned}
\]
$\bar{v}$ (wavenumber) $=\frac{1}{\lambda}=\frac{1}{408 \times 10^{-9} m}=\boxed{2.45e6} m^{-1}$

Final answer: The final answer is 2.45e6. I hope it is correct.

Subproblem 2: the wavelength in angstroms.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Reference the information below to solve the following problems.
$\begin{array}{llll}\text { Element } & \text { Ionization Potential }  & \text { Element } & \text { Ionization Potential } \\ {Na} & 5.14 & {Ca} & 6.11 \\ {Mg} & 7.64 & {Sc} & 6.54 \\ {Al} & 5.98 & {Ti} & 6.82 \\ {Si} & 8.15 & {~V} & 6.74 \\ {P} & 10.48 & {Cr} & 6.76 \\ {~S} & 10.36 & {Mn} & 7.43 \\ {Cl} & 13.01 & {Fe} & 7.9 \\ {Ar} & 15.75 & {Co} & 7.86 \\ & & {Ni} & 7.63 \\ & & {Cu} & 7.72\end{array}$

Subproblem 0: What is the first ionization energy (in J, to 3 decimal places) for Na?

Solution: The required data can be obtained by multiplying the ionization potentials (listed in the Periodic Table) with the electronic charge ( ${e}^{-}=1.6 \times 10^{-19}$ C).
\boxed{0.822} J.

Final answer: The final answer is 0.822. I hope it is correct.

Subproblem 1: What is the first ionization energy (in J, to 2 decimal places) for Mg?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Reference the information below to solve the following problems.
$\begin{array}{llll}\text { Element } & \text { Ionization Potential }  & \text { Element } & \text { Ionization Potential } \\ {Na} & 5.14 & {Ca} & 6.11 \\ {Mg} & 7.64 & {Sc} & 6.54 \\ {Al} & 5.98 & {Ti} & 6.82 \\ {Si} & 8.15 & {~V} & 6.74 \\ {P} & 10.48 & {Cr} & 6.76 \\ {~S} & 10.36 & {Mn} & 7.43 \\ {Cl} & 13.01 & {Fe} & 7.9 \\ {Ar} & 15.75 & {Co} & 7.86 \\ & & {Ni} & 7.63 \\ & & {Cu} & 7.72\end{array}$

Subproblem 0: What is the first ionization energy (in J, to 3 decimal places) for Na?

Solution: The required data can be obtained by multiplying the ionization potentials (listed in the Periodic Table) with the electronic charge ( ${e}^{-}=1.6 \times 10^{-19}$ C).
\boxed{0.822} J.

Final answer: The final answer is 0.822. I hope it is correct.

Subproblem 1: What is the first ionization energy (in J, to 2 decimal places) for Mg?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Reference the information below to solve the following problems.
$\begin{array}{llll}\text { Element } & \text { Ionization Potential }  & \text { Element } & \text { Ionization Potential } \\ {Na} & 5.14 & {Ca} & 6.11 \\ {Mg} & 7.64 & {Sc} & 6.54 \\ {Al} & 5.98 & {Ti} & 6.82 \\ {Si} & 8.15 & {~V} & 6.74 \\ {P} & 10.48 & {Cr} & 6.76 \\ {~S} & 10.36 & {Mn} & 7.43 \\ {Cl} & 13.01 & {Fe} & 7.9 \\ {Ar} & 15.75 & {Co} & 7.86 \\ & & {Ni} & 7.63 \\ & & {Cu} & 7.72\end{array}$

Subproblem 0: What is the first ionization energy (in J, to 3 decimal places) for Na?

Solution: The required data can be obtained by multiplying the ionization potentials (listed in the Periodic Table) with the electronic charge ( ${e}^{-}=1.6 \times 10^{-19}$ C).
\boxed{0.822} J.

Final answer: The final answer is 0.822. I hope it is correct.

Subproblem 1: What is the first ionization energy (in J, to 2 decimal places) for Mg?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Reference the information below to solve the following problems.
$\begin{array}{llll}\text { Element } & \text { Ionization Potential }  & \text { Element } & \text { Ionization Potential } \\ {Na} & 5.14 & {Ca} & 6.11 \\ {Mg} & 7.64 & {Sc} & 6.54 \\ {Al} & 5.98 & {Ti} & 6.82 \\ {Si} & 8.15 & {~V} & 6.74 \\ {P} & 10.48 & {Cr} & 6.76 \\ {~S} & 10.36 & {Mn} & 7.43 \\ {Cl} & 13.01 & {Fe} & 7.9 \\ {Ar} & 15.75 & {Co} & 7.86 \\ & & {Ni} & 7.63 \\ & & {Cu} & 7.72\end{array}$

Subproblem 0: What is the first ionization energy (in J, to 3 decimal places) for Na?

Solution: The required data can be obtained by multiplying the ionization potentials (listed in the Periodic Table) with the electronic charge ( ${e}^{-}=1.6 \times 10^{-19}$ C).
\boxed{0.822} J.

Final answer: The final answer is 0.822. I hope it is correct.

Subproblem 1: What is the first ionization energy (in J, to 2 decimal places) for Mg?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Light of wavelength $\lambda=4.28 \times 10^{-7} {~m}$ interacts with a "motionless" hydrogen atom. During this interaction it transfers all its energy to the orbiting electron of the hydrogen. What is the velocity in m/s of this electron after interaction? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Light of wavelength $\lambda=4.28 \times 10^{-7} {~m}$ interacts with a "motionless" hydrogen atom. During this interaction it transfers all its energy to the orbiting electron of the hydrogen. What is the velocity in m/s of this electron after interaction? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Light of wavelength $\lambda=4.28 \times 10^{-7} {~m}$ interacts with a "motionless" hydrogen atom. During this interaction it transfers all its energy to the orbiting electron of the hydrogen. What is the velocity in m/s of this electron after interaction? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Light of wavelength $\lambda=4.28 \times 10^{-7} {~m}$ interacts with a "motionless" hydrogen atom. During this interaction it transfers all its energy to the orbiting electron of the hydrogen. What is the velocity in m/s of this electron after interaction? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the minimum potential in V (to 2 decimal places) that must be applied to an $\alpha$-particle so that on interaction with a hydrogen atom, a ground state electron will be excited to $n$ $=6$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the minimum potential in V (to 2 decimal places) that must be applied to an $\alpha$-particle so that on interaction with a hydrogen atom, a ground state electron will be excited to $n$ $=6$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the minimum potential in V (to 2 decimal places) that must be applied to an $\alpha$-particle so that on interaction with a hydrogen atom, a ground state electron will be excited to $n$ $=6$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the minimum potential in V (to 2 decimal places) that must be applied to an $\alpha$-particle so that on interaction with a hydrogen atom, a ground state electron will be excited to $n$ $=6$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Reference the information below to solve the following problems.
$\begin{array}{llll}\text { Element } & \text { Ionization Potential }  & \text { Element } & \text { Ionization Potential } \\ {Na} & 5.14 & {Ca} & 6.11 \\ {Mg} & 7.64 & {Sc} & 6.54 \\ {Al} & 5.98 & {Ti} & 6.82 \\ {Si} & 8.15 & {~V} & 6.74 \\ {P} & 10.48 & {Cr} & 6.76 \\ {~S} & 10.36 & {Mn} & 7.43 \\ {Cl} & 13.01 & {Fe} & 7.9 \\ {Ar} & 15.75 & {Co} & 7.86 \\ & & {Ni} & 7.63 \\ & & {Cu} & 7.72\end{array}$

What is the first ionization energy (in J, to 3 decimal places) for Na?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Reference the information below to solve the following problems.
$\begin{array}{llll}\text { Element } & \text { Ionization Potential }  & \text { Element } & \text { Ionization Potential } \\ {Na} & 5.14 & {Ca} & 6.11 \\ {Mg} & 7.64 & {Sc} & 6.54 \\ {Al} & 5.98 & {Ti} & 6.82 \\ {Si} & 8.15 & {~V} & 6.74 \\ {P} & 10.48 & {Cr} & 6.76 \\ {~S} & 10.36 & {Mn} & 7.43 \\ {Cl} & 13.01 & {Fe} & 7.9 \\ {Ar} & 15.75 & {Co} & 7.86 \\ & & {Ni} & 7.63 \\ & & {Cu} & 7.72\end{array}$

What is the first ionization energy (in J, to 3 decimal places) for Na?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Reference the information below to solve the following problems.
$\begin{array}{llll}\text { Element } & \text { Ionization Potential }  & \text { Element } & \text { Ionization Potential } \\ {Na} & 5.14 & {Ca} & 6.11 \\ {Mg} & 7.64 & {Sc} & 6.54 \\ {Al} & 5.98 & {Ti} & 6.82 \\ {Si} & 8.15 & {~V} & 6.74 \\ {P} & 10.48 & {Cr} & 6.76 \\ {~S} & 10.36 & {Mn} & 7.43 \\ {Cl} & 13.01 & {Fe} & 7.9 \\ {Ar} & 15.75 & {Co} & 7.86 \\ & & {Ni} & 7.63 \\ & & {Cu} & 7.72\end{array}$

What is the first ionization energy (in J, to 3 decimal places) for Na?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Reference the information below to solve the following problems.
$\begin{array}{llll}\text { Element } & \text { Ionization Potential }  & \text { Element } & \text { Ionization Potential } \\ {Na} & 5.14 & {Ca} & 6.11 \\ {Mg} & 7.64 & {Sc} & 6.54 \\ {Al} & 5.98 & {Ti} & 6.82 \\ {Si} & 8.15 & {~V} & 6.74 \\ {P} & 10.48 & {Cr} & 6.76 \\ {~S} & 10.36 & {Mn} & 7.43 \\ {Cl} & 13.01 & {Fe} & 7.9 \\ {Ar} & 15.75 & {Co} & 7.86 \\ & & {Ni} & 7.63 \\ & & {Cu} & 7.72\end{array}$

What is the first ionization energy (in J, to 3 decimal places) for Na?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For "yellow radiation" (frequency, $v,=5.09 \times 10^{14} s^{-1}$ ) emitted by activated sodium, determine:

Subproblem 0: the wavelength $(\lambda)$ in m. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.

Solution: The equation relating $v$ and $\lambda$ is $c=v \lambda$ where $c$ is the speed of light $=3.00 \times 10^{8} \mathrm{~m}$.
\[
\lambda=\frac{c}{v}=\frac{3.00 \times 10^{8} m / s}{5.09 \times 10^{14} s^{-1}}=\boxed{5.89e-7} m
\]

Final answer: The final answer is 5.89e-7. I hope it is correct.

Subproblem 1: the wave number $(\bar{v})$ in ${cm}^{-1}$. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For "yellow radiation" (frequency, $v,=5.09 \times 10^{14} s^{-1}$ ) emitted by activated sodium, determine:

Subproblem 0: the wavelength $(\lambda)$ in m. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.

Solution: The equation relating $v$ and $\lambda$ is $c=v \lambda$ where $c$ is the speed of light $=3.00 \times 10^{8} \mathrm{~m}$.
\[
\lambda=\frac{c}{v}=\frac{3.00 \times 10^{8} m / s}{5.09 \times 10^{14} s^{-1}}=\boxed{5.89e-7} m
\]

Final answer: The final answer is 5.89e-7. I hope it is correct.

Subproblem 1: the wave number $(\bar{v})$ in ${cm}^{-1}$. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For "yellow radiation" (frequency, $v,=5.09 \times 10^{14} s^{-1}$ ) emitted by activated sodium, determine:

Subproblem 0: the wavelength $(\lambda)$ in m. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.

Solution: The equation relating $v$ and $\lambda$ is $c=v \lambda$ where $c$ is the speed of light $=3.00 \times 10^{8} \mathrm{~m}$.
\[
\lambda=\frac{c}{v}=\frac{3.00 \times 10^{8} m / s}{5.09 \times 10^{14} s^{-1}}=\boxed{5.89e-7} m
\]

Final answer: The final answer is 5.89e-7. I hope it is correct.

Subproblem 1: the wave number $(\bar{v})$ in ${cm}^{-1}$. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For "yellow radiation" (frequency, $v,=5.09 \times 10^{14} s^{-1}$ ) emitted by activated sodium, determine:

Subproblem 0: the wavelength $(\lambda)$ in m. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.

Solution: The equation relating $v$ and $\lambda$ is $c=v \lambda$ where $c$ is the speed of light $=3.00 \times 10^{8} \mathrm{~m}$.
\[
\lambda=\frac{c}{v}=\frac{3.00 \times 10^{8} m / s}{5.09 \times 10^{14} s^{-1}}=\boxed{5.89e-7} m
\]

Final answer: The final answer is 5.89e-7. I hope it is correct.

Subproblem 1: the wave number $(\bar{v})$ in ${cm}^{-1}$. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

$\mathrm{NH}_{4} \mathrm{OH}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

$\mathrm{NH}_{4} \mathrm{OH}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

$\mathrm{NH}_{4} \mathrm{OH}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

$\mathrm{NH}_{4} \mathrm{OH}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?

Solution: \boxed{0.5}.

Final answer: The final answer is 0.5. I hope it is correct.

Subproblem 2: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}_{2}$ (in decimal form)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?

Solution: \boxed{0.5}.

Final answer: The final answer is 0.5. I hope it is correct.

Subproblem 2: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}_{2}$ (in decimal form)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?

Solution: \boxed{0.5}.

Final answer: The final answer is 0.5. I hope it is correct.

Subproblem 2: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}_{2}$ (in decimal form)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?

Solution: \boxed{0.5}.

Final answer: The final answer is 0.5. I hope it is correct.

Subproblem 2: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}_{2}$ (in decimal form)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Magnesium (Mg) has the following isotopic distribution:
\[
\begin{array}{ll}
24_{\mathrm{Mg}} & 23.985 \mathrm{amu} \text { at } 0.7870 \text { fractional abundance } \\
25_{\mathrm{Mg}} & 24.986 \mathrm{amu} \text { at } 0.1013 \text { fractional abundance } \\
26_{\mathrm{Mg}} & 25.983 \mathrm{amu} \text { at } 0.1117 \text { fractional abundance }
\end{array}
\]
What is the atomic weight of magnesium (Mg) (to 3 decimal places) according to these data?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Magnesium (Mg) has the following isotopic distribution:
\[
\begin{array}{ll}
24_{\mathrm{Mg}} & 23.985 \mathrm{amu} \text { at } 0.7870 \text { fractional abundance } \\
25_{\mathrm{Mg}} & 24.986 \mathrm{amu} \text { at } 0.1013 \text { fractional abundance } \\
26_{\mathrm{Mg}} & 25.983 \mathrm{amu} \text { at } 0.1117 \text { fractional abundance }
\end{array}
\]
What is the atomic weight of magnesium (Mg) (to 3 decimal places) according to these data?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Magnesium (Mg) has the following isotopic distribution:
\[
\begin{array}{ll}
24_{\mathrm{Mg}} & 23.985 \mathrm{amu} \text { at } 0.7870 \text { fractional abundance } \\
25_{\mathrm{Mg}} & 24.986 \mathrm{amu} \text { at } 0.1013 \text { fractional abundance } \\
26_{\mathrm{Mg}} & 25.983 \mathrm{amu} \text { at } 0.1117 \text { fractional abundance }
\end{array}
\]
What is the atomic weight of magnesium (Mg) (to 3 decimal places) according to these data?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Magnesium (Mg) has the following isotopic distribution:
\[
\begin{array}{ll}
24_{\mathrm{Mg}} & 23.985 \mathrm{amu} \text { at } 0.7870 \text { fractional abundance } \\
25_{\mathrm{Mg}} & 24.986 \mathrm{amu} \text { at } 0.1013 \text { fractional abundance } \\
26_{\mathrm{Mg}} & 25.983 \mathrm{amu} \text { at } 0.1117 \text { fractional abundance }
\end{array}
\]
What is the atomic weight of magnesium (Mg) (to 3 decimal places) according to these data?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Electrons are accelerated by a potential of 10 Volts.

Determine their velocity in m/s. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Electrons are accelerated by a potential of 10 Volts.

Determine their velocity in m/s. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Electrons are accelerated by a potential of 10 Volts.

Determine their velocity in m/s. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Electrons are accelerated by a potential of 10 Volts.

Determine their velocity in m/s. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the frequency (in $s^{-1}$ of radiation capable of generating, in atomic hydrogen, free electrons which have a velocity of $1.3 \times 10^{6} {~ms}^{-1}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the frequency (in $s^{-1}$ of radiation capable of generating, in atomic hydrogen, free electrons which have a velocity of $1.3 \times 10^{6} {~ms}^{-1}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the frequency (in $s^{-1}$ of radiation capable of generating, in atomic hydrogen, free electrons which have a velocity of $1.3 \times 10^{6} {~ms}^{-1}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the frequency (in $s^{-1}$ of radiation capable of generating, in atomic hydrogen, free electrons which have a velocity of $1.3 \times 10^{6} {~ms}^{-1}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Electrons are accelerated by a potential of 10 Volts.

Subproblem 0: Determine their velocity in m/s. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.

Solution: The definition of an ${eV}$ is the energy gained by an electron when it is accelerated through a potential of $1 {~V}$, so an electron accelerated by a potential of $10 {~V}$ would have an energy of $10 {eV}$.\\
${E}=\frac{1}{2} m {v}^{2} \rightarrow {v}=\sqrt{2 {E} / {m}}$
\[
E=10 {eV}=1.60 \times 10^{-18} {~J}
\]
\[
\begin{aligned}
& {m}=\text { mass of electron }=9.11 \times 10^{-31} {~kg} \\
& v=\sqrt{\frac{2 \times 1.6 \times 10^{-18} {~J}}{9.11 \times 10^{-31} {~kg}}}= \boxed{1.87e6} {~m} / {s}
\end{aligned}
\]

Final answer: The final answer is 1.87e6. I hope it is correct.

Subproblem 1: Determine their deBroglie wavelength $\left(\lambda_{p}\right)$ in m. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Electrons are accelerated by a potential of 10 Volts.

Subproblem 0: Determine their velocity in m/s. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.

Solution: The definition of an ${eV}$ is the energy gained by an electron when it is accelerated through a potential of $1 {~V}$, so an electron accelerated by a potential of $10 {~V}$ would have an energy of $10 {eV}$.\\
${E}=\frac{1}{2} m {v}^{2} \rightarrow {v}=\sqrt{2 {E} / {m}}$
\[
E=10 {eV}=1.60 \times 10^{-18} {~J}
\]
\[
\begin{aligned}
& {m}=\text { mass of electron }=9.11 \times 10^{-31} {~kg} \\
& v=\sqrt{\frac{2 \times 1.6 \times 10^{-18} {~J}}{9.11 \times 10^{-31} {~kg}}}= \boxed{1.87e6} {~m} / {s}
\end{aligned}
\]

Final answer: The final answer is 1.87e6. I hope it is correct.

Subproblem 1: Determine their deBroglie wavelength $\left(\lambda_{p}\right)$ in m. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Electrons are accelerated by a potential of 10 Volts.

Subproblem 0: Determine their velocity in m/s. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.

Solution: The definition of an ${eV}$ is the energy gained by an electron when it is accelerated through a potential of $1 {~V}$, so an electron accelerated by a potential of $10 {~V}$ would have an energy of $10 {eV}$.\\
${E}=\frac{1}{2} m {v}^{2} \rightarrow {v}=\sqrt{2 {E} / {m}}$
\[
E=10 {eV}=1.60 \times 10^{-18} {~J}
\]
\[
\begin{aligned}
& {m}=\text { mass of electron }=9.11 \times 10^{-31} {~kg} \\
& v=\sqrt{\frac{2 \times 1.6 \times 10^{-18} {~J}}{9.11 \times 10^{-31} {~kg}}}= \boxed{1.87e6} {~m} / {s}
\end{aligned}
\]

Final answer: The final answer is 1.87e6. I hope it is correct.

Subproblem 1: Determine their deBroglie wavelength $\left(\lambda_{p}\right)$ in m. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Electrons are accelerated by a potential of 10 Volts.

Subproblem 0: Determine their velocity in m/s. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.

Solution: The definition of an ${eV}$ is the energy gained by an electron when it is accelerated through a potential of $1 {~V}$, so an electron accelerated by a potential of $10 {~V}$ would have an energy of $10 {eV}$.\\
${E}=\frac{1}{2} m {v}^{2} \rightarrow {v}=\sqrt{2 {E} / {m}}$
\[
E=10 {eV}=1.60 \times 10^{-18} {~J}
\]
\[
\begin{aligned}
& {m}=\text { mass of electron }=9.11 \times 10^{-31} {~kg} \\
& v=\sqrt{\frac{2 \times 1.6 \times 10^{-18} {~J}}{9.11 \times 10^{-31} {~kg}}}= \boxed{1.87e6} {~m} / {s}
\end{aligned}
\]

Final answer: The final answer is 1.87e6. I hope it is correct.

Subproblem 1: Determine their deBroglie wavelength $\left(\lambda_{p}\right)$ in m. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: In all likelihood, the Soviet Union and the United States together in the past exploded about ten hydrogen devices underground per year.

If each explosion converted about $10 \mathrm{~g}$ of matter into an equivalent amount of energy (a conservative estimate), how many $k J$ of energy were released per device? Please format your answer as $n \times 10^{x}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: In all likelihood, the Soviet Union and the United States together in the past exploded about ten hydrogen devices underground per year.

If each explosion converted about $10 \mathrm{~g}$ of matter into an equivalent amount of energy (a conservative estimate), how many $k J$ of energy were released per device? Please format your answer as $n \times 10^{x}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: In all likelihood, the Soviet Union and the United States together in the past exploded about ten hydrogen devices underground per year.

If each explosion converted about $10 \mathrm{~g}$ of matter into an equivalent amount of energy (a conservative estimate), how many $k J$ of energy were released per device? Please format your answer as $n \times 10^{x}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: In all likelihood, the Soviet Union and the United States together in the past exploded about ten hydrogen devices underground per year.

If each explosion converted about $10 \mathrm{~g}$ of matter into an equivalent amount of energy (a conservative estimate), how many $k J$ of energy were released per device? Please format your answer as $n \times 10^{x}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

Subproblem 0: $\mathrm{NH}_{4} \mathrm{OH}$

Solution: $\mathrm{NH}_{4} \mathrm{OH}$ :
$5 \times 1.01=5.05(\mathrm{H})$
$1 \times 14.01=14.01(\mathrm{~N})$
$1 \times 16.00=16.00(\mathrm{O})$
$\mathrm{NH}_{4} \mathrm{OH}= \boxed{35.06}$ g/mole

Final answer: The final answer is 35.06. I hope it is correct.

Subproblem 1: $\mathrm{NaHCO}_{3}$

Solution: $\mathrm{NaHCO}_{3}: 3 \times 16.00=48.00(\mathrm{O})$
$1 \times 22.99=22.99(\mathrm{Na})$
$1 \times 1.01=1.01$ (H)
$1 \times 12.01=12.01$ (C)
$\mathrm{NaHCO}_{3}= \boxed{84.01}$ g/mole

Final answer: The final answer is 84.01. I hope it is correct.

Subproblem 2: $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

Subproblem 0: $\mathrm{NH}_{4} \mathrm{OH}$

Solution: $\mathrm{NH}_{4} \mathrm{OH}$ :
$5 \times 1.01=5.05(\mathrm{H})$
$1 \times 14.01=14.01(\mathrm{~N})$
$1 \times 16.00=16.00(\mathrm{O})$
$\mathrm{NH}_{4} \mathrm{OH}= \boxed{35.06}$ g/mole

Final answer: The final answer is 35.06. I hope it is correct.

Subproblem 1: $\mathrm{NaHCO}_{3}$

Solution: $\mathrm{NaHCO}_{3}: 3 \times 16.00=48.00(\mathrm{O})$
$1 \times 22.99=22.99(\mathrm{Na})$
$1 \times 1.01=1.01$ (H)
$1 \times 12.01=12.01$ (C)
$\mathrm{NaHCO}_{3}= \boxed{84.01}$ g/mole

Final answer: The final answer is 84.01. I hope it is correct.

Subproblem 2: $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

Subproblem 0: $\mathrm{NH}_{4} \mathrm{OH}$

Solution: $\mathrm{NH}_{4} \mathrm{OH}$ :
$5 \times 1.01=5.05(\mathrm{H})$
$1 \times 14.01=14.01(\mathrm{~N})$
$1 \times 16.00=16.00(\mathrm{O})$
$\mathrm{NH}_{4} \mathrm{OH}= \boxed{35.06}$ g/mole

Final answer: The final answer is 35.06. I hope it is correct.

Subproblem 1: $\mathrm{NaHCO}_{3}$

Solution: $\mathrm{NaHCO}_{3}: 3 \times 16.00=48.00(\mathrm{O})$
$1 \times 22.99=22.99(\mathrm{Na})$
$1 \times 1.01=1.01$ (H)
$1 \times 12.01=12.01$ (C)
$\mathrm{NaHCO}_{3}= \boxed{84.01}$ g/mole

Final answer: The final answer is 84.01. I hope it is correct.

Subproblem 2: $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.

Subproblem 0: $\mathrm{NH}_{4} \mathrm{OH}$

Solution: $\mathrm{NH}_{4} \mathrm{OH}$ :
$5 \times 1.01=5.05(\mathrm{H})$
$1 \times 14.01=14.01(\mathrm{~N})$
$1 \times 16.00=16.00(\mathrm{O})$
$\mathrm{NH}_{4} \mathrm{OH}= \boxed{35.06}$ g/mole

Final answer: The final answer is 35.06. I hope it is correct.

Subproblem 1: $\mathrm{NaHCO}_{3}$

Solution: $\mathrm{NaHCO}_{3}: 3 \times 16.00=48.00(\mathrm{O})$
$1 \times 22.99=22.99(\mathrm{Na})$
$1 \times 1.01=1.01$ (H)
$1 \times 12.01=12.01$ (C)
$\mathrm{NaHCO}_{3}= \boxed{84.01}$ g/mole

Final answer: The final answer is 84.01. I hope it is correct.

Subproblem 2: $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?

Solution: \boxed{0.5}.

Final answer: The final answer is 0.5. I hope it is correct.

Subproblem 2: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}_{2}$ (in decimal form)?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 3: If $32.0 \mathrm{~g}$ of oxygen react with $\mathrm{CO}$ to form carbon dioxide $\left(\mathrm{CO}_{2}\right)$, how much CO was consumed in this reaction (to 1 decimal place)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?

Solution: \boxed{0.5}.

Final answer: The final answer is 0.5. I hope it is correct.

Subproblem 2: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}_{2}$ (in decimal form)?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 3: If $32.0 \mathrm{~g}$ of oxygen react with $\mathrm{CO}$ to form carbon dioxide $\left(\mathrm{CO}_{2}\right)$, how much CO was consumed in this reaction (to 1 decimal place)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?

Solution: \boxed{0.5}.

Final answer: The final answer is 0.5. I hope it is correct.

Subproblem 2: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}_{2}$ (in decimal form)?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 3: If $32.0 \mathrm{~g}$ of oxygen react with $\mathrm{CO}$ to form carbon dioxide $\left(\mathrm{CO}_{2}\right)$, how much CO was consumed in this reaction (to 1 decimal place)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}$?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 1: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{O}_{2}$ (in decimal form)?

Solution: \boxed{0.5}.

Final answer: The final answer is 0.5. I hope it is correct.

Subproblem 2: In the balanced equation for the reaction between $\mathrm{CO}$ and $\mathrm{O}_{2}$ to form $\mathrm{CO}_{2}$, what is the coefficient of $\mathrm{CO}_{2}$ (in decimal form)?

Solution: \boxed{1}.

Final answer: The final answer is 1. I hope it is correct.

Subproblem 3: If $32.0 \mathrm{~g}$ of oxygen react with $\mathrm{CO}$ to form carbon dioxide $\left(\mathrm{CO}_{2}\right)$, how much CO was consumed in this reaction (to 1 decimal place)?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For "yellow radiation" (frequency, $v,=5.09 \times 10^{14} s^{-1}$ ) emitted by activated sodium, determine:

the wavelength $(\lambda)$ in m. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For "yellow radiation" (frequency, $v,=5.09 \times 10^{14} s^{-1}$ ) emitted by activated sodium, determine:

the wavelength $(\lambda)$ in m. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For "yellow radiation" (frequency, $v,=5.09 \times 10^{14} s^{-1}$ ) emitted by activated sodium, determine:

the wavelength $(\lambda)$ in m. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For "yellow radiation" (frequency, $v,=5.09 \times 10^{14} s^{-1}$ ) emitted by activated sodium, determine:

the wavelength $(\lambda)$ in m. Please format your answer as $n \times 10^x$, where n is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
For a proton which has been subjected to an accelerating potential (V) of 15 Volts, determine its deBroglie wavelength in m. Please format your answer as $n \times 10^x$, where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
For a proton which has been subjected to an accelerating potential (V) of 15 Volts, determine its deBroglie wavelength in m. Please format your answer as $n \times 10^x$, where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
For a proton which has been subjected to an accelerating potential (V) of 15 Volts, determine its deBroglie wavelength in m. Please format your answer as $n \times 10^x$, where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
For a proton which has been subjected to an accelerating potential (V) of 15 Volts, determine its deBroglie wavelength in m. Please format your answer as $n \times 10^x$, where $n$ is to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For light with a wavelength $(\lambda)$ of $408 \mathrm{~nm}$ determine:

the frequency in $s^{-1}$. Please format your answer as $n \times 10^x$, where $n$ is to 3 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine in units of eV (to 2 decimal places) the energy of a photon ( $h v)$ with the wavelength of $800$ nm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine in units of eV (to 2 decimal places) the energy of a photon ( $h v)$ with the wavelength of $800$ nm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine in units of eV (to 2 decimal places) the energy of a photon ( $h v)$ with the wavelength of $800$ nm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine in units of eV (to 2 decimal places) the energy of a photon ( $h v)$ with the wavelength of $800$ nm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine for barium (Ba) the linear density of atoms along the $<110>$ directions, in atoms/m.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine for barium (Ba) the linear density of atoms along the $<110>$ directions, in atoms/m.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine for barium (Ba) the linear density of atoms along the $<110>$ directions, in atoms/m.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine for barium (Ba) the linear density of atoms along the $<110>$ directions, in atoms/m.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A photon with a wavelength $(\lambda)$ of $3.091 \times 10^{-7} {~m}$ strikes an atom of hydrogen. Determine the velocity in m/s of an electron ejected from the excited state, $n=3$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A photon with a wavelength $(\lambda)$ of $3.091 \times 10^{-7} {~m}$ strikes an atom of hydrogen. Determine the velocity in m/s of an electron ejected from the excited state, $n=3$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A photon with a wavelength $(\lambda)$ of $3.091 \times 10^{-7} {~m}$ strikes an atom of hydrogen. Determine the velocity in m/s of an electron ejected from the excited state, $n=3$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A photon with a wavelength $(\lambda)$ of $3.091 \times 10^{-7} {~m}$ strikes an atom of hydrogen. Determine the velocity in m/s of an electron ejected from the excited state, $n=3$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For the element copper (Cu) determine:

the distance of second nearest neighbors (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For the element copper (Cu) determine:

the distance of second nearest neighbors (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For the element copper (Cu) determine:

the distance of second nearest neighbors (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For the element copper (Cu) determine:

the distance of second nearest neighbors (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A line of the Lyman series of the spectrum of hydrogen has a wavelength of $9.50 \times 10^{-8} {~m}$. What was the "upper" quantum state $\left({n}_{{i}}\right)$ involved in the associated electron transition?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A line of the Lyman series of the spectrum of hydrogen has a wavelength of $9.50 \times 10^{-8} {~m}$. What was the "upper" quantum state $\left({n}_{{i}}\right)$ involved in the associated electron transition?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A line of the Lyman series of the spectrum of hydrogen has a wavelength of $9.50 \times 10^{-8} {~m}$. What was the "upper" quantum state $\left({n}_{{i}}\right)$ involved in the associated electron transition?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A line of the Lyman series of the spectrum of hydrogen has a wavelength of $9.50 \times 10^{-8} {~m}$. What was the "upper" quantum state $\left({n}_{{i}}\right)$ involved in the associated electron transition?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the diffusivity $\mathrm{D}$ of lithium ( $\mathrm{Li}$ ) in silicon (Si) at $1200^{\circ} \mathrm{C}$, knowing that $D_{1100^{\circ} \mathrm{C}}=10^{-5} \mathrm{~cm}^{2} / \mathrm{s}$ and $\mathrm{D}_{695^{\circ} \mathrm{C}}=10^{-6} \mathrm{~cm}^{2} / \mathrm{s}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, in $\mathrm{~cm}^2/\mathrm{sec}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the diffusivity $\mathrm{D}$ of lithium ( $\mathrm{Li}$ ) in silicon (Si) at $1200^{\circ} \mathrm{C}$, knowing that $D_{1100^{\circ} \mathrm{C}}=10^{-5} \mathrm{~cm}^{2} / \mathrm{s}$ and $\mathrm{D}_{695^{\circ} \mathrm{C}}=10^{-6} \mathrm{~cm}^{2} / \mathrm{s}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, in $\mathrm{~cm}^2/\mathrm{sec}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the diffusivity $\mathrm{D}$ of lithium ( $\mathrm{Li}$ ) in silicon (Si) at $1200^{\circ} \mathrm{C}$, knowing that $D_{1100^{\circ} \mathrm{C}}=10^{-5} \mathrm{~cm}^{2} / \mathrm{s}$ and $\mathrm{D}_{695^{\circ} \mathrm{C}}=10^{-6} \mathrm{~cm}^{2} / \mathrm{s}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, in $\mathrm{~cm}^2/\mathrm{sec}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the diffusivity $\mathrm{D}$ of lithium ( $\mathrm{Li}$ ) in silicon (Si) at $1200^{\circ} \mathrm{C}$, knowing that $D_{1100^{\circ} \mathrm{C}}=10^{-5} \mathrm{~cm}^{2} / \mathrm{s}$ and $\mathrm{D}_{695^{\circ} \mathrm{C}}=10^{-6} \mathrm{~cm}^{2} / \mathrm{s}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, in $\mathrm{~cm}^2/\mathrm{sec}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
By planar diffusion of antimony (Sb) into p-type germanium (Ge), a p-n junction is obtained at a depth of $3 \times 10^{-3} \mathrm{~cm}$ below the surface. What is the donor concentration in the bulk germanium if diffusion is carried out for three hours at $790^{\circ} \mathrm{C}$? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, and express it in units of $1/\mathrm{cm}^3$. The surface concentration of antimony is held constant at a value of $8 \times 10^{18}$ $\mathrm{cm}^{-3} ; D_{790^{\circ} \mathrm{C}}=4.8 \times 10^{-11} \mathrm{~cm}^{2} / \mathrm{s}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
By planar diffusion of antimony (Sb) into p-type germanium (Ge), a p-n junction is obtained at a depth of $3 \times 10^{-3} \mathrm{~cm}$ below the surface. What is the donor concentration in the bulk germanium if diffusion is carried out for three hours at $790^{\circ} \mathrm{C}$? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, and express it in units of $1/\mathrm{cm}^3$. The surface concentration of antimony is held constant at a value of $8 \times 10^{18}$ $\mathrm{cm}^{-3} ; D_{790^{\circ} \mathrm{C}}=4.8 \times 10^{-11} \mathrm{~cm}^{2} / \mathrm{s}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
By planar diffusion of antimony (Sb) into p-type germanium (Ge), a p-n junction is obtained at a depth of $3 \times 10^{-3} \mathrm{~cm}$ below the surface. What is the donor concentration in the bulk germanium if diffusion is carried out for three hours at $790^{\circ} \mathrm{C}$? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, and express it in units of $1/\mathrm{cm}^3$. The surface concentration of antimony is held constant at a value of $8 \times 10^{18}$ $\mathrm{cm}^{-3} ; D_{790^{\circ} \mathrm{C}}=4.8 \times 10^{-11} \mathrm{~cm}^{2} / \mathrm{s}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
By planar diffusion of antimony (Sb) into p-type germanium (Ge), a p-n junction is obtained at a depth of $3 \times 10^{-3} \mathrm{~cm}$ below the surface. What is the donor concentration in the bulk germanium if diffusion is carried out for three hours at $790^{\circ} \mathrm{C}$? Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, and express it in units of $1/\mathrm{cm}^3$. The surface concentration of antimony is held constant at a value of $8 \times 10^{18}$ $\mathrm{cm}^{-3} ; D_{790^{\circ} \mathrm{C}}=4.8 \times 10^{-11} \mathrm{~cm}^{2} / \mathrm{s}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: One mole of electromagnetic radiation (light, consisting of energy packages called photons) has an energy of $171 \mathrm{~kJ} /$ mole photons.

Determine the wavelength of this light in nm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: One mole of electromagnetic radiation (light, consisting of energy packages called photons) has an energy of $171 \mathrm{~kJ} /$ mole photons.

Determine the wavelength of this light in nm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: One mole of electromagnetic radiation (light, consisting of energy packages called photons) has an energy of $171 \mathrm{~kJ} /$ mole photons.

Determine the wavelength of this light in nm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: One mole of electromagnetic radiation (light, consisting of energy packages called photons) has an energy of $171 \mathrm{~kJ} /$ mole photons.

Determine the wavelength of this light in nm.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Two lasers generate radiation of (1) $9.5 \mu {m}$ and (2) $0.1 \mu {m}$ respectively.

Determine the photon energy (in eV, to two decimal places) of the laser generating radiation of $9.5 \mu {m}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Two lasers generate radiation of (1) $9.5 \mu {m}$ and (2) $0.1 \mu {m}$ respectively.

Determine the photon energy (in eV, to two decimal places) of the laser generating radiation of $9.5 \mu {m}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Two lasers generate radiation of (1) $9.5 \mu {m}$ and (2) $0.1 \mu {m}$ respectively.

Determine the photon energy (in eV, to two decimal places) of the laser generating radiation of $9.5 \mu {m}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Two lasers generate radiation of (1) $9.5 \mu {m}$ and (2) $0.1 \mu {m}$ respectively.

Determine the photon energy (in eV, to two decimal places) of the laser generating radiation of $9.5 \mu {m}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
At $100^{\circ} \mathrm{C}$ copper $(\mathrm{Cu})$ has a lattice constant of $3.655 \AA$. What is its density in $g/cm^3$ at this temperature? Please round your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
At $100^{\circ} \mathrm{C}$ copper $(\mathrm{Cu})$ has a lattice constant of $3.655 \AA$. What is its density in $g/cm^3$ at this temperature? Please round your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
At $100^{\circ} \mathrm{C}$ copper $(\mathrm{Cu})$ has a lattice constant of $3.655 \AA$. What is its density in $g/cm^3$ at this temperature? Please round your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
At $100^{\circ} \mathrm{C}$ copper $(\mathrm{Cu})$ has a lattice constant of $3.655 \AA$. What is its density in $g/cm^3$ at this temperature? Please round your answer to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the atomic (metallic) radius of Mo in meters. Do not give the value listed in the periodic table; calculate it from the fact that Mo's atomic weight is $=95.94 \mathrm{~g} /$ mole and $\rho=10.2 \mathrm{~g} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the atomic (metallic) radius of Mo in meters. Do not give the value listed in the periodic table; calculate it from the fact that Mo's atomic weight is $=95.94 \mathrm{~g} /$ mole and $\rho=10.2 \mathrm{~g} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the atomic (metallic) radius of Mo in meters. Do not give the value listed in the periodic table; calculate it from the fact that Mo's atomic weight is $=95.94 \mathrm{~g} /$ mole and $\rho=10.2 \mathrm{~g} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the atomic (metallic) radius of Mo in meters. Do not give the value listed in the periodic table; calculate it from the fact that Mo's atomic weight is $=95.94 \mathrm{~g} /$ mole and $\rho=10.2 \mathrm{~g} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Determine the following values from a standard radio dial.

What is the minimum wavelength in m for broadcasts on the AM band? Format your answer as an integer.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Determine the following values from a standard radio dial.

What is the minimum wavelength in m for broadcasts on the AM band? Format your answer as an integer.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Determine the following values from a standard radio dial.

What is the minimum wavelength in m for broadcasts on the AM band? Format your answer as an integer.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Determine the following values from a standard radio dial.

What is the minimum wavelength in m for broadcasts on the AM band? Format your answer as an integer.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Consider a (111) plane in an FCC structure. How many different [110]-type directions lie in this (111) plane?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Consider a (111) plane in an FCC structure. How many different [110]-type directions lie in this (111) plane?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Consider a (111) plane in an FCC structure. How many different [110]-type directions lie in this (111) plane?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Consider a (111) plane in an FCC structure. How many different [110]-type directions lie in this (111) plane?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the velocity of an electron (in $\mathrm{m} / \mathrm{s}$ ) that has been subjected to an accelerating potential $V$ of 150 Volt. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
(The energy imparted to an electron by an accelerating potential of one Volt is $1.6 \times 10^{-19}$ J oules; dimensional analysis shows that the dimensions of charge $x$ potential correspond to those of energy; thus: 1 electron Volt $(1 \mathrm{eV})=1.6 \times 10^{-19}$ Coulomb $\times 1$ Volt $=1.6 \times 10^{-19}$ Joules.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the velocity of an electron (in $\mathrm{m} / \mathrm{s}$ ) that has been subjected to an accelerating potential $V$ of 150 Volt. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
(The energy imparted to an electron by an accelerating potential of one Volt is $1.6 \times 10^{-19}$ J oules; dimensional analysis shows that the dimensions of charge $x$ potential correspond to those of energy; thus: 1 electron Volt $(1 \mathrm{eV})=1.6 \times 10^{-19}$ Coulomb $\times 1$ Volt $=1.6 \times 10^{-19}$ Joules.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the velocity of an electron (in $\mathrm{m} / \mathrm{s}$ ) that has been subjected to an accelerating potential $V$ of 150 Volt. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
(The energy imparted to an electron by an accelerating potential of one Volt is $1.6 \times 10^{-19}$ J oules; dimensional analysis shows that the dimensions of charge $x$ potential correspond to those of energy; thus: 1 electron Volt $(1 \mathrm{eV})=1.6 \times 10^{-19}$ Coulomb $\times 1$ Volt $=1.6 \times 10^{-19}$ Joules.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the velocity of an electron (in $\mathrm{m} / \mathrm{s}$ ) that has been subjected to an accelerating potential $V$ of 150 Volt. Please format your answer as $n \times 10^x$, where $n$ is to 2 decimal places.
(The energy imparted to an electron by an accelerating potential of one Volt is $1.6 \times 10^{-19}$ J oules; dimensional analysis shows that the dimensions of charge $x$ potential correspond to those of energy; thus: 1 electron Volt $(1 \mathrm{eV})=1.6 \times 10^{-19}$ Coulomb $\times 1$ Volt $=1.6 \times 10^{-19}$ Joules.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In a diffractometer experiment a specimen of thorium (Th) is irradiated with tungsten (W) $L_{\alpha}$ radiation. Calculate the angle, $\theta$, of the $4^{\text {th }}$ reflection. Round your answer (in degrees) to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In a diffractometer experiment a specimen of thorium (Th) is irradiated with tungsten (W) $L_{\alpha}$ radiation. Calculate the angle, $\theta$, of the $4^{\text {th }}$ reflection. Round your answer (in degrees) to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In a diffractometer experiment a specimen of thorium (Th) is irradiated with tungsten (W) $L_{\alpha}$ radiation. Calculate the angle, $\theta$, of the $4^{\text {th }}$ reflection. Round your answer (in degrees) to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
In a diffractometer experiment a specimen of thorium (Th) is irradiated with tungsten (W) $L_{\alpha}$ radiation. Calculate the angle, $\theta$, of the $4^{\text {th }}$ reflection. Round your answer (in degrees) to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A metal is found to have BCC structure, a lattice constant of $3.31 \AA$, and a density of $16.6 \mathrm{~g} / \mathrm{cm}^{3}$. Determine the atomic weight of this element in g/mole, and round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A metal is found to have BCC structure, a lattice constant of $3.31 \AA$, and a density of $16.6 \mathrm{~g} / \mathrm{cm}^{3}$. Determine the atomic weight of this element in g/mole, and round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A metal is found to have BCC structure, a lattice constant of $3.31 \AA$, and a density of $16.6 \mathrm{~g} / \mathrm{cm}^{3}$. Determine the atomic weight of this element in g/mole, and round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
A metal is found to have BCC structure, a lattice constant of $3.31 \AA$, and a density of $16.6 \mathrm{~g} / \mathrm{cm}^{3}$. Determine the atomic weight of this element in g/mole, and round your answer to 1 decimal place.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Iron $\left(\rho=7.86 \mathrm{~g} / \mathrm{cm}^{3}\right.$ ) crystallizes in a BCC unit cell at room temperature.

Calculate the radius in cm of an iron atom in this crystal. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Iron $\left(\rho=7.86 \mathrm{~g} / \mathrm{cm}^{3}\right.$ ) crystallizes in a BCC unit cell at room temperature.

Calculate the radius in cm of an iron atom in this crystal. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Iron $\left(\rho=7.86 \mathrm{~g} / \mathrm{cm}^{3}\right.$ ) crystallizes in a BCC unit cell at room temperature.

Calculate the radius in cm of an iron atom in this crystal. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: Iron $\left(\rho=7.86 \mathrm{~g} / \mathrm{cm}^{3}\right.$ ) crystallizes in a BCC unit cell at room temperature.

Calculate the radius in cm of an iron atom in this crystal. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For the element copper (Cu) determine:

Subproblem 0: the distance of second nearest neighbors (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.

Solution: The answer can be found by looking at a unit cell of $\mathrm{Cu}$ (FCC).
\includegraphics[scale=0.5]{set_23_img_00.jpg}
\nonessentialimage
Nearest neighbor distance is observed along $<110>$; second-nearest along $<100>$. The second-nearest neighbor distance is found to be "a".
Cu: atomic volume $=7.1 \times 10^{-6} \mathrm{~m}^{3} /$ mole $=\frac{\mathrm{N}_{\mathrm{A}}}{4} \mathrm{a}^{3}$ ( $\mathrm{Cu}: \mathrm{FCC} ; 4$ atoms/unit cell) $a=\sqrt[3]{\frac{7.1 \times 10^{-6} \times 4}{6.02 \times 10^{23}}}= \boxed{3.61e-10} \mathrm{~m}$

Final answer: The final answer is 3.61e-10. I hope it is correct.

Subproblem 1: the interplanar spacing of $\{110\}$ planes (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For the element copper (Cu) determine:

Subproblem 0: the distance of second nearest neighbors (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.

Solution: The answer can be found by looking at a unit cell of $\mathrm{Cu}$ (FCC).
\includegraphics[scale=0.5]{set_23_img_00.jpg}
\nonessentialimage
Nearest neighbor distance is observed along $<110>$; second-nearest along $<100>$. The second-nearest neighbor distance is found to be "a".
Cu: atomic volume $=7.1 \times 10^{-6} \mathrm{~m}^{3} /$ mole $=\frac{\mathrm{N}_{\mathrm{A}}}{4} \mathrm{a}^{3}$ ( $\mathrm{Cu}: \mathrm{FCC} ; 4$ atoms/unit cell) $a=\sqrt[3]{\frac{7.1 \times 10^{-6} \times 4}{6.02 \times 10^{23}}}= \boxed{3.61e-10} \mathrm{~m}$

Final answer: The final answer is 3.61e-10. I hope it is correct.

Subproblem 1: the interplanar spacing of $\{110\}$ planes (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For the element copper (Cu) determine:

Subproblem 0: the distance of second nearest neighbors (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.

Solution: The answer can be found by looking at a unit cell of $\mathrm{Cu}$ (FCC).
\includegraphics[scale=0.5]{set_23_img_00.jpg}
\nonessentialimage
Nearest neighbor distance is observed along $<110>$; second-nearest along $<100>$. The second-nearest neighbor distance is found to be "a".
Cu: atomic volume $=7.1 \times 10^{-6} \mathrm{~m}^{3} /$ mole $=\frac{\mathrm{N}_{\mathrm{A}}}{4} \mathrm{a}^{3}$ ( $\mathrm{Cu}: \mathrm{FCC} ; 4$ atoms/unit cell) $a=\sqrt[3]{\frac{7.1 \times 10^{-6} \times 4}{6.02 \times 10^{23}}}= \boxed{3.61e-10} \mathrm{~m}$

Final answer: The final answer is 3.61e-10. I hope it is correct.

Subproblem 1: the interplanar spacing of $\{110\}$ planes (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Preamble: For the element copper (Cu) determine:

Subproblem 0: the distance of second nearest neighbors (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.

Solution: The answer can be found by looking at a unit cell of $\mathrm{Cu}$ (FCC).
\includegraphics[scale=0.5]{set_23_img_00.jpg}
\nonessentialimage
Nearest neighbor distance is observed along $<110>$; second-nearest along $<100>$. The second-nearest neighbor distance is found to be "a".
Cu: atomic volume $=7.1 \times 10^{-6} \mathrm{~m}^{3} /$ mole $=\frac{\mathrm{N}_{\mathrm{A}}}{4} \mathrm{a}^{3}$ ( $\mathrm{Cu}: \mathrm{FCC} ; 4$ atoms/unit cell) $a=\sqrt[3]{\frac{7.1 \times 10^{-6} \times 4}{6.02 \times 10^{23}}}= \boxed{3.61e-10} \mathrm{~m}$

Final answer: The final answer is 3.61e-10. I hope it is correct.

Subproblem 1: the interplanar spacing of $\{110\}$ planes (in meters). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?

Solution: \boxed{800}.

Final answer: The final answer is 800. I hope it is correct.

Subproblem 4: What is the working temperature for soda-lime glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?

Solution: \boxed{800}.

Final answer: The final answer is 800. I hope it is correct.

Subproblem 4: What is the working temperature for soda-lime glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?

Solution: \boxed{800}.

Final answer: The final answer is 800. I hope it is correct.

Subproblem 4: What is the working temperature for soda-lime glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Subproblem 0: What is the working temperature for silica glass in Celsius?

Solution: \boxed{1950}.

Final answer: The final answer is 1950. I hope it is correct.

Subproblem 1: What is the softening temperature for silica glass in Celsius?

Solution: \boxed{1700}.

Final answer: The final answer is 1700. I hope it is correct.

Subproblem 2: What is the working temperature for Pyrex in Celsius?

Solution: \boxed{1200}.

Final answer: The final answer is 1200. I hope it is correct.

Subproblem 3: What is the softening temperature for Pyrex in Celsius?

Solution: \boxed{800}.

Final answer: The final answer is 800. I hope it is correct.

Subproblem 4: What is the working temperature for soda-lime glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the wavelength of $\lambda_{K_{\alpha}}$ for molybdenum (Mo). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, in meters.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the wavelength of $\lambda_{K_{\alpha}}$ for molybdenum (Mo). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, in meters.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the wavelength of $\lambda_{K_{\alpha}}$ for molybdenum (Mo). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, in meters.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the wavelength of $\lambda_{K_{\alpha}}$ for molybdenum (Mo). Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places, in meters.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the second-nearest neighbor distance (in pm) for nickel (Ni) at $100^{\circ} \mathrm{C}$ if its density at that temperature is $8.83 \mathrm{~g} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the second-nearest neighbor distance (in pm) for nickel (Ni) at $100^{\circ} \mathrm{C}$ if its density at that temperature is $8.83 \mathrm{~g} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the second-nearest neighbor distance (in pm) for nickel (Ni) at $100^{\circ} \mathrm{C}$ if its density at that temperature is $8.83 \mathrm{~g} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
Determine the second-nearest neighbor distance (in pm) for nickel (Ni) at $100^{\circ} \mathrm{C}$ if its density at that temperature is $8.83 \mathrm{~g} / \mathrm{cm}^{3}$. Please format your answer as $n \times 10^x$ where $n$ is to 2 decimal places.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the working temperature for silica glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the working temperature for silica glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the working temperature for silica glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What is the working temperature for silica glass in Celsius?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What acceleration potential $V$ must be applied to electrons to cause electron diffraction on $\{220\}$ planes of gold $(\mathrm{Au})$ at $\theta=5^{\circ}$ ? Format your answer as an integer, in Volts.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What acceleration potential $V$ must be applied to electrons to cause electron diffraction on $\{220\}$ planes of gold $(\mathrm{Au})$ at $\theta=5^{\circ}$ ? Format your answer as an integer, in Volts.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What acceleration potential $V$ must be applied to electrons to cause electron diffraction on $\{220\}$ planes of gold $(\mathrm{Au})$ at $\theta=5^{\circ}$ ? Format your answer as an integer, in Volts.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
What acceleration potential $V$ must be applied to electrons to cause electron diffraction on $\{220\}$ planes of gold $(\mathrm{Au})$ at $\theta=5^{\circ}$ ? Format your answer as an integer, in Volts.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant


Prompt:
<|im_start|>user
To increase its corrosion resistance, chromium $(\mathrm{Cr})$ is diffused into steel at $980^{\circ} \mathrm{C}$. If during diffusion the surface concentration of chromium remains constant at $100 \%$, how long will it take (in days) to achieve a $\mathrm{Cr}$ concentration of $1.8 \%$ at a depth of $0.002 \mathrm{~cm}$ below the steel surface? Round your answer to 1 decimal place. $\left(D_{o}=0.54 \mathrm{~cm}^{2} / \mathrm{s} ; E_{A}=286 \mathrm{~kJ} / \mathrm{mol}\right.$ )
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant