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

K_{\max}=hf-W_0=h(f-f_0),\quad f\ge f_0

problems.proof.analysis

Einstein's equation partitions photon energy into work function and maximum kinetic energy. Nonnegative kinetic energy requires $f\ge f_0$ .