Problem 3

Monochromatic light of frequency

f

shines on a metal with work function

\phi

; assume

hf>\phi

so photoelectrons are emitted, and let

h

be Planck’s constant. Each photon transfers its energy to one electron, and subsequent collisions are neglected;

e

is the magnitude of the electron charge. The stopping potential

V_s

means the magnitude of the reverse voltage just sufficient to prevent even the fastest electron from reaching the anode. (a) Write the energy balance for one photon and a maximum-energy electron. (b) Find

K_{\max}

and

V_s

. (c) Predict how they depend on light frequency and intensity.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\boxed{K_{\max}=hf-\phi,\qquad V_s=\frac{hf-\phi}{e};\quad \mathcal I\uparrow\Rightarrow N_{e^-}\uparrow,\ K_{\max},V_s\text{ unchanged}}

problems.proof.analysis

The final expressions relate the fastest electron’s energy to the required stopping potential. The stopping potential is stated as a positive magnitude.