Physics beyond Newton
By 1900, many physicists thought physics was nearly complete. Then experiments revealed puzzles that classical physics couldn’t explain. Solving them led to two revolutions: quantum mechanics and nuclear physics.
Light comes in packets
In 1900, Max Planck proposed that energy is emitted in tiny packets, or quanta. In 1905, Albert Einstein extended this: light itself is made of particles called photons.
E = hf = hc ÷ λ
- h = 6.63 × 10⁻³⁴ J·s (Planck’s constant)
- f = frequency; λ = wavelength
Example: a photon of green light (λ = 550 nm):
E = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) ÷ (550 × 10⁻⁹) = 3.6 × 10⁻¹⁹ J (about 2.3 eV)
1 electron volt (eV) = 1.6 × 10⁻¹⁹ J.
The photoelectric effect
When light shines on certain metals, electrons are knocked out. This is the photoelectric effect. Experiments showed puzzling results:
| Observation | Wave theory predicted | What actually happened |
|---|---|---|
| Dim light | Electrons should eventually escape | Below a threshold frequency, no electrons escape, no matter how bright |
| Brighter light | Faster electrons | More electrons, but not faster ones |
| Higher frequency | No special effect | Faster electrons |
| Timing | A delay to build up energy | Instant emission |
Einstein explained it: each photon gives its energy to one electron. If the photon’s energy is less than the work function (φ), the minimum energy to free an electron, nothing happens.
KE_max = hf − φ
Einstein won the 1921 Nobel Prize for this explanation. Solar panels and digital camera sensors rely on related effects.
Wave–particle duality
Light behaves as a wave (interference, diffraction) and as a particle (photoelectric effect). In 1924, Louis de Broglie proposed that matter also has wave properties:
λ = h ÷ (mv)
Electron diffraction experiments in 1927 confirmed it. This wave–particle duality is the foundation of quantum mechanics. Electron microscopes use electron waves to see details far smaller than light allows.
Atomic spectra
Each element emits light only at specific wavelengths, producing a unique line spectrum. Niels Bohr explained that electrons occupy fixed energy levels. When an electron drops from a higher level to a lower one, it emits a photon with energy equal to the difference:
E_photon = E_high − E_low
Astronomers use spectra to identify elements in distant stars. Helium was discovered in the Sun’s spectrum in 1868, before it was found on Earth.
The nucleus and radioactivity
Radioactivity is the spontaneous emission of radiation from unstable nuclei. Henri Becquerel discovered it in 1896; Marie and Pierre Curie discovered polonium and radium.
| Radiation | Identity | Charge | Penetration | Stopped by |
|---|---|---|---|---|
| Alpha (α) | Helium nucleus (2p + 2n) | +2 | Low | Paper or skin |
| Beta (β⁻) | High-speed electron | −1 | Medium | A few mm of aluminum |
| Gamma (γ) | High-energy photon | 0 | High | Thick lead or concrete |
Decay equations
- Alpha: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
- Beta: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e (a neutron becomes a proton)
Mass number and atomic number are conserved on both sides.
Half-life
Half-life is the time for half the radioactive nuclei in a sample to decay. It’s constant for each isotope.
| Isotope | Half-life | Use |
|---|---|---|
| Technetium-99m | 6 hours | Medical imaging |
| Iodine-131 | 8 days | Thyroid treatment |
| Cobalt-60 | 5.3 years | Cancer radiotherapy (pioneered in Canada in 1951) |
| Carbon-14 | 5730 years | Dating organic material up to about 50 000 years old |
| Uranium-238 | 4.5 billion years | Dating rocks |
N = N₀ (½)^(t ÷ t½)
Example: 80 g of a substance with a 10-day half-life. After 30 days (3 half-lives): 80 → 40 → 20 → 10 g.
Nuclear energy
Einstein’s E = mc² shows mass and energy are equivalent. In nuclear reactions, the products have slightly less mass than the reactants; the missing mass (mass defect) becomes energy.
| Nuclear fission | Nuclear fusion | |
|---|---|---|
| Process | Heavy nucleus splits | Light nuclei join |
| Example | ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n | ²H + ³H → ⁴He + n |
| Where | Nuclear power plants (e.g., CANDU reactors in Ontario) | Stars, including the Sun; experimental reactors |
| Waste | Long-lived radioactive waste | Little long-lived waste |
| Status | Commercial since the 1950s | Still experimental |
Fission chain reactions are controlled in reactors by control rods that absorb neutrons. Fusion requires temperatures of millions of degrees; in December 2022, the U.S. National Ignition Facility achieved a fusion reaction that released more energy than the lasers delivered to the fuel.
Safety and uses
Ionizing radiation can damage DNA. Protection relies on time (minimize exposure), distance (stay far away) and shielding. Yet radiation also saves lives through cancer treatment, medical imaging, sterilizing equipment and smoke detectors (which use americium-241).
Common mistakes
- Thinking brighter light gives photoelectrons more energy. Frequency determines energy.
- Thinking a half-life means everything decays in two half-lives.
- Confusing fission and fusion.
Try it yourself
- Find the energy of a photon with frequency 7.5 × 10¹⁴ Hz.
- A metal has a work function of 2.0 eV. Will 600 nm light (2.07 eV) eject electrons? What is their maximum KE?
- Complete: ²²⁶₈₈Ra → ? + ⁴₂He
- A fossil has 25% of its original carbon-14. How old is it?
(Answers: 5.0 × 10⁻¹⁹ J; yes, 0.07 eV; ²²²₈₆Rn; 2 half-lives ≈ 11 460 years)
Quick recap
- Light is quantized into photons with E = hf.
- The photoelectric effect shows light’s particle nature.
- Light and matter both show wave–particle duality.
- Alpha, beta and gamma radiation come from unstable nuclei; half-life measures decay rate.
- Fission and fusion release energy from mass via E = mc².