Specialized Topics
Specialized Topics make up about 9% of the GRE Physics Subject Test. This block samples condensed matter, nuclear and particle physics, and related applications such as astrophysics and materials science. The questions are broad but shallow: definitions, order-of-magnitude estimates, and one-line conservation arguments rather than long derivations.
Core rules
- Crystals: Miller indices label planes, and Bragg's law 2d sinθ = nλ locates diffraction peaks. Cubic packing fractions are 0.74 for FCC and 0.68 for BCC.
- Band theory: metals have a partly filled band; insulators and semiconductors have a gap. Carrier density scales roughly as e^{−E_g/2kT}, so conductivity rises steeply with temperature.
- Free-electron Fermi energy in three dimensions: E_F = (ħ²/2m)(3π²n)^{2/3}, typically a few eV in metals. Only electrons within about kT of E_F contribute to transport and heat capacity.
- Phonons and the Debye model give a T³ heat capacity at low temperature and the Dulong–Petit limit of 3R per mole at high temperature.
- Nuclear physics: binding energy per nucleon peaks near ⁵⁶Fe at about 8.8 MeV. Decay follows N = N₀e^{−λt} with t₁/₂ = ln2/λ. Charge, baryon number, lepton number, and energy-momentum are conserved.
- Particle physics: quarks carry fractional charge; mesons are qq̄ pairs and baryons are qqq states. Strangeness is conserved in strong and electromagnetic interactions but not in weak decays.
- Conservation laws eliminate wrong answers faster than calculation does.
Worked example
X-rays diffract from crystal planes spaced d = 0.20 nm, producing a first-order peak at θ = 30°. Bragg's law gives λ = 2d sinθ = 2(0.20 nm)(0.500) = 0.20 nm. A second-order peak would need sinθ = nλ/2d = 1.0, that is θ = 90°, so no second order is observable at this wavelength.
Traps
Measuring the Bragg angle from the surface normal instead of from the planes; using total binding energy where binding energy per nucleon determines stability; confusing half-life with mean lifetime (τ = t₁/₂/ln2); neglecting reaction threshold energies; treating the Fermi energy as a temperature without the k_B conversion.