Stopping Potential From Incident Wavelength

The stopping potential satisfies $e{V}_0=K_{max}=\frac{hc}{\lambda }-{\varphi }_0$, so dividing the maximum kinetic energy by the electronic charge gives the voltage needed to halt the fastest electrons. First find the photon energy: $\frac{1240}{248}=5.0\text{eV}$ using $hc=1240\text{eV nm}$. The maximum kinetic energy is then $5.0-2.0=3.0\text{eV}$, and since $K_{max}$ in eV equals $V_0$ in volts, $V_0=3.0\text{V}$. The option $5.0\text{V}$ mistakes the photon energy for the stopping potential. The option $2.0\text{V}$ confuses the work function with $K_{max}$. The option $1.0\text{V}$ wrongly halves the kinetic energy. This relation lets experimenters extract work functions directly from stopping-potential measurements, a standard technique highlighted in the NCERT discussion of Millikan's verification. A quick check confirms $V_0$ is positive and smaller than the full photon energy in volts, as it must be once the work function is paid. A useful corollary is that if the same metal were illuminated with longer-wavelength light, the photon energy would drop, the maximum kinetic energy would shrink, and the required stopping potential would fall accordingly, vanishing entirely once the threshold wavelength is reached. This direct link between wavelength and stopping voltage allows the work function of an unknown cathode to be deduced from a single careful measurement, a technique widely used in surface physics.