Nuclear physics: decay, reactions and binding
Key idea: Separate random single-nucleus behaviour from population laws, conserve every required quantity in reactions, and explain released energy through increased binding rather than disappearing mass.
Before you start: Quantum Physics objective chainMeasurement objective chain
By the end, you can
- Interpret nuclear structure, nuclides, random decay and radiation measurements.
- Evaluate radioisotope applications and hazards from physical properties.
- Balance nuclear reactions and use conservation to explain antineutrino evidence.
- Connect mass defect, binding energy and the binding-energy curve to fusion and fission.
Starting-point self-check
1. Check your starting point
Attempt all six groups without notes and mark the first structure, decay, risk, conservation, binding or curve decision you cannot justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Random decay, radiation, activity and half-life 20(d)–(k)
Question 1
A source has A = 800 Bq and λ = 2.0 × 10⁻³ s⁻¹. Find N and t½.
Check the model response
N = A/λ = 4.0 × 10⁵ nuclei and t½ = ln2/λ = 347 s.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Random decay, radiation, activity and half-life 20(d)–(k)
Check this idea
Misconception: Half-life predicts when one nucleus decays.
Repair: It describes a population; individual decay is random.
Check this idea
Misconception: Measured count rate is automatically source activity.
Repair: Subtract background and account for detection efficiency before inference.
worked example
3. Follow six worked models
Follow how each solution uses evidence, corrected data, risk criteria, conservation or the binding-energy curve.
Random decay, radiation, activity and half-life 20(d)–(k)
Model 1
Net activity falls from 960 to 240 Bq in 12 min. Find half-life and λ.
Check the model response
Two halvings occur, so t½ = 6 min = 360 s and λ = ln2/360 = 1.93 × 10⁻³ s⁻¹.
guided practice
4. Guided practice
Use each hint only to select the correct nuclear number, population relation, radiation property or energy comparison.
Random decay, radiation, activity and half-life 20(d)–(k)
Question 1
Three half-lives pass. State the remaining fraction.
Hint: Apply one factor 1/2 per half-life.
Check the model response
1/8.
independent practice
5. Independent practice
Solve without repair notes and state background, conservation, exposure and curve assumptions.
Random decay, radiation, activity and half-life 20(d)–(k)
Question 1
Explain randomness, count fluctuations, background, radiation properties and the equations A = λN and x = x₀e⁻λt.
Check the model response
Individual decay time is unpredictable but population probability is constant. Counts fluctuate statistically and include environmental background. Alpha, beta and gamma differ in nature, ionisation and penetration. λ links activity to undecayed nuclei; exponential decay gives t½ = ln2/λ.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Random decay, radiation, activity and half-life 20(d)–(k)
Question 1
A net count rate is 640 s⁻¹ initially and 80 s⁻¹ after 15 min. Find t½.
Check the model response
The factor 8 is three half-lives, so t½ = 5 min.
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Random decay, radiation, activity and half-life 20(d)–(k)
Question 1
State the expected graph of ln A against t.
Check the model response
A straight line of gradient −λ and intercept ln A₀.