Question

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

• A. $3$
• B. $6$
• C. $10$
• D. $15$

Answer 1

Answer: (B)

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