Question

Monochromatic radiation of specific wavelength is incident on H-atoms in the ground state. H-atoms absorb energy and emit subsequently radiations of six different wavelengths. Find the wavelength of incident radiations:

• A. $9.75nm$
• B. $50nm$
• C. $85.8nm$
• D. $97.25nm$

Answer 1

Answer: (D)

$97.25nm$

H-atom emits 6 spectral lines

$\frac{n(n-1)}{2}=6$; $n=4$

$\therefore \Delta E=E_4-E_1=\frac{-13.6}{{\left(4\right)}^2}-\frac{(-13.6)}{(1{)}^2}$

$=13.6-0.85=12.75eV$

$\Delta E=\frac{hc}{\lambda }$

$\lambda =\frac{hc}{\Delta E}$

$\lambda =\frac{12.42}{12.75}$

$\lambda =97.25$ nm

Hence, the correct option is $D$