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

Hint: The energy required will be equal to the energy difference between the transition levels.
${\mathrm{H}}_{\mathrm{\gamma }}$ in Balmer series corresponds to transition n = 5 to n = 2. So, the electron in the ground state, i.e., from n = 1 must first be placed in state n = 5.
The energy required for the transition from n = 1 to n = 5 is given by
Step 2: Conserve the angular momentum.
Since, angular momentum is conserved,
angular momentum corresponding to ${\mathrm{H}}_{\mathrm{\gamma }}$ photon = change in angular momentum of the electron