Question

Hydrogen atom is excited by means of a monochromatic radiations of wavelength $ 975\,\mathring{A}$ . In emission spectrum the number of possible lines are :

• A. 2
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (B)

Energy of radiations $E=\frac{h c}{\lambda}$
$=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{975 \times 10^{-10} \times 1.6 \times 10^{-19}} \,eV$
$=12.75 \,eV$
Energy of hydrogen atom in first energy level $=-13.6 \,eV$
Energy of atom after absorbing radiations
$=-13.6+12.75=-0.85\, eV$
Number of spectral lines
$E =\frac{13.6}{n^{2}} $
$n^{2} =\frac{13.6}{0.85} $
$n^{2} =16 $
$\Rightarrow n=4$