A stationary $He^+$ ion emits a photon corresponding to the first line of the Lyman series. This pho

Question

A stationary $He^+$ ion emits a photon corresponding to the first line of the Lyman series. This photon then strikes a stationary hydrogen atom in its ground state, liberating a photoelectron. What is the maximum kinetic energy of the liberated photoelectron?

Professor PC Thomas Classes · Answer

The first line of the Lyman series for $He^+$ ($Z=2$) corresponds to the transition from $n=2$ to $n=1$.
Energy of the emitted photon: $E_{\gamma} = 13.6 	imes 2^2 (1/1^2 - 1/2^2) = 54.4 	imes (3/4) = 40.8 	ext{ eV}$.
The ionization energy (work function) for a hydrogen atom in the ground state is $13.6 	ext{ eV}$.
By Einstein's photoelectric equation: $K_{max} = E_{\gamma} - \Phi = 40.8 	ext{ eV} - 13.6 	ext{ eV} = 27.2 	ext{ eV}$.