Separating the Schrödinger Equation for Hydrogen · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Splitting hydrogen: where its three quantum numbers come from

Science · Quantum & Modern Physics · ages 20-22
Name ______________________   Date ____________

  1. In hydrogen, what does the quantum number n restrict?

    • Orbital tilt
    • Energy
    • Proton spin

  2. Why does the hydrogen wavefunction split into a radial part times an angular part?

    • The pull is spherically symmetric
    • The proton is heavy
    • Electrons are point charges

  3. Each hydrogen spectral line equals the energy gap between two levels.

    Circle one:   True   False

  4. Why study separation on the box before tackling hydrogen?

    • It practises the split-solve-quantise rhythm on simpler factors
    • The box sits inside hydrogen
    • Box energies equal hydrogen energies

  5. l restricts the size of the orbital angular momentum. What does m restrict?

    • The energy
    • The radial distance
    • Its tilt (orientation)

  6. An electron drops from E3 to E2. What does the emitted photon carry?

    • The full E3
    • The gap E3 minus E2
    • Half the gap

  7. A student fully labels a hydrogen state with only n. What is missing?

    • l and m, from the angular pieces
    • Nothing: n says everything
    • The proton position

  8. Why does matching measured spectral lines close the loop on hydrogen theory?

    • Maths never needs experiments
    • Lines come from the proton alone
    • It proves separation predicts real colours, not just neat maths
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Answer key

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

Splitting hydrogen: where its three quantum numbers come from W1-mt_Yk2qHB0_v2-s1

  1. Energy · n comes from the radial part and sets the energy level.
  2. The pull is spherically symmetric · Equal pull from every direction lets the parts separate.
  3. True · One jumping electron emits or absorbs one photon carrying the gap.
  4. It practises the split-solve-quantise rhythm on simpler factors · The box rehearses the same moves with one factor per direction.
  5. Its tilt (orientation) · m sets the tilt of the angular momentum vector.
  6. The gap E3 minus E2 · The photon carries exactly the level difference.
  7. l and m, from the angular pieces · Each piece brings its own number, so n alone is incomplete.
  8. It proves separation predicts real colours, not just neat maths · Predicted gaps matching observed lines confirms the whole separation.
Worksheet · LightMySky