Photoelectric effect

What is it about?

Light falling on a metal can release electrons: the photoelectric effect. Below a threshold frequency no electrons are released, however bright the light. More intensity gives more electrons, but not faster ones. Einstein explained this with photons of energy $E_\text{Ph} = h \cdot f$. One photon gives its energy to one electron, which needs the work function $W_\text{A}$ to leave the metal:

With a retarding voltage $U$ between anode and cathode the current vanishes at $e \cdot U_\text{G} = E_\text{kin,max}$. Plotting $e \cdot U_\text{G}$ against $f$ gives Einstein’s line with slope $h \approx 4.14 \cdot 10^{-15}\,\text{eV}\cdot\text{s}$ and threshold frequency $f_\text{G} = \frac{W_\text{A}}{h}$.

Work functions (rounded textbook values): caesium $1.94\,\text{eV}$, potassium $2.25\,\text{eV}$, sodium $2.28\,\text{eV}$, lithium $2.46\,\text{eV}$, zinc $4.34\,\text{eV}$, copper $4.48\,\text{eV}$.

Try it

1. Watch the electrons at $U = 0$, then increase the retarding voltage. Load example
2. Press “Adjust the voltage”. No current
3. Double the intensity from $50\,\%$ to $100\,\%$: the current doubles, $U_\text{G}$ stays. 50 % · 100 %
4. Try red light. Red light
5. Record an automatic series and read off the slope.

Tasks

Task 1: Violet light on caesium

$\lambda = 400\,\text{nm}$, $W_\text{A} = 1.94\,\text{eV}$. Find $E_\text{Ph}$, $E_\text{kin,max}$ and $U_\text{G}$. Load task

Task 2: Threshold frequency

Find $f_\text{G}$ for caesium. Does red light ($650\,\text{nm}$) release electrons?

Task 3: Zinc

Why does $400\,\text{nm}$ light release no electrons from zinc ($W_\text{A} = 4.34\,\text{eV}$)?

Ideas for the classroom

• Collect the three surprising observations first, then compare with the wave model.
• Common stumbling blocks:
  • “Brighter light makes faster electrons.” – More light means more photons, not more energetic ones.
  • “$E_\text{kin} = h \cdot f$.” – The work function is missing.