Photoelectric Effect Simulator
Shine light of different frequencies and intensities on a metal surface. See how photon energy determines electron emission and stopping voltage.
The Photoelectric Effect
The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency strikes it. Einstein's 1905 explanation — which earned him the Nobel Prize — showed that light consists of discrete energy packets (photons) each carrying energy E = hf.
Key Observations
- Electrons are ejected only if the photon frequency f exceeds the threshold f₀ = φ/h.
- The maximum kinetic energy of ejected electrons depends on f, not on intensity.
- Intensity determines the number of electrons emitted, not their energy.
- Emission is instantaneous — no waiting time, unlike classical wave prediction.
- Different metals have different work functions φ (binding energy per electron).
Work Function
The work function φ is the minimum energy needed to remove one electron from the metal surface against the attractive forces of the crystal lattice. It is a material property measured in electron-volts (eV). Cesium has a low work function (2.1 eV) — it releases electrons under visible light. Platinum requires UV (5.7 eV).
| Metal | Work function φ (eV) | Threshold λ (nm) | Threshold f (×10¹⁴ Hz) |
|---|---|---|---|
| Cesium (Cs) | 2.1 | 591 | 5.08 |
| Sodium (Na) | 2.3 | 539 | 5.56 |
| Zinc (Zn) | 4.3 | 288 | 10.4 |
| Copper (Cu) | 4.7 | 264 | 11.4 |
| Gold (Au) | 5.1 | 243 | 12.3 |
Stopping Voltage
The stopping voltage V_s is the reverse voltage needed to stop even the fastest emitted electrons. It directly measures K_max: eV_s = K_max = hf − φ. A plot of V_s vs f is a straight line with slope h/e and x-intercept f₀.
Photoelectric Effect Formulas
Photon Energy
Einstein's Photoelectric Equation
Threshold Frequency
Stopping Voltage
| Symbol | Name | Value / Unit |
|---|---|---|
| h | Planck's constant | 6.626 × 10⁻³⁴ J·s |
| f | Photon frequency | Hz |
| φ | Work function | eV (1 eV = 1.602 × 10⁻¹⁹ J) |
| K_max | Max electron kinetic energy | J or eV |
| V_s | Stopping voltage | V |
| e | Elementary charge | 1.602 × 10⁻¹⁹ C |
| f₀ | Threshold frequency | Hz |
| λ | Photon wavelength | m or nm |
Frequently Asked Questions
Why doesn't higher intensity light eject faster electrons?
Intensity (brightness) means more photons per second, not more energy per photon. Each photon still carries energy hf. More photons means more electrons are ejected, but each electron still only absorbs one photon at a time. The kinetic energy of each electron depends only on hf − φ.
What happens at exactly the threshold frequency?
At f = f₀, the photon energy exactly equals the work function: hf₀ = φ. The electrons are just barely freed with zero kinetic energy. They can escape the surface but have no velocity. K_max = 0 and V_s = 0.
Why is Cesium used in photomultiplier tubes?
Cesium's low work function (2.1 eV) means visible light can eject electrons. Combined with its low threshold frequency (508 THz, corresponding to green light), it is sensitive to almost the entire visible spectrum, making it ideal for light-detection applications.
How did Einstein's explanation differ from the classical wave picture?
Classical wave theory treats light as a continuous wave that spreads energy uniformly. It predicted that with enough time, low-frequency light could build up enough energy to eject electrons. But experiment showed instantaneous ejection (or none at all) based purely on frequency. Einstein's photon model — discrete energy packets — perfectly matched the observations.
Is the photoelectric effect used in modern technology?
Yes — extensively. Solar cells convert photons to electrons using photoelectric-like processes in semiconductors. Photomultiplier tubes detect individual photons. Image sensors (CCD, CMOS) in cameras collect photoelectrons. X-ray detectors rely on the effect. Even scanning electron microscopes use photoelectrons for surface analysis.