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Topic E.3 · SL and HL

Radioactive Decay: notes and practice questions

9 min read Jump to 15 practice questions
Summary
  • This topic introduces the fundamental concepts of radioactive decay, nuclear stability, and energy transformations in nuclear reactions.
  • Isotopes are atoms of the same element with different numbers of neutrons.
  • Nuclear binding energy and mass defect relate to the stability of a nucleus.
  • Mass-energy equivalence is given by E=mc2E = mc^2.
  • The strong nuclear force is a short-range attractive force between nucleons.
  • Radioactive decay is random and spontaneous, involving alpha, beta, and gamma emissions.
  • Decay equations involve α\alpha, β−\beta^-, β+\beta^+, γ\gamma particles, and neutrinos/antineutrinos.
  • Alpha, beta, and gamma radiations have different penetration and ionizing abilities.
  • Activity, count rate, and half-life describe radioactive decay.
  • Activity changes over integer half-lives.
  • Background radiation affects count rate measurements.

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
At HL
  • the evidence for the strong nuclear force
  • the role of the ratio of neutrons to protons for the stability of nuclides
  • the approximate constancy of the binding energy curve above a nucleon number of 60
  • that the spectrum of alpha and gamma radiations provides evidence for discrete nuclear energy levels

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

15 questions · 2 easy · 12 medium · 1 hard
Showing 15 of 15

Question 1

EasyPaper 1A · calculator1 mark

Three statements about alpha particles are:

I. They have a greater mass than beta-minus particles.

II. They have a shorter range in air than beta-minus particles.

III. They are deflected in the opposite direction to beta-minus particles in a uniform magnetic field.

Which statements are correct?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

Question 2

MediumPaper 1A · calculator1 mark

A nucleus of nuclide Q undergoes a series of radioactive decays.

Which series of emissions will produce an isotone of Q?

A. One α\alpha and one β−\beta^-

B. One α\alpha and two β−\beta^-

C. One α\alpha and one β+\beta^+

D. One α\alpha and two β+\beta^+

Question 3

HardPaper 2 · calculator9 marks
(a)(i)

A stationary isotope of 92238_{92}^{238}U (Uranium) undergoes alpha decay, transforming into a new element, Thorium (Th), and an alpha particle.

(a)(i) Identify the proton number of the Thorium nucleus.

[1]
(a)(ii)

(a)(ii) The following data are available:

Atomic mass of 238^{238}U =238.050788= 238.050788 u

Atomic mass of 234^{234}Th =234.043601= 234.043601 u

Mass of α=4.002603\alpha = 4.002603 u

Show that the energy released in this decay is approximately 4.34.3 MeV.

[2]
(a)(iii)

(a)(iii) The following data are available:

Atomic mass of 238^{238}U =238.050788= 238.050788 u

Atomic mass of 234^{234}Th =234.043601= 234.043601 u

Mass of α=4.002603\alpha = 4.002603 u

Calculate the percentage of the total energy released that is carried by the alpha particle.

[2]
(b)(i)

In a historical experiment, a beam of alpha particles was directed at a thin gold foil to probe the structure of the atom.

(b)(i) Describe two key observations from this experiment.

[2]
(b)(ii)

(b)(ii) Outline how these observations led to the nuclear model of the atom.

[2]

Question 4

EasyPaper 1A · calculator1 mark

The radioactive isotope carbon-14 (614C^{14}_6\text{C}) undergoes beta-minus decay to a new nuclide Y according to the following equation:

614C→Y+β−+vˉe^{14}_6\text{C} \rightarrow \text{Y} + \beta^- + \bar{v}_e

What are the proton number and the nucleon number of nuclide Y?

Proton number of YNucleon number of Y
A.514
B.714
C.613
D.715

Question 5

MediumPaper 1A · calculator1 mark

Three statements about alpha radiation are:

I. It is more ionizing than beta radiation.

II. It has a shorter range in air than gamma radiation.

III. It has a continuous energy spectrum.

Which statements are correct?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

Question 6

MediumPaper 1A · calculator1 mark

A laboratory technician is monitoring a sample of Cobalt-60, which decays with a half-life of 66 hours. Initially, a Geiger counter measures a total count rate of 640640 counts per minute from the sample and its surroundings. The measured background count rate in the laboratory is 4040 counts per minute.

What is the measured count rate after 1818 hours?

A. 7575 counts per minute

B. 100100 counts per minute

C. 115115 counts per minute

D. 190190 counts per minute

Question 7

MediumPaper 1A · calculator1 mark

Plutonium-240 (94240Pu^{240}_{94}\text{Pu}) is an unstable nuclide. It undergoes alpha decay followed by a beta minus (β−\beta^-) decay.

What is the number of protons and neutrons in the final nuclide?

OptionNumber of protonsNumber of neutrons
A91145
B93144
C93143
D92144

A. 9191, 145145

B. 9393, 144144

C. 9393, 143143

D. 9292, 144144

Question 8

MediumPaper 1A · calculator1 mark

A sample of a radioactive isotope, Technetium-99m, is used in medical imaging. It has a half-life of 2.02.0 days. Initially, a detector measures a count rate of 660660 counts per second from the sample. The measured background count rate in the laboratory is 3030 counts per second.

What is the measured count rate from the sample after 6.06.0 days?

A. 7979 counts per second

B. 109109 counts per second

C. 113113 counts per second

D. 188188 counts per second

Question 9

MediumPaper 1A · calculator1 mark

A laboratory is monitoring the decay of a radioactive tracer used in a medical study. The table shows how the count rate from a sample of this nuclide varies with time tt.

The nuclide has a half-life of 2020 minutes. The average background count rate is constant.

Time t / minCount rate / Bq085020450\begin{array}{|c|c|} \hline \textbf{Time } t \text{ / min} & \textbf{Count rate / Bq} \\ \hline 0 & 850 \\ 20 & 450 \\ \hline \end{array}

What count rate will the detector measure when t=60t = 60 minutes?

A. 50 Bq50\text{ Bq}

B. 100 Bq100\text{ Bq}

C. 150 Bq150\text{ Bq}

D. 250 Bq250\text{ Bq}

Question 10

MediumPaper 1A · calculator1 mark

A reactor uses plutonium-239 (94239Pu^{239}_{94}\text{Pu}) as fuel. When a nucleus of plutonium-239 absorbs a neutron, it undergoes fission, producing barium-144 (56144Ba^{144}_{56}\text{Ba}) and strontium-94 (3894Sr^{94}_{38}\text{Sr}) as fission products.

How many neutrons are released in this reaction?

A. 11

B. 22

C. 33

D. 44

Question 11

MediumPaper 1A · calculator1 mark

A student monitors the count rate from a sample of a radioactive isotope in a laboratory. The isotope has a half-life of 40 s40\text{ s}. The table shows how the total count rate measured by the detector varies with time tt.

Time tt / sTotal Count Rate / s−1\text{s}^{-1}
0652
40332
80172
12092
16052
20032
24022
28017
32014.5
36013.25

What is the background count rate?

A. 0 s−10\text{ s}^{-1}

B. 6 s−16\text{ s}^{-1}

C. 12 s−112\text{ s}^{-1}

D. 22 s−122\text{ s}^{-1}

Question 12

MediumPaper 1A · calculator1 mark

Two radioactive nuclides P and Q are prepared, so they initially contain the same number of atoms. The half-life of P is TT and the half-life of Q is 2T2T.

What is the ratio activity of Pactivity of Q\frac{\text{activity of P}}{\text{activity of Q}} after a time of 2T2T has elapsed?

A. 12\frac{1}{2}

B. 11

C. 22

D. 44

Question 13

MediumPaper 1B · calculator7 marks
(a)

A student investigates the cooling of a hot liquid. A cup containing hot water is placed in a room where the ambient temperature is constant. The temperature TT of the water is measured at regular time intervals tt.

The data collected is shown in the table below:

Time tt / minTemperature TT / °C
095.0
284.5
475.6
668.0
861.3
1055.5
1250.4
1446.0
1642.2

It is observed that the rate of cooling decreases as the temperature of the water approaches the ambient temperature. The student suggests that the cooling process can be modelled by an exponential decay, similar to radioactive decay, where the temperature difference ΔT=T−Ta\Delta T = T - T_a (where TaT_a is the ambient temperature) decreases exponentially with time.

(a) The ambient temperature in the room is 20.020.0 °C. Estimate the half-cooling time of the water, which is the time taken for the temperature difference ΔT\Delta T to halve.

[2]
(b)

(b) Show that the cooling process follows an exponential decay model by calculating the decay constant kk from two different time intervals and comparing the values. State your chosen time intervals clearly.

The relationship for exponential decay is given by ΔT(t)=ΔT0e−kt\Delta T(t) = \Delta T_0 e^{-kt}, where ΔT0\Delta T_0 is the initial temperature difference.

[3]
(c)

(c) The student wants to stop the experiment when the temperature of the water has dropped to 30.030.0 °C. Predict the time at which the student will stop the experiment.

[2]

Question 14

MediumPaper 1A · calculator1 mark

The measured count rate from a radioactive sample is initially 132 Bq132\text{ Bq}. After two half-lives have elapsed, the measured count rate is 42 Bq42\text{ Bq}. What is the background count rate?

A. 12 Bq12\text{ Bq}

B. 30 Bq30\text{ Bq}

C. 42 Bq42\text{ Bq}

D. 90 Bq90\text{ Bq}

Question 15

MediumPaper 1A · calculator1 mark

A heavy nucleus P with total binding energy BPB_\text{P} undergoes nuclear fission into two lighter nuclei, Q and R, with total binding energies BQB_\text{Q} and BRB_\text{R} respectively. The reaction releases energy. What is the correct relation between these binding energies?

A. BP=BQ+BRB_\text{P} = B_\text{Q} + B_\text{R}

B. BP>BQ+BRB_\text{P} > B_\text{Q} + B_\text{R}

C. BP<BQ+BRB_\text{P} < B_\text{Q} + B_\text{R}

D. BQ<BP<BRB_\text{Q} < B_\text{P} < B_\text{R}

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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 introduces the fundamental concepts of radioactive decay, nuclear stability, and energy transformations in nuclear reactions. Isotopes are atoms of the same element with different numbers of neutrons. Nuclear binding energy and mass defect relate to the stability of a nucleus.

Is Radioactive Decay SL or HL?

Both. SL and HL students study Radioactive Decay, and HL goes further: the evidence for the strong nuclear force.

How do I revise Radioactive Decay for IB Physics?

Start from the core idea: this topic introduces the fundamental concepts of radioactive decay, nuclear stability, and energy transformations in nuclear reactions. 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 15 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.

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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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