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Q. In $H$-atom, the electron is de-excited from $5^{\text {th }}$ shell to $1^{\text {st }}$ shell. How many different lines may appear in line spectrum?

Structure of Atom

Solution:

No. of lines given during a jump $=\Sigma \Delta n$, where $\Delta n=n_{2}-n_{1}$

$\therefore \Sigma \Delta n=\Sigma(5-1)=\Sigma 4=10$