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MMLU-Pro / 4350 / Suppose a nanostructure is modelled by an electron confined to a rectangular…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Suppose a nanostructure is modelled by an electron confined to a rectangular region with sides of lengths $L_1=1.0 \mathrm{~nm}$ and $L_2=2.0 \mathrm{~nm}$ and is subjected to thermal motion with a typical energy equal to kTk T, where kk is Boltzmann's constant. How low should the temperature be for the thermal energy to be comparable to the zero-point energy？
Plain-text mathematical notation (without MathML)
Suppose a nanostructure is modelled by an electron confined to a rectangular region with sides of lengths $L_1=1.0 \mathrm{~nm}$ and $L_2=2.0 \mathrm{~nm}$ and is subjected to thermal motion with a typical energy equal to kT, where k is Boltzmann's constant. How low should the temperature be for the thermal energy to be comparable to the zero-point energy？
Original LaTeX notation
Suppose a nanostructure is modelled by an electron confined to a rectangular region with sides of lengths $L_1=1.0 \mathrm{~nm}$ and $L_2=2.0 \mathrm{~nm}$ and is subjected to thermal motion with a typical energy equal to $k T$, where $k$ is Boltzmann's constant. How low should the temperature be for the thermal energy to be comparable to the zero-point energy？

category

chemistry

options

  1. 2.0 $10^2 \mathrm{~K}$
  2. 5.5 $10^3 \mathrm{~K}$
  3. 2.5 $10^3 \mathrm{~K}$
  4. 7.0 $10^3 \mathrm{~K}$
  5. 1.2 $10^4 \mathrm{~K}$
  6. 6.5 $10^3 \mathrm{~K}$
  7. 9.5 $10^3 \mathrm{~K}$
  8. 1.5 $10^4 \mathrm{~K}$
  9. 8.0 $10^3 \mathrm{~K}$
  10. 3.0 $10^3 \mathrm{~K}$

src

scibench-matter

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Source and history

upstream_id / Original problem ID
4350
task_id
b1b7b312-37af-5bfc-b397-d47697bcd95a
task_key
default--test--4350
task_revision_id
1
config / split
default / test

Official source

initial import