Question

Monochromatic radiation emitted when electron on hydrogen atom jumps from first excited state to the ground state irradiates a photosensitive material. The stopping potential of the material is measured to be 3.57V. The threshold frequency of the material is

1- 1.6x10^15Hz

2-2.5x10^15Hz

3-4x10^15Hz

4-5x10^15Hz

Answer 1

For hydrogen atom,
$$\begin{gathered} {\mathrm{E}}_{\mathrm{n}}=-\frac{13.6}{{\mathrm{n}}^2}\mathrm{eV} \\ \mathrm{In}\mathrm{ground}\mathrm{state},\mathrm{n}=1 \\ \mathrm{So}, \\ {\mathrm{E}}_1=-\frac{13.6}{1^2}\mathrm{eV}=-13.6\mathrm{eV} \\ \mathrm{For}\mathrm{first}\mathrm{excited}\mathrm{state}, \\ \mathrm{n}=2 \\ {\mathrm{E}}_2=-\frac{13.6}{2^2}\mathrm{eV}=-3.4\mathrm{eV} \\ \mathrm{Now}, \\ \mathrm{h\nu }={\mathrm{E}}_2-{\mathrm{E}}_1 \\ =-3.4\mathrm{eV}-(-13.6\mathrm{eV})=10.2\mathrm{eV} \\ \mathrm{Maximum}\mathrm{kinetic}\mathrm{energy}\mathrm{is}\mathrm{given}\mathrm{by} \\ {\mathrm{K}}_{\max }=\mathrm{e}\times \mathrm{stopping}\mathrm{potential}=\mathrm{e}\times 3.57\mathrm{V}\mathrm{Or}3.57\mathrm{eV} \\ \mathrm{According}\mathrm{to}\mathrm{Einstein}\text{'}\mathrm{s}\mathrm{photoelectric}\mathrm{equation}, \\ {\mathrm{K}}_{\max }=\mathrm{h\nu }-{\mathrm{\varphi }}_0 \\ \mathrm{or}{\mathrm{\varphi }}_0=\mathrm{h\nu }-{\mathrm{K}}_{\max }=10.2-3.57=6.63\mathrm{eV} \\ \mathrm{or}{\mathrm{h\nu }}_0=6.63\mathrm{eV} \\ \mathrm{or}{\mathrm{\nu }}_0=\frac{6.63\times 1.6\times {10}^{-19}}{6.6\times {10}^{-34}}=1.6\times {10}^{15} \end{gathered}$$