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Infinite Square Well Transitions

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 Domain GuideQuantum Mechanics FoundationsPhotoelectric EffectCreate a free account to practice

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Sources

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.
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Sources last checked 2026-08-07

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