What is the minimum energy that must be given to a H atom in ground state so that it can emit an `H gamma` line in Balmer series. If the angular momentum of the system is conserved, what would be the angular momentum of such `H gamma` photon ?

Explanation

`H_(gamma)` is Balmer series corresponds to transition `n = 5` to `n = 2`. So, the electron in ground state
i.e., from `n = 1` must first be placed in state `n = 5`.
Energy required for the transition from `n = 2` to `n = 5` is given by
`= E_(1) - E_(5) = 13.6 - 0.54 = 13.06 eV`
Since, angular momentum is conserved,
angular momentum corresponding to Hg proton = change in angular momentum of electron
`= L_(5) - L_(2) = 5h - 2h = 3h = 3 xx 1.06 xx 10^(-34)`
`= 3.18 xx 10^(-34) kg-m^(2)//s`