• Tags: energy-levels, transitions, photon
• Difficulty: Moderate

The energy level diagram shows horizontal lines at E_n = -13.6/$n^{2}$ eV for hydrogen. The ground state (n=1) is at -13.6 eV, and the ionization level (n=∞) is at 0 eV. Transitions are shown as vertical arrows between levels. Downward transitions emit photons (emission spectrum); upward transitions absorb photons (absorption spectrum). The photon energy equals the energy gap: E_photon = E_i - E_f = 13.6(1/n_$f^{2}$ - 1/n_$i^{2}$) eV. The largest energy gaps produce the shortest wavelengths. Within any series, the first line has the longest wavelength (smallest energy gap within that series) and the series limit has the shortest wavelength (electron comes from n=∞).