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  4. A sample consisting of Hydrogen atoms in the ground state is excited by monochromatic radiation of energy 12.75eV . If we were to observe the emission spectrum of this sample, then the number of spectral lines observed, will be

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Q. A sample consisting of Hydrogen atoms in the ground state is excited by monochromatic radiation of energy $12.75eV$ . If we were to observe the emission spectrum of this sample, then the number of spectral lines observed, will be

NTA AbhyasNTA Abhyas 2020Atoms

Solution:

The energy of an electron of a hydrogen atom in the ground state is
$E_{0}=-13.6eV$
The energy of incoming photon = $12.75eV$
The energy of an electron in the excited state is
$-\frac{13 . 6}{n^{2}}=-13.6+12.75=-0.85eV$
$\Rightarrow n^{2}=\frac{13 . 6}{0 . 85}=16$
$\Rightarrow n=4$
No. of spectral lines = $\frac{n \left(n - 1\right)}{2}$ = $6$