What is the minimum energy that must be given to a H atom is 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)` line in Balmer series corresponds to transition form n=5 to n=2. Therefore, electrons in ground state (n=1), must be raised first to the state to the state (n=5). Energy required for this purpose
`E=E_(5)-E_(1)=-13.6/(5^2)-(-13.6/(1^2))eV = -0.54 + 13.6 = 13.06 eV`.
If the angular momentum of the system is conserved, then angular momentum of photon emitted=change in angular momentum of electron
`=L_(5)-L_(2)=5h-2h=3h=3xx1.06xx10^(-34)=3.18xx10^(-34)kgm^(2)s^(-1)`