Two metals, X and Y have work functions, 4 eV and 10 eV, respectively. The ratio of threshold wavelengths of metal X to metal Y is

5 : 2

The correct answer is Option (1) → 5 : 2

The threshold wavelength $\lambda_{\text{th}}$ is related to work function $\phi$ by:

$\lambda_{\text{th}} = \frac{hc}{\phi}$

Given: $\phi_X = 4 \ \text{eV}$, $\phi_Y = 10 \ \text{eV}$

Ratio of threshold wavelengths:

$\frac{\lambda_X}{\lambda_Y} = \frac{hc / \phi_X}{hc / \phi_Y} = \frac{\phi_Y}{\phi_X} = \frac{10}{4} = 2.5$

Ratio of threshold wavelengths $λ_X : λ_Y = 2.5 : 1$