The number of possible spectral lines which may be emitted in bracket series in $H$ atom, if electrons present in 9th excited level returns to ground level, are:

21

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6

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45

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5

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Solution

The correct option is C $45$
Formula,

$\frac{(n_{2} - n_{1}) (n_{2} - n_{1} + 1)}{2}$

$n_{1} = 4$ lower level

$n_{2} = 9 + 4 = 13$ higher level,

$= \frac{(13 - 4) (13 - 4 + 1)}{2}$

$= \frac{90}{2}$

$= 45$

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