AP Physics 2 · Unit 15 · Topic 2 of 5 · 6 min lesson

Photoelectric Effect

A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.

Quiz this topic · 5 questions

The big idea

Light shining on a metal can knock electrons out, but only if each photon has enough energy to free one. That minimum is the work function φ. Whatever’s left over becomes the electron’s kinetic energy: K_max = hf − φ.

1. One photon, one electron

Below the threshold frequency, nothing comes out, however bright the light. Above it, K_max rises in a straight line with slope h.

K_max = hf − φphotoelectric equation

f₀ = φ/hthreshold frequency

Slope of K_max vs. fPlanck’s constant h

Vertical intercept−φ

eV_stop = K_maxstopping potential

2. Why it proves light is particles

If light were only a wave, brighter light should eventually free electrons at any frequency, and dim light should take time to build up energy. Neither happens.

Instead: frequency controls whether electrons come out and how fast they go. Brightness controls only how many come out.

Emission starts instantly, even in very dim light, because a single photon delivers its whole energy to a single electron.

Einstein won the Nobel Prize for this explanation.

3. Example, then try it

Example

400 nm light hits sodium (φ = 2.3 eV). Find the maximum kinetic energy of the electrons and the stopping potential.

Photon energy: 1240 ÷ 400 = 3.1 eV. K_max = 3.1 − 2.3 = 0.80 eV.

Stopping potential: 0.80 V.

Try it · work it on paper first

For sodium (φ = 2.3 eV), find the threshold frequency and wavelength. Does bright red light (650 nm) free electrons? What about 300 nm ultraviolet light, and what happens if it’s made twice as bright?

Threshold: f₀ = φ/h = 2.3 ÷ (4.14 × 10⁻¹⁵) ≈ 5.6 × 10¹⁴ Hz; λ₀ = 1240 ÷ 2.3 ≈ 540 nm.

Red, 650 nm: 1240 ÷ 650 ≈ 1.9 eV, less than 2.3 eV. No electrons, no matter how bright.

UV, 300 nm: 1240 ÷ 300 ≈ 4.1 eV, so K_max = 4.1 − 2.3 ≈ 1.8 eV.

Twice as bright: twice as many electrons per second, same K_max.

Answer: f₀ ≈ 5.6 × 10¹⁴ Hz (540 nm); red frees none; UV gives 1.8 eV electrons; brighter means more of them.

4. Common mistakes

“Brighter light gives faster electrons.”Brighter light gives more electrons with the same K_max.

“Wait long enough and dim red light will work.”Below threshold, no electrons come out at all.

Mixing J and eV.Keep everything in eV with h = 4.14 × 10⁻¹⁵ eV·s and hc = 1240 eV·nm.

Check yourself

Which change increases the maximum kinetic energy of photoelectrons from a metal?

K_max = hf − φ depends only on the photon energy, so only a higher frequency increases it.

Ready to practice?

5 questions on Photoelectric Effect, each with a hint and an explanation for every wrong answer.

Quiz this topic All of Unit 15