The Photoelectric Effect
High-Yield Summary
- Photoelectric effect: light ejects electrons from a metal surface, but only if frequency (not intensity) meets or exceeds the threshold frequency.
- Below threshold frequency, no electrons eject no matter how intense the light — classical wave theory couldn't explain this, which is why it demanded Einstein's photon model.
- Above threshold: ejected electrons' kinetic energy scales with frequency; the number ejected (current) scales with intensity (number of photons).
- Einstein's model: E = hf (photon energy) and Kmax = hf − φ (φ = work function, the binding energy holding an electron to the metal). Won the 1921 Nobel Prize.
- This particle-like evidence for light, combined with light's wave-like diffraction behavior, established wave-particle duality — a cornerstone of quantum mechanics.
Frequency vs. Intensity
| Frequency | Intensity |
|---|---|
| Energy per individual photon | Number of photons per second (brightness) |
| Determines whether ejection happens, and electron KE | Determines how many electrons eject, once ejection is occurring |
Photon Energy and Maximum Kinetic Energy
E = hf, Kmax = hf − φ
- E = Photon energy
- h = Planck's constant ≈ 6.626×10⁻³⁴ J·s
- f = Light frequency
- φ = Work function — energy binding an electron to the metal surface
- Kmax = Maximum kinetic energy of an ejected electron
- Worked example: φ = 3.20×10⁻¹⁹ J, f = 8.00×10¹⁴ Hz → E = hf = 5.30×10⁻¹⁹ J → Kmax = 5.30×10⁻¹⁹ − 3.20×10⁻¹⁹ = 2.10×10⁻¹⁹ J.
- If hf < φ, no ejection occurs regardless of intensity.
Common MCAT Trap
- Brighter (more intense) light below threshold frequency still ejects zero electrons — intensity cannot compensate for insufficient photon energy.
- Kinetic energy of ejected electrons depends on frequency, not intensity — don't assume a brighter light source produces faster electrons.
Quick Recall
A metal's threshold frequency is 5×10¹⁴ Hz. Does very bright light at 4×10¹⁴ Hz eject electrons?
What does the 'leftover' energy (hf − φ) become once an electron is ejected?