Photoelectric Graphs and Stopping Potential
The same photon energy balance can be read from a graph or measured with a reverse potential difference. Keep maximum electron energy separate from photoelectric current.
Read the photoelectric equation as a straight-line graph
For one metal, the work function is fixed. Rearranging the photon energy balance gives the straight-line form below.
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| Graph feature | Physical meaning |
|---|---|
| Gradient | Planck constant h |
| Frequency-axis intercept | Threshold frequency f₀ |
| Backward energy-axis intercept | −Φ |
| No plotted values below f₀ | No photoelectrons exist, so maximum kinetic energy is not defined. |
Common mistake
- A different metal has a different work function, so the intercepts change but the gradient remains h.
- A greater intensity at the same frequencies does not change this graph. It increases the emission rate, not the maximum kinetic energy.
These are graph predictions, not new equations. State the changed physical quantity first, then identify the graph feature it controls (9702/41/M/J/22 Q7(c)).
The intensity is increased while the metal and all frequencies are unchanged. What happens to the maximum-kinetic-energy against frequency graph?
Show worked answer
The graph is unchanged. Intensity changes the emission rate and current, not the energy of each photon or the maximum electron kinetic energy.
Stopping potential measures the fastest photoelectrons
A collector can measure the electrons leaving the illuminated metal. A reverse potential difference opposes their motion and reduces the current.
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At the stopping potential, even the fastest photoelectrons just fail to reach the collector, so the photoelectric current is zero.
Definition
1 markWhat is meant by the stopping potential?
Model answer: The stopping potential is the minimum reverse potential difference that reduces the photoelectric current to zero.
Symbols
- = magnitude of the electron charge (C)
- = stopping potential (V)
- = maximum photoelectron kinetic energy (J)
Combining this electrical energy with Einstein's photoelectric equation gives:
A graph of stopping potential against frequency is therefore a straight line.
Its gradient is h divided by e. Its frequency-axis intercept is the threshold frequency. The magnitude of its potential-axis intercept is numerically equal to the work function in electronvolts (9702/42/M/J/25 Q9(b)).
Common mistake
Why does the stopping potential increase when the frequency of the incident radiation increases?
Show worked answer
Higher frequency gives greater photon energy. The maximum photoelectron kinetic energy increases, so a larger reverse potential difference is needed to stop the fastest electrons.
Start every threshold, kinetic-energy and stopping-potential question from the same photon energy balance.