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Q. A hydrogen-like atom in ground state absorbs $n$ photons having the same energy and its emits exactly $n$ photons when electrons transition takes placed. Then, the energy of the absorbed photon may be

Structure of Atom

Solution:

Exp: Number of dark lines (in absorption), i.e., excitation = Number of bright lines (in emission), i.e., $d e$-excitation
It is possible only when the $e ^{-}$is excited to $n=2$ from ground state
Clearly, $\Delta E=91.8 eV$ and $40.8 eV$ are possible
$\left( Li ^{2+}\right) \,\,\,\ \left( He ^{\oplus}\right)$