§-Unit

Unit 4: Revolutions in modern physics

7 dot points, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

Topic 1: Special relativity

Explain Einstein's two postulates of special relativity (the principle of relativity and the constancy of the speed of light), and apply the time dilation formula

t = \gamma t_0

where

\gamma = 1/\sqrt{1 - v^2/c^2}

to predict the time experienced by moving observers

Special relativity. Explains Einstein's two postulates, defines proper time and the Lorentz factor $\gamma$ , applies time dilation $t = \gamma t_0$ , and works through the muon-decay and twin-paradox examples.

11 min read →

Apply the length contraction formula

L = L_0 / \gamma

and the relativistic momentum formula

p = \gamma m v

to predict the contraction of moving objects and the momentum of relativistic particles

Length contraction and relativistic momentum. Defines proper length, applies $L = L_0 / \gamma$ , and contrasts classical $p = mv$ with relativistic $p = \gamma m v$ .

10 min read →

Apply Einstein's mass-energy equivalence

E = mc^2

(rest energy) and the relativistic energy

E = \gamma m c^2

(total energy) to nuclear reactions, particle physics and astrophysics

$E = mc^2$ . Rest energy, total relativistic energy, the energy-momentum relation, and worked examples in nuclear fission, fusion, and particle creation.

10 min read →

Topic 2: Quantum theory

Explain wave-particle duality through de Broglie's matter-wave hypothesis

\lambda = h/p

, applying it to electron diffraction and to the quantum nature of matter

Wave-particle duality. de Broglie's hypothesis $\lambda = h/p$ , Davisson-Germer electron diffraction, the matter-wave interpretation of Bohr orbits, and the electron microscope application.

10 min read →

Apply the photon model of light (

E = hf

), the photoelectric equation (

E_{k,\max} = hf - \phi

), and the Bohr model of atomic energy levels with transitions producing photons of energy

\Delta E = h f

Quantum theory. Planck's quantum hypothesis, Einstein's photon model, the photoelectric effect with work function and threshold frequency, the Bohr model of the hydrogen atom, and emission/absorption spectra.

11 min read →

Topic 3: The standard model

Identify the elementary particles of the Standard Model (quarks, leptons, gauge bosons, Higgs boson), classify hadrons as baryons (three quarks) and mesons (quark-antiquark pairs), and explain the role of each particle family

Fundamental particles. The six quarks (up, down, charm, strange, top, bottom), the six leptons (electron, muon, tau, three neutrinos), the four gauge bosons (photon, gluon, W, Z), and the Higgs boson; classification of hadrons into baryons (three quarks) and mesons (quark-antiquark).

11 min read →

Describe the four fundamental forces (gravitational, electromagnetic, strong nuclear, weak nuclear), their gauge boson mediators (in the Standard Model), their relative strengths and effective ranges, and applications in nuclear and particle physics

Four fundamental forces. Strong, electromagnetic, weak, gravitational; their mediating bosons, relative strengths and ranges, and roles in atomic structure, nuclear stability, beta decay and gravitation.

10 min read →