Photoelectric Effect: Einstein's Equation question from MHT CET 2025 (21 Apr, Shift 2)

Answer: (d)

1. $\frac{1}{2}mV^2 = \frac{hc}{\lambda} - \phi$
2. At $\frac{2\lambda}{3}$: $\frac{1}{2}mV'^2 = 1.5\frac{hc}{\lambda} - \phi = 1.5\left(\frac{hc}{\lambda} - \phi\right) + 0.5\phi$
3. So $V'^2 > 1.5V^2 \Rightarrow V' > V(1.5)^{1/2}$
4. None of the options says 'greater than'; the nearest is (d) $\sqrt{\frac{3}{2}}\,V$ (exact only if $\phi$ is neglected).