Compare intensity and frequency in the photoelectric effect
Predict how changing light intensity or frequency affects photoelectric current and maximum electron kinetic energy.
Section 22 · Quantum physics
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 22. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use wave frequency and wavelength, energy, momentum, SI prefixes, electronvolts and scientific notation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
At fixed frequency above threshold, what does increasing intensity primarily increase?
What you will learn
- Explain why Kmax is independent of intensity at fixed frequency
- Explain why photoelectric current is proportional to intensity
- Distinguish intensity changes from frequency changes
Intensity changes how many photons arrive
For light at a fixed frequency above threshold, each photon has the same energy hf. Increasing intensity increases the number of photons arriving each second. If the surface emits electrons efficiently and collection conditions are unchanged, more electrons leave per second and the photoelectric current increases in proportion to intensity.
The maximum kinetic energy stays the same when intensity changes alone because the energy of each photon has not changed. It is set by Kmax = hf − Φ, which depends on frequency and the metal work function. Intensity changes photon arrival rate, not energy per photon.
Frequency changes photon energy
Increasing frequency increases hf. Above threshold this increases the maximum kinetic energy of photoelectrons, while the photon arrival rate is not determined by frequency alone. To compare current, hold intensity and other conditions fixed and state the model assumptions.
Below threshold, increasing intensity at that same sub-threshold frequency still gives no emission in the basic model. Increasing frequency past threshold allows emission. Separate controlled comparisons: vary intensity at fixed frequency to test current, or vary frequency with intensity specified to test electron energy.
Pause and explain
At fixed frequency above threshold, what happens to Kmax when light intensity doubles?
Worked example
A photocell is illuminated above threshold. The light intensity is tripled while frequency and collection conditions remain fixed. Predict the changes in photocurrent and Kmax.
Show the worked solution
- More intensity means more photons arrive per second.
- Each photon still has the same frequency and energy.
- Apply the stated proportionality and Einstein equation.
Answer The photoelectric current triples; Kmax remains unchanged.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
At fixed frequency above threshold, intensity rises by 50%. Predict the photoelectric current and Kmax changes.
Give me a hint
Use the proportional current relation and keep photon frequency fixed.
Compare my reasoning
- The photon arrival rate increases by 50%.
- With unchanged collection conditions, photoelectric current rises by 50%.
- Each photon still has energy hf, so Kmax is unchanged.
The current rises by 50%; Kmax does not change.
Look for these in your work
- Intensity interpreted
- Current response proportional
- Kinetic-energy response distinguished
Frequency is increased above threshold while the surface and intensity are kept fixed. What happens to photon energy and Kmax?
Give me a hint
Use E = hf and Kmax = hf − Φ.
Compare my reasoning
- The higher frequency gives each photon greater energy.
- The metal work function is unchanged.
- The excess energy and therefore Kmax increase.
Photon energy and maximum photoelectron kinetic energy increase.
Look for these in your work
- Photon-energy trend stated
- Work function held fixed
- Kinetic-energy trend justified
A graph shows that doubling intensity doubles photoelectric current but leaves the stopping potential unchanged. Explain why this is consistent.
Give me a hint
Connect current to emitted-electron rate and stopping potential to Kmax per electron.
Compare my reasoning
- Greater intensity supplies more photons per second and hence more photoelectrons per second.
- At fixed frequency, the energy per photon and Kmax remain unchanged.
- The stopping potential is linked to maximum electron kinetic energy, so it stays unchanged.
More electrons per second raise current, while unchanged Kmax leaves stopping potential unchanged.
Look for these in your work
- Current mechanism explained
- Kinetic energy held fixed
- Stopping-potential observation linked
Common mistakes
- Saying greater intensity makes each photon more energetic
- Saying Kmax is proportional to intensity
- Claiming sub-threshold light emits electrons if intense enough
- Comparing current without holding collection conditions fixed
What can you explain now?
At fixed frequency above threshold, what does increasing intensity primarily increase?
Compare with the explanation
The photon arrival rate
Intensity reflects how much radiation energy arrives each second; photon energy is unchanged.
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Make it stick
Why can photocurrent change while the maximum kinetic energy stays fixed?
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