Q156 / 160 · TS EAMCET 2019 (06 May Shift 1) · Physics

Monochromatic radiation is incident on hydrogen $(\mathrm{H})$ sample which is in ground state. If the hydrogen atoms emit radiation of ten different wavelengths after absorbing the incident radiation, then the wavelength of the incident radiation is (Let $h c=1242$ eV-nm)

  • A
    $84.4 \mathrm{~nm}$
  • B
    $102.6 \mathrm{~nm}$
  • C
    $72.5 \mathrm{~nm}$
  • Correct answer
    D
    $95.1 \mathrm{~nm}$

Solution

Given, $h c=1242 \mathrm{eV} \cdot \mathrm{nm}$ Since, monochromatic radiation is incident on hydrogen sample which is in ground state. Hence, the energy of ground state is given by $\begin{aligned} & |E|=13.6 \mathrm{eV} \\ & \frac{h c}{\lambda}=13.6 \\ & \lambda=\frac{h c}{136}=\frac{1242}{13.6} \mathrm{~nm} \\ & =91.3 \mathrm{~nm}-95.1 \mathrm{~nm}\end{aligned}$ Hence, the wavelength of incident radiation is $95.1 \mathrm{~nm}$.

Hence, the correct answer is option: 'D'.

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