Modern Physics
Modern physics denotes the body of physical theory that emerged in the early 20th century to explain phenomena where classical mechanics and electromagnetism break down — high speeds, very small scales, and intense gravitational fields. Its twin pillars are relativity (Einstein, 1905, 1915) and quantum theory (Planck, Bohr, Heisenberg, Schrödinger).
The quantum of electromagnetic radiation: a massless particle with energy E = hf and momentum p = h/λ, where h = 6.626 × 10⁻³⁴ J·s is Planck's constant. Photons travel at speed c in vacuum and exhibit both wave and particle properties.
Special relativity
Albert Einstein's 1905 special relativity rests on two postulates:
- The laws of physics are the same in all inertial frames.
- The speed of light in vacuum, c ≈ 3 × 10⁸ m/s, is the same for all inertial observers, independent of the source's motion.
From these follow striking consequences for objects moving at speed v relative to an observer, with Lorentz factor γ = 1/√(1 − v²/c²):
- Time dilation: Δt' = γ Δt — moving clocks run slow.
- Length contraction: L' = L/γ — moving rulers shrink along the direction of motion.
- Relativistic mass-energy: E = γmc² → E² = (pc)² + (mc²)².
- Mass-energy equivalence: a body at rest has energy E₀ = mc².
These predictions are verified daily in particle accelerators and GPS satellites, whose clocks must be corrected for both special and general-relativistic effects.
- Nothing carrying information or mass can travel faster than light.
- Simultaneity is relative — two events simultaneous in one frame may not be in another.
- The total energy of a particle includes rest energy plus kinetic energy.
- Particle accelerators routinely produce particles with γ > 1000.
The quantum revolution
Several experiments in the late 19th and early 20th centuries defied classical physics:
| Experiment | Discoverer | Year | Significance |
|---|---|---|---|
| Black-body radiation | Planck | 1900 | E = hf; introduction of the quantum |
| Photoelectric effect | Einstein | 1905 | Light comes in discrete photons |
| Atomic spectra | Bohr | 1913 | Quantised electron orbits in atoms |
| Compton effect | Compton | 1923 | Photon momentum p = h/λ |
| Matter waves | de Broglie | 1924 | Particles also behave as waves: λ = h/p |
| Electron diffraction | Davisson–Germer | 1927 | Experimental confirmation of matter waves |
The photoelectric effect
When light shines on a metal surface, electrons may be ejected. Classically the kinetic energy of ejected electrons should grow with intensity, but experiment showed it depends only on frequency. Einstein resolved the paradox:
KE_max = hf − φ
where φ is the work function of the metal. Below the threshold frequency f₀ = φ/h, no electrons are emitted regardless of intensity. This work earned Einstein the 1921 Nobel Prize and confirmed the particle nature of light.
Atomic structure
The Rutherford scattering experiment (1911) revealed that atoms have a tiny, dense, positively charged nucleus surrounded by electrons. Niels Bohr (1913) explained the hydrogen spectrum by postulating:
- Electrons orbit only in allowed circular orbits of quantised angular momentum L = nℏ.
- Atoms absorb or emit photons only when electrons jump between orbits: hf = E_n − E_m.
- The energy levels of hydrogen are E_n = −13.6 eV / n².
The Rydberg formula gives spectral wavelengths: 1/λ = R(1/n₁² − 1/n₂²), where R = 1.097 × 10⁷ m⁻¹.
Nuclear physics
The atomic nucleus contains protons (charge +e, mass ≈ 1 u) and neutrons (charge 0, mass ≈ 1 u), bound by the strong nuclear force. Key facts:
- Atomic number Z = number of protons (determines the element).
- Mass number A = Z + N (protons + neutrons).
- Isotopes have same Z but different N (e.g., C-12 and C-14).
- Binding energy per nucleon peaks at ~8.8 MeV around iron-56, explaining why heavier nuclei fission and lighter nuclei fuse.
Radioactive decay
Three classical decay modes:
- Alpha (α) decay: emission of a helium-4 nucleus. Reduces A by 4, Z by 2.
- Beta (β) decay: emission of an electron (β⁻) or positron (β⁺). A is unchanged; Z changes by ±1.
- Gamma (γ) decay: emission of a high-energy photon from an excited nucleus. A and Z unchanged.
Decay follows an exponential law: N(t) = N₀ e^(−λt), with half-life t₁/₂ = ln 2 / λ.
Useful half-lives to remember: Carbon-14 (5,730 years, basis of carbon dating), Iodine-131 (8 days, used in thyroid imaging), Uranium-238 (4.47 × 10⁹ years, used in geological dating). Activity is measured in becquerel (1 Bq = 1 decay/s) or the older curie (1 Ci ≈ 3.7 × 10¹⁰ Bq).
Fission, fusion and the standard model
Nuclear fission (Hahn & Strassmann, 1938) — splitting of a heavy nucleus (e.g., U-235) by neutron absorption, releasing ~200 MeV per event. Basis of reactors and atomic bombs.
Nuclear fusion — combining of light nuclei (e.g., H-2 + H-3 → He-4 + n) to release energy. Powers the Sun and stars; still being developed for civilian power (ITER).
The modern Standard Model classifies fundamental particles into:
- Quarks (6 flavours, in 3 generations) — form protons, neutrons and other hadrons.
- Leptons (electron, muon, tau and their neutrinos) — do not feel the strong force.
- Gauge bosons (photon, W, Z, gluon, Higgs) — mediate the four interactions.
The discovery of the Higgs boson at CERN in 2012 confirmed the mechanism that gives elementary particles mass.