Question bank/JEE Advanced/Physics

A photoelectric material having work-function $\phi_{0}$ is illuminated with light of wavelength $\lambda\left(\lambda<\frac{h c}{\phi_{0}}\right)$. The fastest photoelectron has a de Broglie wavelength $\lambda_{d}$. A change in wavelength of the incident light by $\Delta \lambda$ results in a change $\Delta \lambda_{d}$ in $\lambda_{d}$. Then the ratio $\Delta \lambda_{d} / \Delta \lambda$ is proportional to

$[\mathrm{A}] \quad \lambda_{d} / \lambda$

$[\mathrm{B}] \quad \lambda_{d}^{2} / \lambda^{2}$

$[\mathrm{C}] \lambda_{d}^{3} / \lambda$

$[\mathrm{D}] \lambda_{d}^{3} / \lambda^{2}$

Source: JEEBench (IIT Delhi) / JEE Adv 2017 Paper 2