AIIMS 2018 Chemistry Einstein's Photoelectric Equation MCQ Question

In the photoelectric effect, the kinetic energy (KE) of the emitted electrons is given by the equation $KE = \frac{hc}{\lambda} - \phi$, where $\phi$ is the work function of the metal. For two wavelengths $\lambda_1$ and $\lambda_2$, the velocities $v_1$ and $v_2$ relate to their kinetic energies as $KE_1 = \frac{1}{2}mv_1^2$ and $KE_2 = \frac{1}{2}mv_2^2$. By equating the kinetic energies, we find that $v_2^2 - v_1^2 = \frac{2hc}{m} \left( \frac{1}{\lambda_2} - \frac{1}{\lambda_1} \right)$, which corresponds to option B.

Options A and C incorrectly apply the factor of 2 or the order of $\lambda_1$ and $\lambda_2$, while option D misrepresents the relationship by introducing an incorrect factor. Understanding the derivation of kinetic energy from the photoelectric effect is crucial for solving such problems.