Skip to content
GRE Physics overview

Public question explainer

Original public content

Infinite Square Well Transitions: Public Worked Question

A public quantum question showing how infinite-square-well energies scale with the square of the quantum number and set photon transition energies.

Question

An electron in a one-dimensional infinite square well has ground-state energy E1=2.0 eVE_1 = 2.0\,\text{eV}. What is the energy of the photon emitted when the electron drops from the n=3n = 3 level to the n=2n = 2 level?

  1. a.2.0 eV2.0\,\text{eV}
  2. b.8.0 eV8.0\,\text{eV}
  3. c.10 eV10\,\text{eV}
  4. d.18 eV18\,\text{eV}

Correct answer

C. 10 eV10\,\text{eV}

Full reasoning

  1. 1Infinite-well levels scale as En=n2E1E_n = n^2E_1, so E2=4(2.0)=8.0 eVE_2 = 4(2.0) = 8.0\,\text{eV} and E3=9(2.0)=18 eVE_3 = 9(2.0) = 18\,\text{eV}.
  2. 2The emitted photon carries the level difference: Eγ=E3−E2=18−8.0=10 eVE_\gamma = E_3 - E_2 = 18 - 8.0 = 10\,\text{eV}.
  3. 3Watch the classic trap: (3−2)2E1=2.0 eV(3-2)^2E_1 = 2.0\,\text{eV} is wrong — you must difference the squares, (32−22)E1=5E1(3^2 - 2^2)E_1 = 5E_1, not square the difference.

Why each choice is right or wrong

Choice A

This squares the difference of the quantum numbers, (3−2)2E1(3-2)^2E_1, instead of differencing the squares, (32−22)E1(3^2 - 2^2)E_1.

Choice B

This is the energy of the final n=2n = 2 level, 4E14E_1, not the difference between the two levels.

Choice C

Correct. E3−E2=(9−4)E1=5(2.0 eV)=10 eVE_3 - E_2 = (9 - 4)E_1 = 5(2.0\,\text{eV}) = 10\,\text{eV} is carried away by the photon.

Choice D

This is the energy of the initial n=3n = 3 level, 9E19E_1; the photon carries only the drop between levels, not the full level energy.

Related formula

Infinite square well energy levels

En=n2h28mL2E_n = \frac{n^2h^2}{8mL^2}

Assumptions: The walls are infinitely high, so the wavefunction vanishes at both boundaries.

Related topic and practice

Quantum Mechanics FoundationsSign in for current practice

This public explainer is separate from the protected practice bank. Current practice coverage varies.

Source and public-release record

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. University Physics Volume 3, Section 7.4: The Quantum Particle in a Box — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.

Review and maintenance

Source-checked by publisher
Publisher record
Keiko Study editorial owner
Publisher placeholder; no individual credential claim is made yet.
Reviewer record
Technical reviewer pending
Placeholder only; this content is not labeled as reviewed by a named specialist.
Last source check
2026-08-07
Next scheduled review
2026-11-07

Recheck the cited OpenStax reference before each major GRE Physics preparation cycle.

Report an issue with this page