(a)Use the Bohr model to determine the ionization energy of the `He^+` ion, which has a single electron. (b)Also calculate the maximum wavelength a photon can have to cause ionization.

Explanation

Strategy:We want to determine the minimum energy required to lift the electron from its ground state and to barely reach the free stable at E=0. The ground state energy of `He^+` is given by `E=-(me^4Z^2)/(8epsilon_0^2h^2n^2)` with n=1 and Z=2 .
(a)Since all the symbols in above equation are the same as for the calculation for hydrogen , except that Z is 2 instead of 1 , we see that `E_1` will be `Z^2=2^2=4` times the `E_1` for hydrogen. That is `E_1` =4(-13.6 eV)=-54.4 eV
Thus, to ionize the `He^+` ion should require 54.4 eV, and this value agrees with experiment.
(b)The maximum wavelength photon that can cause ionization will have energy hf=54.4 eV and wavelength `lambda=c/f="hc"/"hf"`
`=((6.63xx10^(-34) J.s)(3.00xx10^8 m//s))/((54.4 eV)(1.60xx10^(-19) J//eV))`
=22.8 nm
If `lambda gt 22.8` nm , ionization cannot occur.