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` line in Balmer series corresponds to the transition from n = 5 (`4^(th)` excited state) to n = 2 (`1^(st)` excited state). If the atom is in ground state (n = 1), it must first be raised to the state n = 5.
Energy required to excite the electron from n=1 to n=5 is
`E=E_1-E_5`
`=[13.6/1^2-13.6/5^2]` eV
=[13.6-0.54]eV = 13.06eV
`L=L_5-L_2`
`=(5h)/(2pi)-(2h)/(2pi)=(5-2)h/(2pi)=3h`
`=3xx1.06xx10^(-34)kg m^2 s^(-1)`
`=3.18xx10^(-34)kg m^2 s^(-1)`