The Infinite Square Well and Energy Quantisation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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A trapped wave can only sing some notes

Science · Quantum & Modern Physics · ages 19-20
Name ______________________   Date ____________

  1. In an infinite square well, the n=2 energy is four times the ground-state energy.

    Circle one:   True   False

  2. Why does an infinite square well have discrete allowed energies?

    • An extra rule excludes selected energies
    • The wall conditions select fitting waves
    • Friction selects the slowest wave

  3. How many nodes lie strictly between the walls for the n=3 infinite-well wavefunction?

    • 0
    • 2
    • 3

  4. The width of an infinite square well is halved while particle mass stays fixed. What happens to its ground-state energy?

    • It falls to one half
    • It stays at its old value
    • It rises to four times

  5. For an electron in an infinite square well, use E_n=0.376 n²/L² eV, with L measured in nm. For L=2 nm, what is E2 in eV? Treat 0.376 as exact for this calculation.

    Answer: ______________

  6. An infinite-well state is a superposition containing only n=1 and n=2, with both present. What can one energy measurement return?

    • Either E1 or E2
    • Their midpoint
    • Any value from E1 to E2

  7. An infinite-well particle has E1=0.5 eV. It emits one photon carrying all the energy lost in a transition from n=2 to n=1. What is the photon energy in eV?

    Answer: ______________

  8. For the n=2 infinite-well state, the probability density is nonzero at the centre of the well.

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

A trapped wave can only sing some notes W1-mt_VV9ItoW7ew-s1

  1. True · Substituting n=2 into E_n=n²E1 gives E2=4E1.
  2. The wall conditions select fitting waves · A nonzero wave must vanish at both walls. This requires kL=nπ, selecting discrete wave numbers and energies.
  3. 2 · State n has n-1 interior nodes. For n=3, there are two, at L/3 and 2L/3.
  4. It rises to four times · Energy varies as 1/L². Replacing L by L/2 multiplies the energy by four.
  5. 0.376 · Here n²=4 and L²=4, so E2=0.376×4/4=0.376 eV.
  6. Either E1 or E2 · The two components have energies E1 and E2. One energy measurement returns one of those levels, not an intermediate value.
  7. 1.5 · E2=4×0.5=2.0 eV. The photon carries 2.0-0.5=1.5 eV.
  8. False · The centre is a node of the n=2 wavefunction. There ψ=0, so the probability density |ψ|² is also zero.
Worksheet · LightMySky