Photoelectric Effect Calculator
Inputs
| Incident wavelength | 400 nm |
|---|---|
| Work function | 2 eV |
Photoelectric Effect Calculator
Calculate photon energy, maximum kinetic energy of ejected electrons, threshold wavelength, and stopping voltage for the photoelectric effect. Enter the incident wavelength and the work function of the material.
Inputs
Results
Enter a value to see results.
Details
The photon energy is less than the work function — no electrons are emitted. Use a shorter wavelength (higher-frequency) light to trigger emission.
Photoelectric Effect
When light strikes a metal surface, electrons can be ejected if the light's frequency exceeds a material-specific threshold. This phenomenon, known as the photoelectric effect, was explained by Albert Einstein in 1905 using the concept of light quanta — what we now call photons. Classical wave theory predicted that any frequency of light, given sufficient intensity, should eventually liberate electrons. Experiment showed the opposite: below a certain frequency, no electrons emerge regardless of intensity, while above it, electrons appear immediately even in very dim light. Einstein's explanation earned him the 1921 Nobel Prize in Physics and laid a cornerstone of quantum mechanics.
This calculator computes the photon energy, maximum electron kinetic energy, threshold wavelength, and stopping voltage for any incident wavelength and work function.
The Equations
The energy carried by a single photon of wavelength is:
Ephoton=λh⋅cwhere and .
If exceeds the work function of the material, an electron is emitted with maximum kinetic energy:
KEmax=Ephoton−φ=λh⋅c−φThe threshold wavelength — the longest wavelength that can eject electrons — is:
λ0=φh⋅cThe stopping voltage (the reverse potential needed to arrest the fastest electrons) is:
Vs=eKEmaxwhere is the elementary charge.
Formula Summary
| Quantity | Symbol | Formula |
|---|---|---|
| Photon energy | ||
| Work function | material property | |
| Max kinetic energy | (if positive) | |
| Threshold wavelength | ||
| Stopping voltage |
Worked Example
Ultraviolet light of wavelength () strikes a metal with work function ().
EphotonKEmaxλ0Vs=4×10−76.626×10−34×299792458≈4.97×10−19 J≈3.10 eV=3.10−2.0=1.10 eV≈1.76×10−19 J=3.204×10−196.626×10−34×299792458≈620 nm=1.602×10−191.76×10−19≈1.10 VSince 400 nm is shorter than the threshold wavelength of 620 nm, emission occurs. If the wavelength were 700 nm (red light), the photon energy would be only about 1.77 eV — below the 2.0 eV work function — and no electrons would be ejected.
Key Observations
Intensity does not trigger emission below threshold. Sending more photons of insufficient energy never provides enough energy to free an electron. Emission is an all-or-nothing event for each photon.
Kinetic energy increases linearly with frequency. Above the threshold, , where is the threshold frequency. Millikan verified this linear relationship experimentally in 1916, measuring Planck's constant to within 0.5%.
The stopping voltage measures kinetic energy directly. Multiplying by the electron charge gives , providing a purely electrical method for determining photon energies.
Work Functions of Common Materials
| Material | Work function |
|---|---|
| Caesium | 2.1 eV |
| Sodium | 2.3 eV |
| Aluminium | 4.1 eV |
| Copper | 4.7 eV |
| Gold | 5.1 eV |
| Platinum | 5.7 eV |
Alkali metals such as caesium respond to visible light, which is why they are used in photodetectors and photomultiplier tubes. Platinum requires deep-UV photons to emit electrons.
Frequently Asked Questions (FAQ)
What is the photoelectric effect?
The photoelectric effect is the emission of electrons from a material when light of sufficient frequency shines on its surface. Albert Einstein explained the effect in 1905 by proposing that light consists of discrete packets of energy (photons), each carrying energy E = h·f. An electron is ejected only if the photon energy exceeds the work function φ of the material. Increasing the intensity of light that is below the threshold frequency sends more photons but does not eject any electrons — this contradicted classical wave theory and confirmed the quantum nature of light, earning Einstein the 1921 Nobel Prize.
What is the work function of a material?
The work function φ is the minimum energy required to remove an electron from the surface of a material in vacuum. It represents the binding energy of the most loosely held surface electrons. Alkali metals have low work functions (caesium ≈ 2.1 eV, sodium ≈ 2.3 eV), making them photoelectrically active even under visible light. Noble metals have higher work functions (gold ≈ 5.1 eV, platinum ≈ 5.7 eV), requiring ultraviolet photons to eject electrons.
What is the threshold wavelength?
The threshold wavelength λ₀ = h·c/φ is the maximum wavelength at which the photoelectric effect can occur. Light with a wavelength longer than λ₀ (lower frequency, lower energy) cannot eject electrons no matter how bright it is, because no single photon carries enough energy to overcome the work function. For a work function of 2 eV, the threshold wavelength is about 620 nm — in the red region of visible light.
What is the stopping voltage?
The stopping voltage V_s is the reverse electric potential needed to bring the fastest emitted electrons to rest. Setting up this potential in the circuit means no current flows, allowing the kinetic energy to be measured precisely: KE_max = e·V_s, where e = 1.602 × 10⁻¹⁹ C. Millikan used this technique in 1916 to measure Planck's constant to high accuracy, confirming Einstein's photoelectric equation.