The Photoelectric Effect
Distinguish intensity from frequency and use a photoelectric threshold and stopping voltage.
AP Physics 2 Topic 15.5 · College Board CED printed p. 144, 145 / PDF p. 151, 152 · See this topic in the course outline
Brighter light means more photons. Bluer light means greater energy per photon. A threshold experiment separates those two ideas.
Before you start
- Photon energy
- Energy conservation
- Electric potential energy
One photon supplies one emission event in the model
The photoelectric effect ejects electrons from a photoactive material when light supplies enough energy. The material's work function φ is the minimum energy needed to remove an electron. In the ordinary single-photon model, one absorbed photon transfers hf to one electron; emission requires . At the exact threshold the maximum emerging kinetic energy is zero, an ideal limiting case.
Below threshold, increasing the number of incident photons does not combine their energies to liberate an electron in this model. Above threshold, even low-intensity light can produce individual emissions when photons are absorbed; greater intensity at fixed f usually means more photoelectrons per second, not faster maximum photoelectrons. Ordinary single-photon experiments support energy arriving in discrete packets. Multiphoton effects at extreme intensities require a different model.
Pay the work function before assigning kinetic energy
Energy conservation gives for emitted electrons when hf ≥ φ. Some electrons lose additional energy before leaving the surface, so this is a maximum rather than every electron's energy. For hf < φ there is no emission in this model: do not report a negative kinetic energy as a physical outgoing electron.
A graph of Kmax versus f is a straight line above threshold with slope h and frequency intercept φ/h. Raising f increases Kmax; raising intensity at the same f does not change that line's value. The work function depends on the material and is provided where needed; AP students do not memorize work-function values or the material variables that determine them.
Measure maximum kinetic energy with a retarding field
Place two plates in a vacuum chamber, illuminate one with monochromatic light, and adjust a variable potential difference. A collecting voltage draws emitted electrons toward the other plate. A retarding voltage pushes them back; at the smallest retarding magnitude that stops the photocurrent, even the fastest electrons cannot reach the collector.
Using the positive magnitude of stopping potential Vs, . Therefore . Plot Vs against f for frequencies above threshold; the slope gives h/e and the negative vertical intercept gives −φ/e. Use the intercept or frequency intercept to infer the work function. Reverse-polarity confusion is avoided by labeling Vs as the retarding magnitude. Increasing above-threshold intensity changes current size but not the ideal stopping voltage.
Check the threshold, then stopping voltage
A material has provided work function 2.20 eV. Light of wavelength 400 nm shines on it. Find Kmax and the stopping-potential magnitude using hc = 1240 eV·nm.
Eγ = 1240/400 = 3.10 eV, which exceeds 2.20 eV.
Why this step? Emission is possible only after the threshold comparison.
Kmax = 3.10 − 2.20 = 0.90 eV.
Why this step? The photon energy pays the minimum removal cost first.
eVs = Kmax gives Vs = 0.90 V. Doubling intensity leaves this voltage unchanged, while photocurrent generally increases.
Why this step? One electron accelerated through one volt changes energy by one eV; maximum energy depends on frequency.
Answer and check
Kmax = 0.90 eV and Vs = 0.90 V.
Make the model respond
Focused Physics 2 model
Photon energy and photoelectric threshold
Predict first. Can brighter light eject electrons if each photon has too little energy?
Ephoton = hf = hc/λ; Kmax = hf − φ when hf ≥ φ; f₀ = φ/h
- Above-threshold KE; zero below threshold means no emission
- Selected or reference point
On a narrow screen, scroll within a figure to read its labels. The table and explanation provide the same physics in text.
Ephoton = 3.1 eV exceeds or meets φ = 2 eV; Kmax = 1.1 eV.
Read the model data and comparisons
| Quantity | Value | Unit | Meaning or limit |
|---|---|---|---|
| Wavelength | 4.000 × 10^−7 | m | |
| Frequency | 7.495 × 10^14 | Hz | |
| Photon energy | 4.966 × 10^−19 | J | |
| Work function | 3.204 × 10^−19 | J | |
| Threshold frequency | 4.836 × 10^14 | Hz | |
| Threshold wavelength | 6.199 × 10^−7 | m | |
| Photoemission energetically allowed | yes | ||
| Maximum kinetic energy | 1.762 × 10^−19 | J | At threshold the maximum is zero |
| Stopping potential magnitude | 1.1 | V | |
| Illuminated area | 1.000 × 10^−4 | m² | Fixed 1 cm² |
| Incident irradiance | 5 | W/m² | |
| Incoming photon rate on this area | 1.007 × 10^15 | s⁻¹ | Photon rate is not measured electron current |
Frequency determines energy per photon. The material’s work function sets the minimum energy needed to escape; any remaining energy sets the maximum electron kinetic energy. Irradiance changes the number of incoming photons per second at fixed wavelength, not the energy of each photon or the maximum kinetic energy. Actual emitted current also depends on absorption, quantum efficiency, and charge collection, which are not calculated here.
Assumptions and limits. Ideal one-photon photoelectric effect, fixed work function, monochromatic light over 1 cm². No multiphoton processes, material absorption spectrum, space charge, electron energy distribution, or detector efficiency. A plotted zero KE below threshold means no emission, not electrons emitted at rest.
Try it from memory
Write your answer and reason before opening the worked answer. Your self-assessment is a study decision; it is not an automatically graded score.
Question 1
φ = 2.50 eV and Eγ = 2.00 eV. What happens after increasing photon flux 100-fold?
Worked answer and reason
No single-photon photoemission occurs; every photon is still below the work function.
More insufficient packets do not raise each packet’s energy in the ordinary photoelectric model.
Question 2
How would increasing φ alter a graph of Kmax versus f for a new surface, if h is unchanged?
Worked answer and reason
The slope stays h; the line shifts down and the threshold-frequency intercept shifts right.
A material’s minimum removal cost changes the intercept rather than the photon-energy slope.
JavaScript enables saved drafts and self-assessment. You can always work on paper.
Catch the tempting mistake
- Brighter monochromatic light produces greater stopping voltage.
- At fixed frequency it supplies more photons, but maximum electron energy and ideal stopping voltage stay fixed.
Put it to work
Give the physical reason as well as the calculation. The worked solutions are on a separate page.
- Problem 9 · mixed
- Problem 10 · experimental
- Problem 17 · mixed
Scientific calculator workspace
Keep intermediate precision and report units. This calculator supports arithmetic and elementary functions.
Scientific calculator
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For the teacher
- Require a threshold check before computing Kmax. Ask why the current can change without changing stopping voltage.
Source objectives and scope
- 15.5.A — Describe an interaction between photons and matter using the photoelectric effect.
Where applicable, work functions for materials will be provided on the exam; students are not expected to know values of work functions or variables of a material that influence the magnitude of its work function.
Suggested skills are teaching guidance. The course applies all science practices across its objectives.
Science references for this teaching
- AP Physics 2 Course and Exam Description, official Unit 15 — Official topic/LO/EK scope and boundaries; local pinned pages 143–158, equations and relevant clauses visually checked on 143–144,146,149–150,152–158.
- AP Physics 2 Course and Exam Description Clarifications, effective Fall 2026 — 15.7.B.1 current definition includes decay to a lower energy level of the same nucleus.
- OpenStax University Physics 3, Blackbody Radiation — Verification of Wien peak and integrated spectral intensity versus Stefan–Boltzmann total power.
- OpenStax University Physics 3, Photoelectric Effect — Verification of threshold, maximum kinetic energy, intensity distinctions, and retarding-potential experiment.
- OpenStax University Physics 3, The Compton Effect — Verification of positive electron-at-rest shift and photon energy/momentum accounting.
- OpenStax University Physics 3, Nuclear Binding Energy — Verification of all-nucleon mass defect and atomic-mass convention.
- OpenStax University Physics 3, Radioactive Decay — Verification of exponential survival, half-life, and nuclear transformation balances.
- OpenStax University Physics, Volume 3: 6.1 Blackbody Radiation — Primary textbook verification of the wavelength-based blackbody spectral shape, the distinction between peak height and complete spectrum area, Wien’s displacement law, and Stefan–Boltzmann emitted intensity and power.
Related source reading
These alternative explanations and examples retain their source context. Draft placement does not add accepted exam coverage.
- Carbon-surface photoemission · source context; placement review pending
Glossary and deeper reading · 9 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Photon
A photon is a quantum of electromagnetic radiation with energy proportional to its frequency. It has zero rest mass and no electric charge but carries energy and momentum. For example, increasing light’s frequency increases the energy of each photon, while increasing the number of same-frequency photons increases the total energy.
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Conservation of energy
Conservation of energy means total energy is unchanged when the full isolated system is considered. Energy can transfer between objects or change form, so one selected energy store need not remain constant. For example, friction can reduce a sliding block’s kinetic energy while increasing the thermal energy of the block and floor.
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Electric potential energy
Electric potential energy is energy associated with the configuration of interacting charges. Its value depends on the chosen reference, and a charge pair is counted once when calculating a system’s total pair energy. For example, bringing two positive point charges closer requires positive external work in a slow controlled approach.
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Work function
A work function is the minimum energy needed to remove an electron from the specified material surface. For single-photon photoemission, the photon energy first pays this energy requirement before contributing to the emitted electron’s kinetic energy. For example, two different surfaces can have different threshold frequencies because their work functions differ.
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Kinetic energy
Kinetic energy is energy associated with motion relative to a chosen reference frame. For a nonrelativistic translating object it is one half of its mass times speed squared. For example, doubling a cart’s speed quadruples its translational kinetic energy when its mass stays fixed.
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Wave intensity
Wave intensity is the time-averaged energy-transfer rate per area perpendicular to propagation. It is measured in watts per square meter and differs from total power because area matters. For example, spreading the same sound power over a larger area reduces the intensity there.
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Potential difference
Potential difference is the change in electric potential between two locations. It represents electric potential-energy change per unit charge and is measured in volts. For example, the potential difference across a resistor describes the energy transferred per coulomb passing through it.
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Stopping potential
Stopping potential is the smallest retarding-voltage magnitude that stops the fastest photoelectrons from reaching the collector. Its electric energy barrier measures the maximum kinetic energy of the emitted electrons. For example, increasing above-threshold light frequency raises the maximum kinetic energy and therefore raises the required stopping-potential magnitude.
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Electric current
Electric current is the net rate of charge flow through a specified cross section. It is measured in amperes, or coulombs per second, with direction defined by positive-charge motion. For example, the same steady current passes through each element of a simple unbranched series loop.