• Tags: einstein, equation, stopping-potential
• Difficulty: Moderate

Einstein's equation: KE_max = hf - φ = e$V_{0}$, where φ = hf_{0} is the work function (minimum energy to free an electron from the metal surface). The stopping potential $V_{0}$ is the retarding potential that stops the most energetic photoelectron.

The $V_{0}$ vs f graph is crucial for JEE: it's a straight line with slope h/e ≈ $4.14 \times 10^{-15}$ V·s, x-intercept at f_{0} (threshold frequency), and y-intercept at -φ/e. For two different metals, the $V_{0}$-f lines are parallel (same slope h/e) but have different x-intercepts (different work functions). The metal with higher work function has a higher threshold frequency and its line starts further right on the f-axis.

Important: not all electrons have KE_max. The energy distribution ranges from 0 to KE_max, depending on how tightly bound each electron is.