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BCS Written Physics study materials
BCS Written Physics study resources

BCS Written Physics: Atomic, Nuclear and Particle Physics

BCS Written Physics · Work through your exam, one topic at a time.

All guide sections

Atomic, Nuclear and Particle Physics

Core concepts

Atomic models (Rutherford, Bohr), energy levels and spectra, the photoelectric effect, nuclear structure, radioactivity (alpha, beta, gamma), half-life, binding energy, mass defect, fission and fusion, and the standard model of particles (quarks, leptons, bosons). You should understand conservation laws in nuclear reactions: charge, nucleon number, energy, momentum.

Traps

  • Forgetting that beta-minus decay converts a neutron into a proton, increasing atomic number by one.
  • Mixing up atomic number (protons) with mass number (protons + neutrons).
  • Using half-life incorrectly: after n half-lives, remaining fraction is (½)ⁿ.
  • Forgetting that gamma emission changes neither Z nor A.
  • Confusing the photoelectric effect (photon energy must exceed work function) with Compton scattering.

Rule of thumb

Binding energy per nucleon peaks near iron-56, so fusion releases energy for light nuclei and fission for heavy ones.

Worked example

A sample with half-life 5 days starts at 80 g. After 15 days, three half-lives have passed: remaining = 80 × (½)³ = 10 g. Alternatively, activity A = A₀e^(−λt) with λ = ln2/5.

Modern Physics

Core concepts

Modern physics covers wave–particle duality, the photoelectric effect, de Broglie wavelength, Bohr's model, X-ray production, and introductory ideas from relativity and quantum mechanics. You should know Einstein's photoelectric equation (hf = φ + K_max) and be able to compute photon energies and de Broglie wavelengths.

Traps

  • Assuming intensity affects the maximum kinetic energy of photoelectrons - it affects only the number emitted.
  • Forgetting that below the threshold frequency no emission occurs, regardless of intensity.
  • Using the wrong mass in de Broglie calculations (electron vs proton).
  • Mixing up the work function (material property) with the stopping potential (experimental).
  • Forgetting that photon energy depends only on frequency, not intensity.

Rule of thumb

Photon energy in eV: E(eV) ≈ 1240/λ(nm). De Broglie wavelength: λ = h/p.

Worked example

Light of 400 nm strikes a metal with work function 2.0 eV. Photon energy = 1240/400 = 3.1 eV. Maximum kinetic energy = 3.1 − 2.0 = 1.1 eV. Stopping potential = 1.1 V.

Quantum Mechanics and Relativity

Core concepts

Quantum: wavefunctions, the Schrödinger equation, uncertainty principle (ΔxΔp ≥ ħ/2), quantisation of energy in a box, and probability interpretation. Relativity: postulates of special relativity, time dilation, length contraction, relativistic mass–energy (E = mc²), and the Lorentz factor. You should be able to compute γ = 1/√(1 − v²/c²) and apply it to time and length.

Traps

  • Applying Galilean velocity addition at speeds close to c.
  • Forgetting that proper time is measured in the rest frame of the clock.
  • Mixing up time dilation (moving clocks run slow) with length contraction (moving lengths shorten along motion only).
  • Ignoring that the uncertainty principle applies to conjugate variables, not arbitrary pairs.
  • Confusing rest energy with total relativistic energy.

Rule of thumb

At v = 0.6c, γ = 1.25; at 0.8c, γ = 5/3 ≈ 1.67; at 0.866c, γ = 2.

Worked example

A particle has proper lifetime 2 μs and travels at 0.8c. γ ≈ 1.67, so observed lifetime = 2 × 1.67 ≈ 3.33 μs. Distance travelled in the lab frame ≈ 0.8 × 3×10⁸ × 3.33×10⁻⁶ ≈ 800 m.

Solid State, Semiconductor and Electronics

Core concepts

Solid state: crystal structures, band theory (conductors, semiconductors, insulators), and doping (n-type, p-type). Semiconductors: p–n junctions, diodes, rectification, transistors (BJT and FET basics), and simple amplifier or switching circuits. Electronics: operational amplifiers, logic gates, and basic circuit design.

Traps

  • Confusing n-type (donor, electrons majority) with p-type (acceptor, holes majority).
  • Forgetting that a forward-biased diode conducts; reverse-biased blocks.
  • Mixing up BJT terminals (base, emitter, collector) or current relations (Ie = Ib + Ic).
  • Assuming an ideal op-amp has infinite output; real ones saturate at supply rails.
  • Forgetting that a half-wave rectifier produces ripple at the supply frequency; a full-wave one at twice.

Rule of thumb

For a silicon diode, forward voltage drop ≈ 0.7 V; for germanium, ≈ 0.3 V. For an inverting op-amp, gain = −Rf/Rin.

Worked example

An inverting op-amp with Rf = 100 kΩ and Rin = 10 kΩ has gain −10. Input 0.2 V gives output −2.0 V, provided the supply rails exceed 2 V.

Mathematical Physics and Computational Methods

Core concepts

Mathematical methods: vector calculus (gradient, divergence, curl), differential equations, Fourier series, complex numbers, matrices and eigenvalues, and probability and statistics. Computational methods: numerical integration (trapezoidal, Simpson), root finding (Newton–Raphson, bisection), and error analysis. You should be comfortable with dimensional analysis and order-of-magnitude estimates.

Traps

  • Forgetting sign conventions in the gradient (points uphill) versus the force (points downhill).
  • Applying Simpson's rule with an odd number of intervals (requires even).
  • Mixing up degrees and radians in trigonometric derivatives.
  • Ignoring round-off versus truncation error in numerical methods.
  • Using the wrong boundary conditions for a differential equation.

Rule of thumb

Simpson's rule: ∫f dx ≈ (h/3)[f₀ + 4f₁ + 2f₂ + 4f₃ + … + f_n], with n even. Newton–Raphson: x_{n+1} = x_n − f(x_n)/f'(x_n).

Worked example

Estimate ∫₀¹ x² dx using Simpson's rule with h = 0.5. f₀ = 0, f₁ = 0.25, f₂ = 1. Integral ≈ (0.5/3)(0 + 4×0.25 + 1) = (0.1667)(2) ≈ 0.333, matching the exact 1/3.

Scientific Method, Measurement and Laboratory Practice

Core concepts

Scientific method: hypothesis, controlled experiment, variables (independent, dependent, controlled), reproducibility, and the difference between precision and accuracy. Measurement: SI units, significant figures, uncertainty propagation, systematic versus random errors, calibration, and use of instruments such as vernier callipers, micrometer, and stopwatch.

Traps

  • Reporting too many significant figures; the result should match the least precise input.
  • Confusing precision (repeatability) with accuracy (closeness to true value).
  • Forgetting that a zero error in a micrometer must be subtracted from readings.
  • Adding absolute uncertainties when multiplying or dividing (should add fractional uncertainties).
  • Ignoring parallax error when reading scales.

Rule of thumb

For products and quotients, add fractional (percentage) uncertainties. For sums and differences, add absolute uncertainties.

Worked example

A rectangle measures 5.0 ± 0.1 cm by 3.0 ± 0.1 cm. Area = 15 cm². Fractional uncertainties: 0.1/5 = 2%, 0.1/3 ≈ 3.3%. Combined ≈ 5.3%, so absolute uncertainty ≈ 0.8 cm². Report area = 15 ± 0.8 cm².