Problem 3

A metal of work function

W_0

is illuminated by monochromatic light of frequency

f

; photoemission occurs only if a photon has enough energy. Let Planck's constant be

h

, the electron charge magnitude be

e

, and define positive stopping voltage

V_s

as the voltage just sufficient to stop the fastest electron. (a) Find threshold frequency

f_0

. (b) Express maximum kinetic energy

K_{\max}

in terms of

f

and give the emission condition. (c) Find

V_s

and describe the slope and intercept of a plot of

V_s

versus

f

on the emission range.

problems.proof.stepOf

\boxed{f_0=\frac{W_0}{h},\quad K_{\max}=h(f-f_0),\quad V_s=\frac he(f-f_0)}

problems.proof.analysis

The units are consistent: $hf$ is energy and division by $e$ gives voltage. The measured graph slope can determine Planck's constant.

problems.proof.pitfall. Light intensity affects the number of emitted electrons, not their maximum energy; photon energy is set by frequency.