Photons of frequencies equal to the frequencies of $H_\beta$ and $H_{\infty}$ lines of hydrogen incident on…
Photons of frequencies equal to the frequencies of $H_\beta$ and $H_{\infty}$ lines of hydrogen incident on a photosensitive plate, whose threshold frequency is equal to the frequency of $H_\alpha$ line of hydrogen. The ratio of the maximum kinetic energies of the emitted electrons is
7 : 16
3 : 4
8 : 27
5 : 36
Solution
Energy of photons of
$
\begin{aligned}
\mathrm{H}_\alpha \text { line }=\Delta E(3 & \rightarrow 2) \\
& =13.6\left(\frac{1}{4}-\frac{1}{9}\right)=\frac{13.6 \times 5}{36}=1.89 \mathrm{eV}
\end{aligned}
$
Energy of photons of $\mathrm{H}_\beta$ line $=\Delta E(4 \rightarrow 2)$
$
=13.6\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{12 \times 13.6}{64}=2.55 \mathrm{eV}
$
Energy of photons of $\mathrm{H}_{\infty}$ line $=\Delta E(\infty \rightarrow 2)$
$
=\frac{13.6}{4}=3.4 \mathrm{eV}
$
Ratio of kinetic energy of emitted photons
$
=\frac{255-1.89}{3.4-1.89}=\frac{0.66}{1.51} \approx \frac{0.7}{1.6} \approx \frac{7}{16}
$