The photoelectric effect
The clue that light is particles
- Shine UV on a metal and electrons fly out — the photoelectric effect.
- Strangely, dim blue light works but bright red light does nothing.
- The wave picture can't explain this; photons can.
Threshold frequency
- Below a metal's threshold frequency $f_0$, no electrons come out — however bright the light.
- At or above $f_0$, electrons (photoelectrons) are emitted instantly, even in dim light.
Below the threshold frequency, shining a brighter light on the metal:
Each photon is below $\Phi$, so no single photon can free an electron — brightness cannot help.
Work function and Einstein's equation
- The work function $\Phi = hf_0$ is the least energy to free an electron.
- One photon, one electron: $hf = \Phi + \tfrac{1}{2}mv_{\text{max}}^{2}$, so max KE $= h(f - f_0)$ — linear in frequency.
The minimum energy needed to free an electron from the surface is the ____ function.
The work function $\Phi = hf_0$ — the least energy to release a surface electron.
A $5.0\ \text{eV}$ photon hits a metal with work function $2.0\ \text{eV}$. What is the maximum KE of the photoelectron?
Max KE $= hf - \Phi = 5.0 - 2.0 = 3.0\ \text{eV}$.
The maximum KE of photoelectrons depends on the frequency, not the brightness.
Max KE $= h(f - f_0)$ — set by frequency alone. Brightness changes the number of electrons.
Frequency vs brightness
- Max KE is set by the frequency only (one photon's energy $hf$).
- Brightness = more photons per second → more electrons → bigger current, but the same max KE.
Doubling the brightness at the same frequency:
More photons per second → more electrons (more current), but each photon still carries the same $hf$.
The wave model wrongly predicts that any frequency would emit electrons if you wait long enough.
Waves would let energy build up gradually — but experiment shows a sharp threshold frequency, which the photon model explains.
You've got it
- below $f_0$: no emission, however bright; at/above $f_0$: instant emission
- $hf = \Phi + \tfrac{1}{2}mv_{\text{max}}^{2}$ — max KE rises linearly with frequency
- brightness sets the current (number of electrons), not the max KE