Photoelectric effect: stopping potential versus frequency
Above the threshold frequency, the stopping potential rises linearly with light frequency and makes photoelectron energy measurable.
Free to browse · flashcards or a multiple-choice quiz · import from Essential
Formula
Ug in volts; h/e in V·s; f and f0 in hertz.
Variables & units
| Symbol | Meaning | Unit |
|---|---|---|
| Magnitude of retarding voltage at zero photocurrent | V | |
| Slope of the stopping-potential versus frequency line | V·s | |
| Incident light frequency | Hz | |
| Threshold frequency of the material | Hz |
LaTeX
U_g=\frac{h}{e}(f-f_0)
Original schematic by Quanta
Free with a Quanta account. Your download stays ready after registration.
Derivation & background
A retarding field slows emitted electrons. At the stopping potential, even the fastest electron just fails to reach the collector, so eU_g=Ekin,max. Combining this with Einstein’s balance and f0=WA/h gives Ug=(h/e)(f−f0). The line has universal slope h/e and crosses the frequency axis at the material-specific threshold. Below f0, the single-photon model predicts no emission.
Exam blueprint
Validity range
Photoemission occurs and the retarding voltage is raised just enough to reduce photocurrent to zero.
Derivation steps
Photon energy minus work function is the maximum electron energy; the retarding field does work eU_g.
- 1Compute hf or hc/λ and subtract WA.
- 2Set Ekin,max=eU_g and keep energy units consistent.
Rearrangements
Find stopping potential from light and work function
Photoemission occurs and the retarding voltage is raised just enough to reduce photocurrent to zero.
Task variant
λ=500 nm gives 2.48 eV; for WA=2.00 eV, Ug≈0.48 V.
Light with λ=500 nm has Eγ=hc/λ≈2.48 eV.
For WA=2.00 eV, Ekin,max≈0.48 eV and therefore Ug≈0.48 V, since 1 eV is the energy gained by an electron through 1 V.
Check: 2.48−2.00=0.48 eV.
Common mistakes
Mixing eV and joules or assigning the stopping voltage the wrong sign.
Ug is given as a positive magnitude; energy in eV has the same numerical value as voltage in V after dividing by e.
Exam context
- Measuring work function from stopping voltage or characteristic curves and testing the photon model.
Formula cluster
Photoelectric measurement
The stopping potential converts maximum electron energy into a directly measurable voltage.
Worked example
At λ=500 nm, f=c/λ≈6.00×1014 Hz. For a material with f0=4.84×1014 Hz, Ug=(4.136×10−15 V·s)(1.16×1014 Hz)≈0.48 V. Check: slope times frequency difference gives volts, and eU_g≈0.48 eV equals hf−WA.
Applications
Photocells, measuring work functions and experimentally testing the linear frequency dependence of the photoelectric effect.
How do you calculate with Photoelectric effect: stopping potential versus frequency?
Here is how to work through a typical Photoelectric effect: stopping potential versus frequency (Ug = (h/e)(f − f₀)) task step by step:
- 1
Task
λ=500 nm gives 2.48 eV; for WA=2.00 eV, Ug≈0.48 V.
Solution path
Light with λ=500 nm has Eγ=hc/λ≈2.48 eV.
For WA=2.00 eV, Ekin,max≈0.48 eV and therefore Ug≈0.48 V, since 1 eV is the energy gained by an electron through 1 V.
Check: 2.48−2.00=0.48 eV.
Frequently asked questions about Photoelectric effect: stopping potential versus frequency
What does stopping potential measure?+
It is the magnitude of voltage at which photocurrent just vanishes. Electrons with maximum kinetic energy then just fail to reach the collector. Hence Ekin,max=eU_g. Real curves require care because of contact potentials and energy distributions. Experimentally, increase the retarding voltage while monitoring photocurrent. Current does not vanish for all electrons at once because their initial energies differ. The stopping potential corresponds to the most energetic electron and therefore measures Ekin,max, not the mean energy. The highest-energy electrons set the endpoint even though most emitted electrons stop at a smaller opposing voltage.
What is the threshold frequency?+
f0=WA/h is the minimum frequency at which one photon has enough energy to overcome the work function. At f=f0, maximum kinetic energy is zero; below it, the single-photon model predicts no emission, even at higher intensity. Threshold frequency depends on the material because electrons are bound differently at different surfaces. Compare metals using f0, not merely photocurrent measured under one light source. For example, raising intensity can increase the measured current even when the photon frequency remains just above threshold.
How do intensity and frequency differ?+
Above threshold, greater intensity mainly increases photon and therefore electron count. Maximum electron energy instead depends linearly on f: Ekin,max=hf−WA. This distinguishes the photon model from the classical expectation that energy is transferred solely through light intensity. At fixed frequency, doubling intensity mainly increases the number of incident photons per time. Photocurrent rises, while maximum energy and stopping potential stay the same. This separation between photon count and photon energy is a central prediction of the quantum model. A frequency increase of 1014 Hz raises the energy cutoff by about 0.414 eV; changing intensity does not cause that energy shift.
How can I convert eV directly to volts?+
An electron gains 1 eV of energy when crossing 1 V. Thus a maximum energy of 0.48 eV corresponds to a stopping potential of 0.48 V. This convenient numerical equality applies to an electron and should not be transferred blindly to other charges; generally E=qU. Keep electronvolt calculations consistent. With energy in joules, divide eU by the elementary charge; with energy in eV, its numerical value equals the corresponding electron voltage in volts. The circuit voltage is negative in sign, but the formula uses its positive magnitude.
How can work function be found from measurements?+
Plot Ug against light frequency f. From eU_g=hf−WA, the graph is a line with slope h/e and intercept −WA/e. Its crossing at Ug=0 gives f0, hence WA=hf0. Contact potentials, spectral width and surface condition can cause deviations. A linear fit across several frequencies is more robust than one measurement. Its slope should be h/e and its frequency-axis intercept f0. Contact potentials can shift the intercept. A careful measurement controls electrode material and voltage reference before interpreting the slope as a measurement of h/e. In the ideal model, slope h/e determines Planck’s constant independently of the metal. Use several data points and report the uncertainty of the linear fit.
Quanta exam set
Curated exam set for "Photoelectric effect: stopping potential versus frequency":
Question (front)
Which formula describes Photoelectric effect: stopping potential versus frequency?
Answer in your set
Question (front)
How do you rearrange Photoelectric effect: stopping potential versus frequency for Find stopping potential from light and work function?
Answer in your set
Question (front)
Which common mistake happens with Photoelectric effect: stopping potential versus frequency?
Answer in your set
+ 7 more cards: units, variables, derivation, example, exam task
The formula set contains 10 cards. After importing, review them and start practicing; your ratings determine later review intervals.
Subject references and further reading
This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.
More formulas: Atomic and nuclear physics
Retain Photoelectric effect: stopping potential versus frequency for exams
Create a curated FSRS exam set for Ug = (h/e)(f − f₀): formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
Curated formula set · LaTeX · FSRS spaced repetition · import from Essential