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Topic E.3 · HL only

Radioactive Decay: notes and practice questions

2 min read Jump to 3 practice questions
Summary
  • This topic covers the higher level aspects of radioactive decay, including evidence for nuclear forces and the quantitative description of decay.
  • Evidence for the strong nuclear force and the role of the neutron-to-proton ratio for nuclide stability.
  • The binding energy curve is approximately constant above a nucleon number of 60.
  • Alpha and gamma spectra provide evidence for discrete nuclear energy levels; beta decay's continuous spectrum evidences the neutrino.
  • The radioactive decay law is N=N0e−λtN = N_0e^{-\lambda t}, where λ\lambda is the decay constant.
  • Activity A=λN=λN0e−λtA = \lambda N = \lambda N_0e^{-\lambda t}.
  • Half-life T12=ln⁡2λT_{\frac{1}{2}} = \frac{\ln 2}{\lambda}.

How it is examined

Both papers, with the exponential law HL only. May 2025 HL Paper 2 TZ1 question 3(b) did the HL version cleanly: calculate the decay constant in s⁻¹ from a half-life of 2.69 days (1 mark), then determine the mass of the daughter present after one week (2 marks). The mark scheme accepted either the exponential form or the (12)t/T1/2\left(\tfrac{1}{2}\right)^{t/T_{1/2}} form and said the unit was not required, but warned examiners that if a unit is given the power of ten and the prefix must match. Part (c) then asked for a 2-mark explain that discrete gamma energies evidence discrete nuclear energy levels, with an instruction not to award the mark if the answer discussed electron transitions.

Given in the booklet

SL: E=mc2E = mc^2, the unified atomic mass unit and its energy equivalent, the electron and nucleon masses. HL adds N=N0e−λtN = N_0 e^{-\lambda t}, A=λN=λN0e−λtA = \lambda N = \lambda N_0 e^{-\lambda t} and T1/2=ln⁡2/λT_{1/2} = \ln 2/\lambda. The SL/HL split here is exactly the split between whole-number half-lives and the exponential law. An SL question may say "after three half-lives"; it may not say "after 7 days" and expect an exponential.

Key ideas
  • isotopes
  • nuclear binding energy and mass defect
  • the variation of the binding energy per nucleon with nucleon number
  • mass-energy equivalence as given by E=mc2E = mc^2 in nuclear reactions

Guiding questions

  • Why are some isotopes more stable than others?
  • In what ways can a nucleus undergo change?
  • How do large, unstable nuclei become more stable?
  • How can the random nature of radioactive decay allow for predictions to be made?

Linking questions

  • Are there differences between the photons emitted as a result of atomic versus nuclear transitions?
  • How does equilibrium within a star compare to stability within the nucleus of an atom?
  • Would a nucleus be able to exist if only gravitational and electric forces were considered?
  • How did conservation lead to experimental evidence of the neutrino? (NOS)
  • Which areas of physics involve exponential change? (NOS)

Practice questions

3 questions · 1 easy · 2 medium
Showing 3 of 3

Question 1

EasyPaper 1A · calculator1 mark

A radioactive sample has an initial activity A0A_0 and a half-life TT. Which expression gives the initial number of undecayed nuclei in the sample?

A. A0Tln⁡2\frac{A_0 T}{\ln 2}

B. A0ln⁡2T\frac{A_0 \ln 2}{T}

C. TA0ln⁡2\frac{T}{A_0 \ln 2}

D. ln⁡2A0T\frac{\ln 2}{A_0 T}

Question 2

MediumPaper 2 · calculator7 marks
(a)

This question is about radioactive decay.

Carbon-1414 is a radioactive isotope used in radiocarbon dating. Its half-life is 5.73×1035.73 \times 10^3 years.

(a) Calculate the decay constant of carbon-1414 in s−1^{-1}.

[2]
(b)(i)

(b) A different radioactive isotope, used in medical imaging, has a decay constant of 1.2×10−51.2 \times 10^{-5} s−1^{-1}.

(i) Calculate the half-life of this isotope.

[2]
(b)(ii)

(ii) Calculate the percentage of this isotope that remains after 22 days.

[3]

Question 3

MediumPaper 1A · calculator1 mark

A laboratory technician prepares a pure sample of 2.5 g2.5\text{ g} of Cobalt-60 (60Co^{60}\text{Co}) for a medical application. The measured activity of this sample is 1.8×1015 Bq1.8 \times 10^{15}\text{ Bq}.

What is the decay constant of Cobalt-60?

(The molar mass of Cobalt-60 is approximately 60.0 g mol−160.0\text{ g mol}^{-1}. Avogadro's constant is 6.022×1023 mol−16.022 \times 10^{23}\text{ mol}^{-1}.)

A. 7.17×10−9 s−17.17 \times 10^{-9}\text{ s}^{-1}

B. 7.17×10−8 s−17.17 \times 10^{-8}\text{ s}^{-1}

C. 7.17×10−7 s−17.17 \times 10^{-7}\text{ s}^{-1}

D. 1.20×10−6 s−11.20 \times 10^{-6}\text{ s}^{-1}

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Where marks are lost

  • Stopping one step short of the conclusion. Two numbers and no sentence is two marks out of three.
  • Answering a procedure question with a platitude.
  • Losing precision in Paper 1B. Uniquely to this paper, quoting the right number badly loses marks.
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What does Radioactive Decay cover in IB Physics?

This topic covers the higher level aspects of radioactive decay, including evidence for nuclear forces and the quantitative description of decay. Evidence for the strong nuclear force and the role of the neutron-to-proton ratio for nuclide stability. The binding energy curve is approximately constant above a nucleon number of 60.

Is Radioactive Decay SL or HL?

Radioactive Decay is HL only. SL students are not examined on it.

How do I revise Radioactive Decay for IB Physics?

Start from the core idea: this topic covers the higher level aspects of radioactive decay, including evidence for nuclear forces and the quantitative description of decay. In the exam: both papers, with the exponential law HL only. May 2025 HL Paper 2 TZ1 question 3(b) did the HL version cleanly: calculate the decay constant in s⁻¹ from a half-life of 2.69 days (1 mark), then determine the mass of the daughter present after one week (2 marks). Then practise exam-style questions, easiest first, writing out every step of your working before you check it.

How does FourtyFive help me practise Radioactive Decay?

FourtyFive has 3 Radioactive Decay questions. Every answer you write is marked mark by mark, IB-style, and you see where each mark was won or lost. Every part has a hint, the AI tutor helps you through the step you are stuck on, and your Study Profile picks what to practise next.

Is FourtyFive free for Radioactive Decay practice?

Yes. A free account gives you 50 marked answers a month, and you do not need a card to sign up.

Can I handwrite Radioactive Decay answers on an iPad?

Yes. In the FourtyFive iPad app you write your working by hand with Apple Pencil, the way you would on paper, and it is marked the same way.

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