Question

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

• A. 7 : 16
• B. 3 : 4
• C. 8 : 27
• D. 5 : 36

Answer 1

Answer: (A)

Energy of photons of
$H _{\alpha}$ line $=\Delta E(3 \rightarrow 2)$
$=13.6\left(\frac{1}{4}-\frac{1}{9}\right)=\frac{13.6 \times 5}{36}=1.89\, eV$
Energy of photons of $H _{\beta}$ line
$=\Delta E(4 \rightarrow 2)$
$=13.6\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{12 \times 13.6}{64}=2.55\, eV$
Energy of photons of $H _{\infty}$ line $=\Delta E(\infty \rightarrow 2)$
$=\frac{13.6}{4}=3.4\, eV$
Ratio of kinetic energy of emitted photons
$=\frac{255-1.89}{3.4-1.89}=\frac{0.66}{1.51} \approx \frac{0.7}{1.6} \approx \frac{7}{16}$