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MMLU-Pro / 3546 / Suppose that the normalized wavefunction for an electron in a carbon nanotube of…

Problem

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

question

Suppose that the normalized wavefunction for an electron in a carbon nanotube of length $L=10.0 \mathrm{~nm}$ is: ψ=(2/L)1/2sin(πx/L)\psi=(2 / L)^{1 / 2} \sin (\pi x / L). Calculate the probability that the electron is between $x=4.95 \mathrm{~nm}$ and $5.05 \mathrm{~nm}$.
Plain-text mathematical notation (without MathML)
Suppose that the normalized wavefunction for an electron in a carbon nanotube of length $L=10.0 \mathrm{~nm}$ is: ψ=(2/L)^(1/2)sin(πx/L). Calculate the probability that the electron is between $x=4.95 \mathrm{~nm}$ and $5.05 \mathrm{~nm}$.
Original LaTeX notation
Suppose that the normalized wavefunction for an electron in a carbon nanotube of length $L=10.0 \mathrm{~nm}$ is: $\psi=(2 / L)^{1 / 2} \sin (\pi x / L)$. Calculate the probability that the electron is between $x=4.95 \mathrm{~nm}$ and $5.05 \mathrm{~nm}$.

category

chemistry

options

  1. 0.020
  2. 0.050
  3. 0.030
  4. 0.045
  5. 0.010
  6. 0.015
  7. 0.035
  8. 0.060
  9. 0.025
  10. 0.040

src

scibench-matter

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Source and history

upstream_id / Original problem ID
3546
task_id
57f2ffd1-ac3b-5906-a7a6-24305278e612
task_key
default--test--3546
task_revision_id
1
config / split
default / test

Official source

initial import