• Tags: excitation, collision, selection-rules
• Difficulty: Advanced

There is a crucial difference between excitation by electron collision and photon absorption. A photon must have exactly the right energy to be absorbed (quantum condition: $E_{photon}$ = $E_f$ - $E_i$). A free electron can transfer any fraction of its kinetic energy (the remaining energy stays as KE of the electron after collision). However, the energy transferred must be at least equal to the first excitation energy (10.2 eV for hydrogen).

Important: when a free electron of KE = 10.2 eV hits a stationary hydrogen atom, not all 10.2 eV can go into excitation due to conservation of momentum. The available energy for excitation = KE × $\frac{M}{m+M}$, where M is the atom mass and m is the electron mass. For hydrogen: available ≈ 10.2 × 1836/1837 ≈ 10.194 eV, which is still sufficient for 1→2 transition. But for heavier atoms, this correction matters less. JEE occasionally tests this subtlety.