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