Photoelectric Effect: Einstein's Equation question from MHT CET 2025 (25 Apr, Shift 1)

Answer: (d)

1. $\frac{1}{2}mV^2 = \frac{hc}{\lambda_1} - \phi$ and $\frac{1}{2}m(2V)^2 = \frac{hc}{\lambda_2} - \phi$
2. Second $= 4 \times$ first: $\frac{hc}{\lambda_2} - \phi = \frac{4hc}{\lambda_1} - 4\phi$
3. $3\phi = \frac{4hc}{\lambda_1} - \frac{hc}{\lambda_2} = \frac{hc(4\lambda_2 - \lambda_1)}{\lambda_1\lambda_2}$
4. $\phi = \frac{hc}{3\lambda_1\lambda_2}(4\lambda_2 - \lambda_1)$. So the answer is (d).