Atomic Energy Levels
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.
Electrons in an atom can only have certain energies. When an electron drops to a lower level, the atom emits a photon carrying exactly the difference: Ephoton = Ehigh − Elow. It can absorb only photons that match a gap exactly. That’s why each element has its own set of spectral lines.
1. Energy-level diagrams
2. Emission and absorption
Emission: a hot gas glows at only certain wavelengths, a bright-line spectrum.
Absorption: white light through a cool gas comes out with dark lines at the same wavelengths, where photons matching gaps were absorbed.
A photon that doesn’t match any gap (and can’t ionize the atom) passes straight through.
From level n, an electron can drop by many routes. The number of different photon energies possible is n(n − 1)/2: from n = 4, that’s 6.
Any photon with more energy than the ionization energy can free the electron; the extra becomes kinetic energy.
3. Example, then try it
An electron in hydrogen drops from n = 3 to n = 2. Find the photon’s energy and wavelength.
E = (−1.51) − (−3.40) = 1.89 eV.
λ = 1240 ÷ 1.89 ≈ 656 nm: red light.
A hydrogen electron is in n = 4 (−0.85 eV). Find the highest- and lowest-energy photons it can emit on the way down, and the one it emits dropping to n = 2.
Highest, 4 → 1: −0.85 − (−13.6) = 12.75 eV, λ = 1240 ÷ 12.75 ≈ 97 nm (ultraviolet).
Lowest, 4 → 3: −0.85 − (−1.51) = 0.66 eV, λ ≈ 1900 nm (infrared).
4 → 2: −0.85 − (−3.40) = 2.55 eV, λ ≈ 486 nm (blue-green, visible).
Answer: 12.75 eV (UV), 0.66 eV (IR), and 2.55 eV (486 nm).
4. Common mistakes
How much energy does it take to ionize a hydrogen atom whose electron is in n = 3 (−1.51 eV)?
Ionizing means raising the electron to 0 eV. From −1.51 eV, that takes 1.51 eV.
Ready to practice?
4 questions on Atomic Energy Levels, each with a hint and an explanation for every wrong answer.