To excite an atom, an incoming photon must have energy

Question

BlackTom AI · Accepted Answer

An atom absorbs a photon only when the photon's energy matches the difference between two allowed electronic energy levels: Ephoton = hν = ΔE = Efinal − Einitial.

1. Relevant concepts
- Atomic energy levels are quantized: electrons can occupy only discrete energies.
- Photon energy is E = hν (h = Planck’s constant, ν = frequency).
- Conservation of energy requires the photon's energy to supply exactly the energy gap for a bound–bound transition.
- If the photon energy equals the gap, absorption (excitation) occurs; if it exceeds the ionization threshold, it can ionize the atom instead.

2. Step-by-step reasoning
Step 1: Identify the energy gap between shells: ΔE = Eupper − Elower (a positive value for absorption).
Step 2: Equate photon energy to this gap for absorption: hν = ΔE.
Step 3: If hν exactly equals ΔE, the electron can be promoted to the higher level and the excess energy is zero, satisfying energy conservation.
Step 4: If hν > ΔE but is less than the ionization energy, the photon is not resonantly absorbed for that bound–bound transition (the atom generally will not absorb “extra” energy); if hν exceeds the ionization energy, the photon can instead remove the electron (photoionization), not merely excite to a higher bound shell.

3. Calculation/formula
Given ΔE = E2 − E1, absorption requires:
hν = ΔE.
No other numeric steps are needed; this equality is the condition for excitation.

4. Why the correct answer is correct
Option b states the photon energy must be equal to the energy difference between two shells, which directly follows from quantized energy levels and conservation of energy.

5. Why other options are incorrect
- a (greater than): If photon energy is greater but below ionization threshold, it will not be absorbed for a simple bound–bound excitation; if it is greater than the ionization energy it causes ionization, not excitation between shells.
- c (less than): A photon with less energy cannot supply the required ΔE and cannot cause the transition.
- d (both a and b): Contradictory; excitation requires equality, so “both” is incorrect.

Conclusion: The correct answer is b. This matches the provided answer: "b. equal to the energy difference between two shells."

To excite an atom, an incoming photon must have energy单项选择题

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