Theory — Intensity, Photon Count, and Photocurrent
- Discuss the photoelectric effect and how it relates to quantum theory.
- Solve problems involving light intensity and electron emission.
- Show that photocurrent is proportional to intensity while electron energy is not.
What "Intensity" Means for a Beam of Photons
The intensity of a light beam is the energy it delivers per second per unit area — how bright it is. In the photon picture, brightening a beam (at a fixed colour) means sending more photons per second, each still carrying the same energy E = hf. Intensity changes the photon count, never the energy per photon.
At fixed frequency: energy per photon is constant, so
Intensity ∝ number of photons per second
Photocurrent
Above the threshold frequency, each photon can free one electron. If you double the number of photons arriving each second, you double the number of electrons ejected each second — and the electric current they produce. The photocurrent is therefore directly proportional to the light intensity.
more photons/s → more electrons/s → larger current
Why the Kinetic Energy Does NOT Change
Each electron is freed by absorbing a single photon. Since every photon in the beam has the same energy (the frequency hasn't changed), every freed electron gets the same energy budget, and the maximum kinetic energy KE_max = hf − ϕ is unchanged no matter how bright the light is. Brighter light makes more electrons, not faster ones.
Stopping voltage V_stop = KE_max / e → also independent of intensity
Why This Defeats the Wave Picture
If light were purely a wave, a brighter beam would pour more energy into each electron, so the electrons should come out faster (higher KE). They don't. Instead, brightness only changes how many electrons appear, while their maximum energy is fixed by frequency. This is direct evidence that light arrives in discrete energy packets — photons — and is one of the foundations of quantum theory.
Raise the intensity (this lab)
More photons per second → more electrons per second → larger photocurrent. KE_max and stopping voltage are unchanged.
Raise the frequency (Part 1)
More energetic photons → larger KE_max and stopping voltage. Studied in the Work Function lab (Part 1).
| Quantity changed | Photocurrent | Max kinetic energy | Conclusion |
|---|---|---|---|
| Intensity ↑ (fixed f) | increases (∝ intensity) | no change | more electrons, same energy |
| Frequency ↑ (fixed intensity) | ≈ same number | increases | same count, faster electrons |
| Frequency below threshold | zero | none | no emission at any intensity |
Instructions — Running the Virtual Experiment
Use the built-in simulation to investigate how light intensity affects the number of electrons emitted while the frequency is kept constant. Record every reading in your lab notebook; include your current-versus-intensity graph in your report.
Simulation — Intensity & Photoelectron Emission
Controls
Fixed: 300 nm on Sodium
Frequency is held constant above threshold; only intensity changes.
Set intensity
| Intensity (%) | Photocurrent (nA) | KE_max (eV) |
|---|---|---|
| No readings yet — pick an intensity and click "Record reading". | ||
Team Questions
Example Lab Report
Sample report demonstrating the expected format and level of detail. Use as a guide for your own submission.
Photoelectric Effect — The Effect of Light Intensity on Electron Emission
Physics | Section: [Your Section] | Date: [Date]
Lab Members: [Names of all members present]
Purpose
To investigate how the intensity of light affects the photoelectric emission of electrons while the frequency is held constant, by measuring the photocurrent at several intensities and confirming that the maximum kinetic energy of the electrons is independent of intensity. The result tests the particle (photon) model of light.
Theory
At a fixed frequency above the threshold, each photon carries the same energy E = hf and frees one electron with maximum kinetic energy KE_max = hf − ϕ. Increasing the intensity increases the number of photons arriving per second, so it increases the number of electrons emitted per second and the photocurrent, but it does not change the energy delivered to any individual electron.
Photocurrent ∝ intensity (line through origin)
KE_max = hf − ϕ (independent of intensity)
If light behaved purely as a wave, brighter light would transfer more energy to each electron and raise KE_max. The photon model instead predicts a higher count of equally energetic electrons — exactly what is observed.
Calculations — Sample: Sodium (ϕ = 2.28 eV) at λ = 300 nm
Photon energy: E = 1240/300 = 4.13 eV (above the 2.28 eV work function, so emission occurs at every intensity)
Maximum kinetic energy: KE_max = 4.13 − 2.28 = 1.85 eV — the same value at every intensity
Current–intensity ratio: I_photo / intensity = 80 nA / 80% = 1.0 nA per % — constant across the data set, confirming proportionality
Results Table — Photocurrent and KE_max vs Intensity (λ = 300 nm, Sodium)
| Intensity (%) | Photocurrent (nA) | I / intensity (nA/%) | KE_max (eV) |
|---|---|---|---|
| 20 | 20 | 1.0 | 1.85 |
| 40 | 40 | 1.0 | 1.85 |
| 60 | 60 | 1.0 | 1.85 |
| 80 | 80 | 1.0 | 1.85 |
| 100 | 100 | 1.0 | 1.85 |
Discussion
The photocurrent rose in direct proportion to the light intensity: doubling the intensity from 40% to 80% doubled the current from 40 nA to 80 nA, and the ratio of current to intensity stayed constant at 1.0 nA per percent. A graph of photocurrent against intensity was therefore a straight line passing through the origin — when the light is off (0% intensity) there is no current.
Critically, the maximum kinetic energy stayed fixed at 1.85 eV across the entire range of intensities, because the frequency — and hence the energy of each photon — never changed. Brighter light produced more electrons, not faster ones. Below the threshold frequency, raising the intensity to maximum produced no current at all. Together these observations cannot be explained by a wave model, in which more intense light should deliver more energy to each electron; they confirm that light is absorbed as discrete photons.
Conclusion
The experiment confirmed that, at a fixed frequency above threshold, photocurrent is directly proportional to light intensity while the maximum kinetic energy of the photoelectrons is independent of intensity. Intensity controls the number of photons (and therefore electrons), not the energy of each one — direct evidence for the particle nature of light and a cornerstone of quantum theory.
Practice Questions
Show all work or give a clear explanation for each answer.