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  4. The minimum energy that must be given to a H atom in ground state so that it can emit an Hγ line in Balmer series is

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Q. 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 is

Atoms

Solution:

$H_{\gamma}$ line in Balmer series corresponds to transition from $n = 5$ to $n = 2$ states. Hence, the energy required for this purpose
$E = E_5 - E_1 $
$= - \frac{13.6}{5^2} - (-\frac{13.6}{1^2})$
$ = -0.54 + 13. 6$
$ = 13.06 \,eV$