The number of spectral lines that are possible when electrons in $7$ th shell in different hydrogen atoms return to the $2$ nd shell is:

12

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15

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14

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10

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Solution

The correct option is C $15$
The general formula for calculating number of spectral lines
$= \frac{(n_{2} - n_{1}) (n_{2} - n_{1} + 1)}{2}$
Here $n_{2} = 7, n_{1} = 2$
Number of spiral lines $= \frac{(7 - 1) (7 - 2 + 1)}{2}$
$= \frac{(5) (6)}{2}$
$= 15$

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