Unit 5 High-Yield Topics
Free resource by Flowxiom — Edexcel A-level Physics
Not everything. Just what’s on the paper. High-frequency topics only — covering ~80% of exam marks.
Edexcel A-level Physics | Thermal, Nuclear, SHM & Astrophysics | WPH14 & WPH15
Topic 1: Simple Harmonic Motion (frequent 6-mark question)
Question types: Identify SHM; describe phase relationships; calculate velocity/acceleration; energy graphs.
Two Conditions for SHM (both required)
Acceleration is proportional to displacement from equilibrium
Acceleration is always directed towards the equilibrium position (opposite to displacement)
\[a = -\omega^2 x\]
Formulae
\[x = A\cos(\omega t) \qquad v = -A\omega\sin(\omega t) \qquad a = -A\omega^2\cos(\omega t)\]
\[v_{max} = \omega A \text{ (at equilibrium)} \qquad a_{max} = \omega^2 A \text{ (at maximum displacement)}\]
Phase Relationships
| Position | Displacement \(x\) | Velocity \(v\) | Acceleration \(a\) |
|---|---|---|---|
| Equilibrium | 0 | maximum | 0 |
| Maximum displacement | \(\pm A\) | 0 | maximum (opposite direction) |
- \(v\) leads \(x\) by 90°
- \(a\) is in antiphase with \(x\) (180° phase difference)
Period Formulae
\[T_{spring} = 2\pi\sqrt{\frac{m}{k}} \qquad T_{pendulum} = 2\pi\sqrt{\frac{L}{g}}\]
SHM Energy
\[E_k = \frac{1}{2}m\omega^2(A^2 – x^2) \qquad E_p = \frac{1}{2}m\omega^2 x^2 \qquad E_{total} = \frac{1}{2}m\omega^2 A^2\]
Total energy is constant; \(E_k + E_p = \text{constant}\).
Common Mistakes
- ❌ Both conditions must be stated: proportional to displacement AND directed towards equilibrium
- ❌ At equilibrium: maximum velocity, zero acceleration
- ❌ Pendulum period is independent of mass — depends only on \(L\) and \(g\)
Topic 2: Kinetic Theory of Gases (frequent 6-mark question)
Question types: Explain how gas pressure changes with temperature or volume.
Answer Chain — Temperature ↑ → Pressure ↑
Temperature increases → mean kinetic energy of molecules increases
Mean speed of molecules increases
Greater change in momentum per collision with the wall
Molecules collide with the wall more frequently
Greater resultant force on the wall
Area unchanged → pressure increases
⚠️ Both steps 3 and 5 are required — neither can be omitted.
Ideal Gas Law
\[\frac{pV}{T} = \text{constant} \qquad pV = nRT \qquad R = 8.31\ \text{J mol}^{-1} \text{K}^{-1}\]
Temperature must be in Kelvin: \(T = \theta + 273\)
Common Mistakes
- ❌ Using °C instead of K — most common error
- ❌ Must mention both: greater force per collision and higher collision frequency
Topic 3: Nuclear Decay and Half-Life
Question types: Balance nuclear equations; half-life calculations; explain randomness and spontaneity.
Three Types of Radiation
| Radiation | Nature | Example equation | Ionisation & penetration |
|---|---|---|---|
| \(\alpha\) | Helium nucleus \(^4_2\text{He}\) | \(^A_ZX \to ^{A-4}_{Z-2}Y + ^4_2\alpha\) | Strongly ionising; stopped by paper |
| \(\beta^-\) | Electron \(^0_{-1}e\) | \(^A_ZX \to ^A_{Z+1}Y + ^0_{-1}\beta + \bar{\nu}_e\) | Moderately ionising; stopped by aluminium |
| \(\gamma\) | High-energy EM radiation | Accompanies α/β decay | Weakly ionising; requires lead shielding |
⚠️ β⁻ decay: neutron → proton + electron + electron antineutrino — do not omit the antineutrino.
Balancing Nuclear Equations
- Mass number \(A\) (top): sum must be equal on both sides
- Atomic number \(Z\) (bottom): sum must be equal on both sides
Half-Life Calculations
\[N = N_0 \left(\frac{1}{2}\right)^{t/T_{1/2}} \qquad A = \lambda N \qquad T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}\]
Randomness and Spontaneity
- Random: It is impossible to predict which specific nucleus will decay or at what time
- Spontaneous: Decay is unaffected by external conditions such as temperature, pressure or chemical state
Common Mistakes
- ❌ Omitting the electron antineutrino \(\bar{\nu}_e\) in β⁻ decay
- ❌ Both activity \(A\) and number of nuclei \(N\) follow the same exponential decay law
- ❌ Must subtract background radiation count rate — measure it first
Topic 4: Binding Energy and Mass Defect
Question types: Calculate binding energy; judge whether fission/fusion releases energy; read binding energy per nucleon graph.
Calculation Steps
Mass defect: \(\Delta m = \text{sum of individual nucleon masses} – \text{actual nuclear mass}\)
Binding energy: \(E = \Delta mc^2\)
If \(\Delta m\) in atomic mass units: \(E\text{(MeV)} = \Delta m\text{(u)} \times 931.5\)
Binding Energy Per Nucleon Curve
- Iron-56 (\(^{56}\)Fe) is at the peak — most stable nucleus
- Fission: heavy nucleus splits from right side (low) to middle (higher) → energy released
- Fusion: light nuclei fuse from left side (low) to middle (higher) → energy released
Common Mistakes
- ❌ If \(\Delta m\) in kg: use \(E = \Delta mc^2\); if \(\Delta m\) in u: multiply by 931.5 MeV/u
- ❌ Energy is released when binding energy per nucleon increases
Topic 5: Gravitational Fields
Question types: Calculate gravitational field strength and potential; satellite orbits; comparison with electric fields.
Key Formulae
\[g = \frac{GM}{r^2} \qquad \phi = -\frac{GM}{r} \qquad g = -\frac{\Delta\phi}{\Delta r}\]
- Gravitational potential \(\phi\) is always negative (zero at infinity, more negative closer to source)
- Field strength = negative of potential gradient
Satellite Orbits
\[\frac{GMm}{r^2} = \frac{mv^2}{r} \implies v = \sqrt{\frac{GM}{r}} \implies T^2 = \frac{4\pi^2}{GM}r^3\]
Higher orbit → smaller speed, longer period.
Common Mistakes
- ❌ Gravitational potential increases (becomes less negative) as distance from source increases
- ❌ Orbital speed decreases as orbital radius increases
Topic 6: Thermodynamics — Specific Heat Capacity and Latent Heat
Question types: Calculate energy for heating; explain molecular reason why temperature stays constant during change of state.
Key Formulae
\[Q = mc\Delta\theta \quad \text{(temperature change — specific heat capacity, J kg}^{-1}\text{ K}^{-1}\text{)}\]
\[Q = mL \quad \text{(change of state — temperature constant — specific latent heat, J kg}^{-1}\text{)}\]
\[\Delta U = Q + W \quad \text{(first law of thermodynamics)}\]
Why Temperature Stays Constant During a Change of State
Energy supplied goes into increasing molecular potential energy (overcoming intermolecular forces), not kinetic energy. Temperature is proportional to mean kinetic energy — which does not change → temperature stays constant.
Common Mistakes
- ❌ Temperature constant does NOT mean internal energy constant — internal energy increases (as potential energy)
- ❌ Heat loss to surroundings → smaller measured temperature rise → calculated \(c\) is too large
- ❌ Temperature difference may use K or °C (same magnitude); absolute temperature must use K
Topic 7: Damping and Resonance
Question types: Describe features of different oscillations; explain resonance; sketch resonance curves for different damping.
Types of Oscillation
| Type | Amplitude | Frequency | Graph |
|---|---|---|---|
| Free | Constant | Natural frequency \(f_0\) | Constant-amplitude sine wave |
| Light damping | Gradually decreases | Approximately \(f_0\) | Exponentially decaying sine wave |
| Heavy damping | Monotonically → 0 | No oscillation | Slowly returns to equilibrium |
| Critical damping | Fastest return | No oscillation | Fastest return with no oscillation |
Forced Oscillation and Resonance
- Forced oscillation: system driven at driving frequency \(f_d\) — oscillates at \(f_d\), not \(f_0\)
- Resonance: when \(f_d = f_0\) → maximum amplitude
Effect of Damping on Resonance Curve
- More damping → lower, broader resonance peak; peak shifts slightly below \(f_0\)
- Light damping → tall, sharp peak
Common Mistakes
- ❌ Resonance occurs when driving frequency = natural frequency
- ❌ Damping reduces amplitude — it does not change the natural frequency
- ❌ Frequency of forced oscillation = driving frequency, not natural frequency
Topic 8: Astrophysics — Stellar Physics and the H-R Diagram
Question types: Use Wien’s law to find temperature; Stefan-Boltzmann law to compare luminosity; identify star types on H-R diagram.
Two Key Laws
\[\lambda_{max} T = 2.898 \times 10^{-3}\ \text{m K} \quad \text{(Wien’s displacement law)}\]
\[L = 4\pi R^2 \sigma T^4 \qquad \sigma = 5.67\times10^{-8}\ \text{W m}^{-2}\text{K}^{-4}\]
- Smaller \(\lambda_{max}\) → higher temperature → bluer colour
- Luminosity is extremely sensitive to temperature (\(T^4\))
Four Regions of the H-R Diagram
| Region | Position | Temperature | Luminosity | Example |
|---|---|---|---|---|
| Main Sequence | Diagonal (top-left → bottom-right) | High → low | High → low | Sun |
| Red Giant | Top-right | Low (red) | Very high | Betelgeuse |
| White Dwarf | Bottom-left | High (white) | Very low | Sirius B |
| Supergiant | Top-right (above red giant) | Low | Highest | — |
H-R diagram temperature axis increases from right to left — opposite to the usual convention.
Stellar Evolution
Low-mass stars (\(< 8M_\odot\), e.g. Sun): Main sequence → Red giant → Planetary nebula → White dwarf
High-mass stars (\(> 10M_\odot\)): Main sequence → Red supergiant → Supernova → Neutron star (\(M_{remnant} < 3M_\odot\)) or Black hole (\(M_{remnant} > 3M_\odot\))
Chandrasekhar limit: \(1.4M_\odot\) — upper mass limit for a white dwarf.
Common Mistakes
- ❌ Right side of H-R diagram = low temperature (cool, red stars)
- ❌ White dwarf: high \(T\), low \(L\) → very small radius. Red giant: low \(T\), high \(L\) → very large radius
- ❌ Main sequence stars fuse hydrogen, not helium
Topic 9: Astrophysics — Cosmic Distances and Hubble’s Law
Question types: Stellar parallax; Hubble’s law for recession speed or age of universe; Doppler redshift calculation.
Distance Ladder
| Method | Range | Key formula |
|---|---|---|
| Stellar parallax | \(< 1000\ \text{pc}\) (within galaxy) | \(d\text{(pc)} = 1/p\text{(arcsec)}\) |
| Standard candle (Cepheid / Type Ia supernova) | \(< 100\ \text{Mpc}\) | \(I = L / 4\pi d^2\) |
| Hubble’s law | Very distant galaxies | \(v = H_0 d\) |
Doppler Redshift
\[\frac{\Delta\lambda}{\lambda} \approx \frac{v}{c} \quad (v \ll c)\]
- Galaxy receding → wavelength increases (redshift)
- Galaxy approaching → wavelength decreases (blueshift)
Hubble’s Law
\[v = H_0 d \qquad H_0 \approx 70\ \text{km s}^{-1}\text{Mpc}^{-1}\]
Age of universe estimate: \(t \approx 1/H_0\) (convert \(H_0\) to s⁻¹ first)
Evidence for the Big Bang
Hubble redshift: All distant galaxies are receding → universe is expanding → implies a beginning
CMBR: Uniform 2.7 K microwave radiation from all directions → relic of the hot early universe
Common Mistakes
- ❌ Parallax angle must be in arcseconds, not degrees
- ❌ \(d\) must be in Mpc to match the units of \(H_0\)
- ❌ \(\Delta\lambda = \lambda_{observed} – \lambda_{rest}\) (positive for receding source)
- ❌ Convert \(H_0\) to s⁻¹ first: \(1\ \text{Mpc} = 3.09\times10^{22}\ \text{m}\)
Practice Questions
Q1. SHM: amplitude \(A = 0.1\ \text{m}\), \(\omega = 10\ \text{rad/s}\). Find maximum speed and maximum acceleration.
Answer
\(v_{max} = \omega A = 10 \times 0.1 = \mathbf{1.0\ \text{m/s}}\)
\(a_{max} = \omega^2 A = 100 \times 0.1 = \mathbf{10\ \text{m/s}^2}\)
Q2. Mass defect \(\Delta m = 0.00318\ \text{u}\). Find the energy released in MeV.
Answer
\(E = 0.00318 \times 931.5 = \mathbf{2.96\ \text{MeV}}\)
Q3. Initial activity \(A_0 = 800\ \text{Bq}\), half-life \(T_{1/2} = 2\ \text{h}\). Find the activity after \(6\ \text{h}\).
Answer
\(6/2 = 3\) half-lives:
\(A = 800 \times (1/2)^3 = \mathbf{100\ \text{Bq}}\)
Q4. A star has surface temperature \(T = 6000\ \text{K}\) and radius \(R = 8.0\times10^8\ \text{m}\). Find: (a) peak wavelength; (b) total luminosity.
Answer
(a) \(\lambda_{max} = \dfrac{2.898\times10^{-3}}{6000} = \mathbf{4.83\times10^{-7}\ \text{m}}\) (483 nm)
(b) \(L = 4\pi \times (8.0\times10^8)^2 \times 5.67\times10^{-8} \times (6000)^4 = \mathbf{5.9\times10^{26}\ \text{W}}\)
Q5. Hydrogen spectral line at rest: \(\lambda_0 = 656\ \text{nm}\); observed: \(\lambda = 669\ \text{nm}\). Find the recession speed and estimate the distance. (\(H_0 = 70\ \text{km s}^{-1}\text{Mpc}^{-1}\))
Answer
\(\Delta\lambda = 13\ \text{nm}\)
\(v = 3.0\times10^8 \times \dfrac{13}{656} = \mathbf{5.95\times10^6\ \text{m/s}}\)
\(d = 5950 \div 70 = \mathbf{85\ \text{Mpc}}\)
Want more? Visit flowxiom.com