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A-Level The nuclear atom, radioactive decay, nuclear reactions and conservation laws, and binding energy
What the A-Level syllabus expects for The nuclear atom, radioactive decay, nuclear reactions and conservation laws, and binding energy, and how to practise it.
What the syllabus expects
- Draw from Rutherford's α-particle scattering results the conclusion that a tiny nucleus sits at the atom's centre
- Separate nucleon number, the mass number, from proton number, the atomic number
- Understand that a single element comes in several isotopes, differing by neutron count, and write nuclides using the AZX notation
- Understand that nuclear decay happens spontaneously and at random
- Read the randomness of decay off the jitter seen in a measured count rate
- Understand where background radiation originates and why it matters
- Understand what α, β and γ radiations are and how each behaves
Scope: positron emission is not required - Give definitions for the pair of quantities activity and decay constant, then solve problems with A = λN
- Recognise and sketch the exponential fall-off of decay, and apply x = x0 e^(−λt) in problems
Scope: x may stand for activity, the number of undecayed nuclei, or the detected count rate - Define half-life as the interval over which a quantity x drops to one half of where it began, and use it
- Apply the relation t½ = ln2/λ in problems
- Discuss in words the uses and dangers of radioactivity, drawing on the half-life of the materials involved
Scope: medical and industrial uses are examples - Discuss in words the uses and dangers of radioactivity, drawing on how far the emissions penetrate and how strongly they ionise
- Write basic nuclear reactions as balanced nuclear equations
Scope: for example ¹⁴₇N + ⁴₂He → ¹⁷₈O + ¹₁H - State, and use in problem solving, that every nuclear process keeps nucleon number, charge and mass-energy fixed
- Understand how conserving energy and momentum in β decay led physicists to predict the (anti)neutrino
Scope: detail on the antineutrino and the wider particle zoo is not required - Understand what is meant by mass defect
- Apply the mass-energy equivalence E = mc2 in problems
- Understand nuclear binding energy and how it ties back to mass defect
- Draw how binding energy per nucleon changes across nucleon number
- Explain why binding energy per nucleon matters for both nuclear fusion and nuclear fission
How it's examined
Questions on this topic most often ask you to find. About 7% of the past-paper style questions in Rae's bank for this subject sit in this topic.
Worked examples
Example 1 (3 marks)
A 2.2e-11 kg sample of Nitrogen-13 is collected. Using lambda_eff = 6.9e-2 per min, find the number of Nitrogen-13 nuclei left after 15 minutes. (One N-13 atom has mass about 13 x 1.66e-27 kg.)
Show the worked answer
Step 1 - find how many Nitrogen-13 nuclei you start with. Divide the mass of the whole sample by the mass of one atom. Mass of one N-13 atom = 13 × 1.66e-27 kg = 2.16e-26 kg N0 = mass of sample / mass of one atom N0 = 2.2e-11 / 2.16e-26 N0 = 1.0e15 nuclei Step 2 - apply the exponential decay law. The number left after time t is N = N0 e^(-lambda t) Check the units before substituting: lambda_eff is per minute and t is in minutes, so they are already consistent and no conversion to seconds is needed. lambda t = 6.9e-2 × 15 = 1.035 Step 3 - substitute. N = 1.0e15 × e^(-1.035) e^(-1.035) = 0.355 N = 3.6e14 nuclei So roughly a third of the sample is still Nitrogen-13 after 15 minutes.
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