Photoelectric Effect: Einstein's Equation question from MHT CET 2023 (11 May, Shift 2)

Answer: (b)

1. Einstein: $\frac{hc}{\lambda} = \phi + eV_s$; write $A = \frac{hc}{\lambda}$.
2. $A - \phi = eV$ and $\frac{A}{2} - \phi = \frac{eV}{4}$
3. $A - \phi = 4\left(\frac{A}{2} - \phi\right) = 2A - 4\phi \Rightarrow \phi = \frac{A}{3}$
4. $\lambda_0 = \frac{hc}{\phi} = 3\lambda$
5. So the answer is (b) $3\lambda$.