Question

In $He^{\oplus}$ ion sample $e^{-}$ is in ground state, if photon of energy $52.24\,eV$ is given to the sample all the atom goes to higher energy state. It again falls back up to ground state. If it is not emitting any lines in Balmer series then what is the maximum possible number of spectral lines observed

Answer 1

Energy absorbed by electron will be equal to the energy difference of orbits in between electron transition is taking place.
$13.6\times 2^{2}\left(1 - \frac{1}{n^{2}}\right)=52.24$
$\Rightarrow 13.6-\frac{13 .6}{n^{2}}=13.06$
$\Rightarrow \frac{13 .6}{n^{2}}=0.54$
$\Rightarrow n=5$
Total line $=\frac{5 \left(5 - 1\right)}{2}=10$
But it is not emitting balmer lines hence
$\Rightarrow $ total line $=10-3=7$
But it will also bit enquit $2 \rightarrow 1$ line
Hence total line $=7-1=6$