Table of Contents
Overview#
In 1905, Albert Einstein explained the photoelectric effect by proposing that light consists of discrete energy packets called quanta (later named photons). This work earned him the Nobel Prize in Physics in 1921.
The Photoelectric Effect#
When light shines on a metal surface, electrons can be ejected:
Light (hν) ────→ [Metal] ────→ Electrons (KE)Experimental Observations#
| Observation | Classical Prediction | Actual Result |
|---|---|---|
| Threshold frequency | No threshold | Sharp cutoff below \(\nu_0\) |
| Intensity effect | More intensity = more energy/electron | More intensity = more electrons (same energy) |
| Time delay | Time needed to accumulate energy | Instantaneous emission |
Classical wave theory could not explain these results.
Einstein’s Quantum Explanation#
Light Quanta (Photons)#
Light consists of discrete particles, each with energy:
$$ E_{photon} = h\nu $$Where:
- \(h\): Planck’s constant
- \(\nu\): Light frequency
Photoelectric Equation#
$$ h\nu = \phi + KE_{max} $$Or equivalently:
$$ KE_{max} = h\nu - \phi $$Where:
- \(\phi\): Work function (minimum energy to free electron)
- \(KE_{max}\): Maximum kinetic energy of ejected electron
Threshold Frequency#
Below threshold frequency \(\nu_0\):
$$ \nu_0 = \frac{\phi}{h} $$No electrons ejected, regardless of intensity.
Explanation of Observations#
Why Threshold Exists#
Each photon carries energy \(h\nu\). If \(h\nu < \phi\), even one photon cannot free an electron.
Why Intensity Doesn’t Matter for Energy#
- More intensity = more photons
- Each photon still has same energy
- More electrons ejected, but same max KE
Why No Time Delay#
Energy transfer is instantaneous (one photon → one electron interaction).
Stopping Potential#
Apply voltage to stop fastest electrons:
$$ eV_{stop} = KE_{max} = h\nu - \phi $$Measuring \(V_{stop}\) vs \(\nu\) gives:
- Slope = \(h/e\)
- Intercept = \(-\phi/e\)
Millikan’s Verification#
Robert Millikan (1916) precisely measured:
$$ h = 6.57 \times 10^{-34} \text{ J·s} $$Close to modern value, confirming Einstein’s theory.
Photon Properties#
| Property | Formula |
|---|---|
| Energy | \(E = h\nu = hc/\lambda\) |
| Momentum | \(p = h/\lambda = E/c\) |
| Rest mass | 0 |
Applications#
Solar Cells#
Photovoltaic effect uses photoelectric principle:
- Photons excite electrons in semiconductor
- Built-in field separates charges
- Current flows through external circuit
Photomultiplier Tubes#
- Photoelectric emission from cathode
- Electron multiplication
- Sensitive light detection
Digital Cameras#
CCD/CMOS sensors:
- Photons create electron-hole pairs
- Charge collected and measured
- Forms digital image
Historical Significance#
Wave-Particle Duality#
Einstein showed light has particle nature:
- Interference, diffraction: wave behavior
- Photoelectric effect: particle behavior
This was revolutionary and initially controversial.
From Planck to Einstein#
| Planck (1900) | Einstein (1905) |
|---|---|
| Energy quantization of oscillators | Light itself is quantized |
| Mathematical necessity | Physical reality |
| Emission/absorption quantized | Light travels as quanta |
Einstein’s Annus Mirabilis#
1905, Einstein’s “miracle year,” included:
- Photoelectric effect (Nobel Prize)
- Brownian motion
- Special relativity
- Mass-energy equivalence (E=mc²)
Nobel Prize#
Einstein received the 1921 Nobel Prize in Physics:
“For his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect”
Notably, not for relativity, which was still considered controversial.