Two metals, X and Y have work functions, 4 eV and 10 eV, respectively. The ratio of threshold wavelengths of metal X to metal Y is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5 : 2
At the threshold wavelength the photon energy just equals the work function, so the threshold wavelength is inversely proportional to the work function.
\( \displaystyle \frac{hc}{\lambda_0} = \phi_0 \;\Rightarrow\; \lambda_0 = \frac{hc}{\phi_0} \)
\( \displaystyle \frac{\lambda_X}{\lambda_Y} = \frac{\phi_Y}{\phi_X} = \frac{10\,\mathrm{eV}}{4\,\mathrm{eV}} = \frac{5}{2} \)