JEE Main 2026 — Dual Nature of Matter Question with Solution

From Einstein's photoelectric equation, the maximum kinetic energy of emitted photoelectrons is given by:

$K_{\text{max}}=\frac{hc}{\lambda }-\Phi$

where $\lambda$ is the wavelength of incident radiation and $\Phi$ is the work function of the metal.

The work function is related to the threshold frequency ${\nu }_0$ by $\Phi =h{\nu }_0$. From the given graph, the x-intercept represents the threshold frequency. We can observe that:

${\nu }_0(X_1)<{\nu }_0(X_2)<{\nu }_0(X_3)$

Therefore, the work functions of the metals follow the order:

$\Phi (X_1)<\Phi (X_2)<\Phi (X_3)$

For the same wavelength $\lambda$ of incident radiation, the term $\frac{hc}{\lambda }$ is constant. Thus, the kinetic energy $K_{\text{max}}$ will be greatest for the metal with the smallest work function.

Since metal $X_1$ has the minimum work function, it will emit electrons with the greatest kinetic energy.

Answer: $X_1$