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Q.
What is the minimum energy that must be given to a H atom in ground state so that it can emit an $H_γ$ line in Balmer series ?
Atoms
Solution:
$H_γ$ line in the Balmer series corresponds to transition from $n = 5$ to $n = 2$.
Therefore, electron in the ground state $(n = 1)$ must be raised first to the state $(n = 5)$.
The minimum energy required for this purpose is $E = E_5 - E_1$
$= -\frac{13.6}{5^{2}}eV - \left(-\frac{13.6}{1^{2}}eV \right)$ (As $\quad E_{n} = -\frac{13.6}{n^{2}}eV$)
$= - 0.54 \,eV + 13.6 \,eV = 13.06 \,eV$