The photoelectric effect is the release of electrons from a metal surface by light. Each electron is freed by one photon of energy E = hf. Emission happens only if that energy is at least the work function W.
This lesson is part of SPM Physics. It leads into relating photon energy, frequency and wavelength. Use h = 6.63 × 10⁻³⁴ J s.
How does one photon free one electron?
Light arrives as packets of energy called photons, and each photon has energy E = hf. One photon gives all its energy to one electron in the metal.
If the photon energy is less than the work function, the electron cannot escape. If it is greater, the extra energy becomes the kinetic energy of the ejected electron.
What does the equation say?
Einstein’s equation is hf = W + KEmax. The threshold frequency f₀ is the lowest frequency that can eject an electron, so at f₀ the kinetic energy is zero and hf₀ = W.
Worked example: two beams, one metal
An original metal has work function W = 3.2 × 10⁻¹⁹ J. Its threshold frequency is f₀ = W ÷ h = 3.2 × 10⁻¹⁹ ÷ 6.63 × 10⁻³⁴ = 4.8 × 10¹⁴ Hz.
Beam A: ultraviolet, f = 1.0 × 10¹⁵ Hz. Photon energy = 6.63 × 10⁻³⁴ × 1.0 × 10¹⁵ = 6.63 × 10⁻¹⁹ J, which exceeds W. KEmax = 6.63 × 10⁻¹⁹ − 3.2 × 10⁻¹⁹ = 3.4 × 10⁻¹⁹ J.
Beam B: bright red, f = 4.0 × 10¹⁴ Hz. Photon energy = 2.65 × 10⁻¹⁹ J, which is less than W. No electrons are emitted, however bright the beam is.
The mistake that costs marks
The slip is to think a brighter beam can make up for a low frequency.
| Statement about beam B | Wrong | Right |
|---|---|---|
| Brighter red light | Eventually ejects electrons | Still none: each photon is below W |
| Reason | More total energy | Energy is delivered one photon to one electron |
Brightness changes the number of photons each second. It does not change the energy of any single photon.
Why is emission immediate?
Each electron absorbs a whole photon in one event, so there is no build-up time. Emission starts as soon as light of high enough frequency arrives, even from a very dim source.
Check yourself
A metal has W = 4.0 × 10⁻¹⁹ J. Light of frequency 8.0 × 10¹⁴ Hz falls on it. Is an electron emitted, and what is the maximum kinetic energy?
Answer
Photon energy = 6.63 × 10⁻³⁴ × 8.0 × 10¹⁴ = 5.3 × 10⁻¹⁹ J, which is greater than 4.0 × 10⁻¹⁹ J, so electrons are emitted.
KEmax = 5.3 × 10⁻¹⁹ − 4.0 × 10⁻¹⁹ = 1.3 × 10⁻¹⁹ J.
What to study next
The next lesson handles the conversions between frequency, wavelength and photon energy. Continue with relating photon energy, frequency and wavelength, then try reading threshold-frequency graphs.
For help with the photon-energy comparison, see online one-to-one Physics tuition.