For the photoelectric effect, the maximum kinetic energy (Eₖ) of the photoelectrons is plotted against the frequency (v) of the incident photons as shown in figure. The slope of the graph gives

Solution

Physics sir · 3 steps

Write Einstein's equation in the form y = mx + c, and the slope is sitting right in front of you.

1. Einstein's equation. A photon of energy hν spends part of it, the work function φ, to free the electron. Whatever is left becomes the electron's maximum kinetic energy.

   Eₖ = hν - φ

2. Match with a line. Compare with y = mx + c, taking y = Eₖ and x = ν. The slope is m = h and the intercept is c = -φ. Since h is a universal constant, the line has the same slope tan θ = h for every metal.
3. So. The slope of the Eₖ versus ν graph is Planck's constant, option (a).

The idea to keep. Before reading any graph, write its equation with the plotted quantities as y and x. The slope and intercept then name themselves. For Eₖ versus ν, the slope is h and the intercept on the Eₖ axis is -φ.

Answer from the NTA final answer key. Solution by PrepWiser.