Worked example: stopping voltage for sodium

Problem

Sodium has a work function $W_\text{Na} = 2{,}28\;\text{eV}$. It is illuminated with ultraviolet light of wavelength $\lambda = 300\;\text{nm}$. Calculate the stopping voltage $V_s$.

Solution

Step 1 — Photon energy.

$E_f = \frac{hc}{\lambda} = \frac{1240\;\text{eV·nm}}{300\;\text{nm}} \approx 4{,}13\;\text{eV}$

Step 2 — Einstein’s formula for the photoelectric effect. The maximum kinetic energy of the photoelectrons is the photon energy minus the work function:

$E_\text{cin,max} = E_f - W = 4{,}13 - 2{,}28 = 1{,}85\;\text{eV}$

Step 3 — Stopping voltage. This is the potential difference that stops even the fastest electrons, $eV_s = E_\text{cin,max}$:

$\ev{V_s = \frac{E_\text{cin,max}}{e} = 1{,}85\;\text{V}}$

Links

Topics: Quantum physics Concepts: Photoelectric effect · Photon