A photoelectric material having work-function ${\varphi }_0$ is illuminated with a light of wavelength $\lambda \left(\lambda <\frac{hc}{{\varphi }_0}\right)$. The fastest photoelectron has a de Broglie wavelength ${\lambda }_d$. A change in wavelength of the incident light by $\mathrm{\Delta }\lambda$ results in a change $\mathrm{\Delta }{\lambda }_d$ in ${\lambda }_d$. The ratio $\frac{\mathrm{\Delta }{\lambda }_d}{\mathrm{\Delta }\lambda }$ is proportional to

• Correct answer
  A

  $\frac{{\lambda }_d^3}{{\lambda }^2}$
• B

  $\frac{{\lambda }_d^3}{\lambda }$
• C

  $\frac{{\lambda }_d^2}{{\lambda }^2}$
• D

  $\frac{{\lambda }_d}{\lambda }$

Hence, the correct answer is option: 'A'.