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A electron of hydrogen atom on an excited state is having energy $E_{n} = - 0.544 e v$ The maximum number of allowed transitions to lower energy level is ________

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answer is 10.

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Detailed Solution

$E$ $n$ $$ $=$ $n$ $2$ $-13.6$ $$ $=$ $-0.54$ $n = 5$ $n$ $=$ $5$

no of transition

$\frac{n(n-1)}{2} = \frac{5(5-1)}{2} = 10$ $2$ $n$ $($ $n$ $-$ $1$ $)$ $$ $=$ $25$ $($ $5$ $-$ $1$ $)$ $$ $=$ $10$

This shows the calculation of the energy level of hydrogen at $n=5$ $n$ $=$ $5$ , and the number of possible electronic transitions ( $10$ $10$ ) from that level.

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