# Hydrogen atom in ground state is excited by a monochromatic radiation of = 975 . Number of spectral lines in the resulting spectrum emitted will be: Option 1) 3 Option 2) 2 Option 3) 6 Option 4) 10

@8762

$\lambda -975 A^{o}$

$\therefore$ Energy associated with it =  $\frac{12400}{975}ev$

$=12.7^{o}ev$

$\Delta E=13.6 \left( \frac{1}{m^{2}} - \frac{1}{n^{2}}\right )\:\:\:\:\: Or, \:\:\:\:\:12.70=13.60 \left( 1- \frac{1}{n^{2}} \right )$

$Or, \:\: 1- \frac{1}{n^{2}}= \frac{12.70}{13.60}\:\:\:\:\Rightarrow n=4$
So total number of spectral line will be = $\frac{n(n-1)}{2}=\frac{4 \times 3}{2}=6$

Option 1)

3

This option is incorrect.

Option 2)

2

This option is incorrect.

Option 3)

6

This option is correct.

Option 4)

10

This option is incorrect.

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