AP® Physics 2: Algebra-Based · Unit 15 · Topic 15.2
Energy Levels and Quantization
An electron bound in an atom can only have certain allowed energies, like rungs on a ladder. It absorbs or emits a photon only when that photon's energy exactly matches the gap between two rungs.
An electron orbiting a nucleus can't have just any energy. Quantum mechanics restricts it to a discrete set of allowed states, labeled n = 1, 2, 3 and so on, each with its own fixed energy. Think of these as rungs on a ladder bolted to the atom: the electron can stand on a rung, but never hang between them. Because the rungs are fixed, the gaps between them are fixed too, and a photon can only be absorbed if its energy exactly equals one of those gaps. That's why an atom looks transparent to most photon energies and only grabs very particular ones.
An energy level diagram lists these allowed energies as horizontal lines, with n = 1 (the ground state) at the bottom and energy rising toward zero as n increases, since zero marks the electron fully freed from the atom. Every possible transition is a vertical arrow between two lines. An arrow jumping up means the electron absorbed a photon with energy equal to that gap; an arrow jumping down means it emitted one. For hydrogen, En = -13.6 eV / n2, so the gaps shrink as n grows and the rungs bunch up near the top. The transitions ending on n = 2 (the Balmer series) happen to release photons in the visible range, which is why hydrogen's visible spectrum has exactly four bright lines.
This ladder picture is what makes atomic spectra act like fingerprints, connecting directly to the photoelectric effect and spectral line topics nearby: light hits matter in exact energy packets, and matter only accepts packets that fit its internal structure exactly.
Key terms
- Energy level
- One of the fixed, allowed energy values an electron in an atom can occupy.
- Ground state
- The lowest energy level an electron can occupy, labeled n = 1.
- Ionization energy
- The energy needed to remove an electron completely from an atom, raising it to E = 0.
- Energy level diagram
- A chart of horizontal lines showing an atom's allowed energies, with vertical arrows marking possible absorption or emission transitions.
- Balmer series
- The set of hydrogen transitions ending on n = 2, which produce lines in the visible spectrum.
Watch it explained
- How it worksHow does an energy level diagram encode every jump an electron in that atom can make?
- How it worksDraw the hydrogen energy ladder and mark the jumps that land in visible light.
- Worked exampleFind the energy needed to ionize a hydrogen atom sitting in its n = 2 state.
- Common mistakeWhy doesn't a photon with more than enough energy get partly absorbed by an atom?
Check yourself
End of topic.