Questions: Photon Absorption and Emission by Atoms

Question 1

A hydrogen atom in its ground state (n=1) is illuminated with photons of several different energies. Which photon will it absorb?

• A. The photon with energy closest to any energy level, since partial absorption is possible
• B. Only a photon whose energy exactly matches the gap between n=1 and an allowed upper level (e.g., 10.2 eV for the n=1→n=2 transition)
• C. Any photon with energy greater than 13.6 eV, since that exceeds all bound-state energies
• D. The highest-energy photon, since more energetic photons are more likely to interact with electrons

Answer: (B)

Energy conservation is exact — the photon's energy must precisely match an energy level gap (hf = E_upper − E_lower) for absorption to occur. There is no such thing as partial absorption of a photon. A photon with energy slightly above or below 10.2 eV will simply pass through without interacting. This selectivity is the direct cause of line spectra: atoms absorb and emit at specific discrete frequencies, not across a continuous range.

Question 2

Which of the following hydrogen transitions is 'forbidden' by the electric dipole selection rule (Δℓ = ±1)?

• A. 1s → 2p (Δℓ = +1)
• B. 2p → 1s (Δℓ = −1)
• C. 1s → 2s (Δℓ = 0)
• D. 3d → 2p (Δℓ = −1)

Answer: (C)

The selection rule Δℓ = ±1 comes from conservation of angular momentum: a photon carries spin-1, so the atom must gain or lose one unit of orbital angular momentum. The 1s → 2s transition has Δℓ = 0, violating this rule. 'Forbidden' doesn't mean impossible — the transition can still occur through weaker mechanisms (two-photon emission, magnetic dipole) with lifetimes orders of magnitude longer than allowed transitions (~ns vs. seconds).

Question 3

The dark absorption lines in the solar spectrum and the bright emission lines in laboratory hydrogen spectra occur at exactly the same frequencies.

• T. True
• F. False

Answer: True

Absorption and emission are reciprocal processes involving identical energy gaps. Cool solar gas absorbs photons from the background continuum at precisely the frequencies that match its energy level gaps, producing dark Fraunhofer lines. Hot gas in emission produces bright lines at those same frequencies as excited electrons de-excite. Same energy gaps — same frequencies. The solar spectrum's dark lines directly reveal the elemental composition of the solar atmosphere.

Question 4

The Balmer series encompasses most observable spectral lines of hydrogen.

• T. True
• F. False

Answer: False

The Balmer series covers only transitions to the n=2 level, which happen to fall in the visible range — which is why it was the first series discovered. Hydrogen has multiple series: Lyman (transitions to n=1, ultraviolet), Balmer (to n=2, visible), Paschen (to n=3, infrared), and others. The Rydberg formula ν = R_H(1/n_f² − 1/n_i²) predicts all series with the same formula, just different values of n_f.

Question 5

Why do atoms produce line spectra — discrete frequencies — rather than continuously absorbing and emitting across all frequencies?

Model answer: Because atomic energy levels are quantized — electrons can only occupy specific allowed energies. A photon is absorbed only if its energy exactly matches the gap between two energy levels (hf = E_upper − E_lower); photons with other energies don't interact with the atom. De-excitation emits photons at exactly those same gap frequencies. The result is a set of discrete bright or dark lines, each corresponding to a specific transition between specific energy levels.

This is the direct observational consequence of quantized energy levels. A classical electron orbiting continuously could absorb and emit any frequency — leading to continuous spectra and the spiral collapse of the electron into the nucleus (the ultraviolet catastrophe for atoms). Quantization resolves both: it explains discrete spectra and stable ground states. The exact photon-matching condition is both the constraint that produces line spectra and the tool that makes spectroscopy so powerful for identifying atomic composition.