7.4 Atomic Energy States

Electrons occupy discrete energy states

In atoms, electrons can only exist in specific quantized energy levels, not just anywhere. Each element has its own unique set of allowed energies. The lowest energy level is called the ground state, and any higher level is an excited state. Atoms absorb or emit energy only in amounts that exactly match the difference between two allowed levels.

Absorption and emission of photons

When an electron jumps to a higher energy level, it must absorb a photon with energy exactly equal to the gap, ΔE = hf. When it falls to a lower level, it emits a photon of that same energy. Since energy levels are unique to each element, the emitted/absorbed photon energies (and wavelengths) act like a fingerprint, producing characteristic spectral lines.

Energy level diagrams and ionization

Energy level diagrams show allowed energies as horizontal lines, usually negative (bound electron) with zero energy at ionization. The energy needed to remove an electron completely from the atom is the ionization energy, the difference between the ground state and n = ∞ (E = 0). Transitions between any two levels correspond to a specific photon energy, hf = |ΔE|.

Key terms

Quantized energy levels

Electrons in atoms can only have specific, discrete allowed energy values, unique to each element.

Ground state

The lowest possible energy level an electron in an atom can occupy.

Excited state

Any energy level above the ground state that an electron can temporarily occupy after absorbing energy.

Photon absorption/emission rule

A photon is absorbed or emitted only if its energy (E = hf) exactly matches the difference between two energy levels.

Ionization energy

The energy needed to remove an electron completely from an atom, taking it from its bound state to E = 0.

Try an AP-style question

Hydrogen's levels are Eₙ = −13.6/n² eV. What photon energy is emitted when an electron drops from n = 3 to n = 2?

1. 1.51 eV
2. 13.6 eV
3. 3.40 eV
4. 1.89 eV