Nuclear Physics
Nuclear physics is an A-level Physics option topic covering radioactive decay, half-life, activity, mass-energy equivalence and binding energy per nucleon, explaining why both fission and fusion release energy. It builds directly on the particle and nuclide-notation ideas met earlier in the course.
Before you start
Make sure you're comfortable with these topics first:
Method
- Use nuclide notation to write and balance nuclear equations for alpha, beta-minus and gamma decay, checking that both nucleon number and proton number balance.
- Use A = lambda x N and A = A0 x exp(-lambda x t), with lambda = ln2 / half-life, to calculate activity, decay constant or the number of undecayed nuclei remaining after a given time.
- For a GM tube experiment, always subtract the background count rate from every raw reading before drawing conclusions about the source or absorbers used.
- Calculate mass defect (the difference between the total mass of separate nucleons and the mass of the nucleus) and convert it to binding energy using E = m x c^2, then divide by nucleon number for binding energy per nucleon.
- Use the shape of the binding energy per nucleon against nucleon number graph (rising steeply for light nuclei, peaking near iron, falling slowly for heavy nuclei) to explain why fission of heavy nuclei and fusion of light nuclei both release energy.
- For an inverse-square law practical (count rate against distance), plot ln(count rate) against ln(distance): a gradient of -2 supports count rate being proportional to 1/(distance^2).
Worked example
A sample of iodine-131 has a half-life of 8.0 days and an initial activity of 4.8 x 10^10 Bq. Calculate the activity of the sample after 24 days.
- Calculate the decay constant: lambda = ln2 / half-life = ln2 / 8.0 = 0.0866 per day.
- Write down A = A0 x exp(-lambda x t).
- Substitute the values: A = 4.8 x 10^10 x exp(-0.0866 x 24).
- Evaluate the exponent: -0.0866 x 24 = -2.08.
- Evaluate the exponential term: exp(-2.08) = 0.125.
- Final answer: A = 4.8 x 10^10 x 0.125 = 6.0 x 10^9 Bq.
Practice questions
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Q1State what is meant by the half-life of a radioactive isotope.Show answer
Answer: The time taken for the activity (or number of undecayed nuclei) of a sample to halve.
Q2A GM tube records 620 counts per minute from a source, with a background count rate of 20 counts per minute. Calculate the corrected count rate.Show answer
Answer: 600 counts per minute (620 - 20)
Q3Calculate the decay constant of a radioactive isotope with a half-life of 12 days.Show answer
Answer: 0.0578 per day (lambda = ln2/12 = 0.6931/12)
Q4A sample contains 2.0 x 10^18 undecayed nuclei of an isotope with decay constant 5.0 x 10^-4 per second. Calculate the activity of the sample.Show answer
Answer: 1.0 x 10^15 Bq (A = lambda x N = 5.0 x 10^-4 x 2.0 x 10^18)
Q5The mass defect of a nucleus is 0.0200 u, where 1 u is equivalent to 931.5 MeV. Calculate the binding energy of the nucleus in MeV.Show answer
Answer: 18.6 MeV (E = 0.0200 x 931.5)
Q6A radioactive source has an initial activity of 8.0 x 10^6 Bq and a half-life of 5.0 hours. Calculate the activity after 15 hours.Show answer
Answer: 1.0 x 10^6 Bq (15 hours = 3 half-lives, so activity is multiplied by (1/2)^3 = 1/8: 8.0 x 10^6/8)
Exam-style questions
Written in the style of a A Level Science exam paper, with a full mark scheme.
State the number of protons and neutrons in a nucleus of uranium-235.
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A radioactive isotope has a decay constant of 2.5 x 10^-6 per second. Calculate its half-life, in hours.
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Explain, using ideas about binding energy per nucleon, why energy is released both when a very heavy nucleus such as uranium-235 undergoes fission, and when very light nuclei such as isotopes of hydrogen undergo fusion.
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See real A Level Science past-paper questions, with official mark schemes →
Free printable worksheet
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