• $summary_{type}$: application
• $word_{count}$: 180

Ionization energy from ground state = 13.6 eV; from nth level = 13.6/$n^2$ eV. First excitation energy (n=1 to n=2) = 13.6 - 3.4 = 10.2 eV. Second excitation energy (n=1 to n=3) = 13.6 - 1.51 = 12.09 eV. A photon must have exactly the right energy to be absorbed (all-or-nothing quantum condition). If 10.2 eV photon hits ground-state hydrogen, the electron goes to n=2. A 10.5 eV photon cannot be absorbed because it matches no transition. If photon energy exceeds 13.6 eV, the electron is freed with KE = $E_{photon}$ - 13.6 eV. Crucially, electron collisions are different: a free electron can transfer any fraction of its energy (not quantized), but at least 10.2 eV must be transferred for excitation. If the colliding electron has KE < 10.2 eV, only elastic collision occurs. Subtle point: due to momentum conservation, the available excitation energy from electron collision is KE * $\frac{M}{m+M}$, which is slightly less than KE but almost equal for hydrogen.