Two photons of equal energy 8 eV each, strikes two different metal sheets having work functions 4 eV and 6 eV, respectively. The ratio of maximum velocity of electrons emitted from two metal sheets respectively is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \sqrt{2}:1 \)
By Einstein’s photoelectric equation the maximum kinetic energy of an emitted electron is \( K_{\max} = h\nu - \phi_0 \), and with \( K_{\max} = \frac{1}{2}mv^{2} \) the maximum speed is proportional to \( \sqrt{K_{\max}} \).
\( K_1 = 8-4 = 4\,\mathrm{eV} \)
\( K_2 = 8-6 = 2\,\mathrm{eV} \)
\( \displaystyle \frac{v_1}{v_2} = \sqrt{\frac{K_1}{K_2}} = \sqrt{\frac{4}{2}} = \sqrt{2} \)
The ratio of the maximum speeds is \( \sqrt{2}:1 \).