Physics

The photoelectric effect tells us that $K_{\text{max}} = hf - \phi$, so a graph of $K_{\text{max}}$ versus $f$ is a straight line with slope $h$ and y-intercept $-\phi$. Since X and Y have parallel lines, they share the same slope (same $h$, obviously), but different y-intercepts—meaning different work functions. At the same frequency, metal X has higher kinetic energy than Y, which means X must have a lower work function: less energy is lost to escape, so more is left over as motion. The difference in $K_{\text{max}}$ values directly reveals the difference in work functions.

The photoelectric effect tells us that $K_{\text{max}} = hf - \phi$, so a graph of $K_{\text{max}}$ versus $f$ is a straight line with slope $h$ and y-intercept $-\phi$. Since X and Y have parallel lines, they share the same slope (same $h$, obviously), but different y-intercepts—meaning different work functions. At the same frequency, metal X has higher kinetic energy than Y, which means X must have a lower work function: less energy is lost to escape, so more is left over as motion. The difference in $K_{\text{max}}$ values directly reveals the difference in work functions.