Slope Of Stopping Potential Versus Frequency Graph

Writing Einstein's equation as a stopping-potential relation, $e{V}_0=h\nu -{\varphi }_0$, and dividing by $e$ gives $V_0=\frac{h}{e}\nu -\frac{{\varphi }_0}{e}$. This is a straight line in the variables $V_0$ and $\nu$, with slope $\frac{h}{e}$ and intercept $-\frac{{\varphi }_0}{e}$ on the potential axis. The slope contains only the universal constants $h$ and $e$, so it is exactly the same for every photosensitive material; only the intercept and the threshold frequency shift with work function. Hence the two graphs are parallel lines. The claim that a larger work function gives a steeper slope is wrong, because work function affects only the intercept. Equating the slope to the work function is dimensionally incorrect. The slope cannot depend on intensity, which influences only the saturation current. Millikan exploited exactly this universal slope to measure Planck's constant, a landmark experiment described in NCERT. As a check, the parallel-line prediction has been confirmed for many metals, strongly supporting the photon hypothesis over classical wave theory. A further insight is that extrapolating each parallel line back to zero stopping potential reveals that metal's threshold frequency on the horizontal axis, while the negative vertical intercept measures its work function divided by the charge. Thus a single linear graph encodes three quantities at once: the universal slope giving Planck's constant, and the two metal-specific intercepts giving the threshold and the work function.