Syllabus Edition

First teaching 2023

First exams 2025

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Radioactive Decay (CIE A Level Physics)

Exam Questions

1 hour6 questions
1a
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6 marks

Radioactive decay is often described as a spontaneous and random process.

State what is meant by

(i)
radioactive decay
[2]
(ii)
a spontaneous process
[2]
(iii)
a random process
[2]
1b
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2 marks

The graph in Fig. 1.1 shows the count rate of a radioactive substance measured by a Geiger-Müller tube.

7-1-q2d-question-sl-sq-easy-phy

Fig. 1.1

State the feature of Fig. 1.1 which provides evidence for 

 
(i)
the random nature of radioactive decay
[1]
(ii)
the spontaneous nature of radioactive decay 
[1]
1c
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6 marks

The element neptunium has at least 24 isotopes. One of the isotopes is neptunium-231 open parentheses Np presubscript 93 presuperscript 231 close parentheses, which has a half-life of 49 minutes.

(i)
State what is meant by isotopes and circle the possible isotopes of neptunium
 

Np presubscript 93 presuperscript 239     Np presubscript 94 presuperscript 231     Np presubscript 93 presuperscript 219     Np presubscript 90 presuperscript 231     Np presubscript 93 presuperscript 244

[3]

(ii)
Define half-life and circle the correct expression for calculating the probability per second of decay of a nucleus of neptunium-231.
 

fraction numerator 49 over denominator 0.693 end fraction      fraction numerator 0.693 over denominator 49 end fraction      fraction numerator 0.693 over denominator 49 cross times 60 end fraction      fraction numerator 49 cross times 60 over denominator 0.693 end fraction

[3]

1d
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3 marks

Fig. 1.2 shows a diagram in which nucleon number A is plotted against proton number Z.

The diagram shows the position of three isotopes of neptunium and their respective decay products.

23-2-1d-e--23-2-e-a-z-nucleon-proton-graph-cie-ial-sq

Fig. 1.2

Use Fig. 1.2 to complete the following nuclear decay equations

 

Np presubscript... end presubscript presuperscript... end presuperscript space rightwards arrow space Pu presubscript... end presubscript presuperscript... end presuperscript space plus space.....................

Np presubscript... end presubscript presuperscript... end presuperscript space rightwards arrow space straight U presubscript... end presubscript presuperscript... end presuperscript space plus space.....................

Np presubscript... end presubscript presuperscript... end presuperscript space rightwards arrow space Pa presubscript... end presubscript presuperscript... end presuperscript space plus space.....................

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2a
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2 marks

Define half−life.

2b
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5 marks

A student investigates the half−life of technetium with time. This list shows the variables in the experiment.

time      size of sample      distance from the detector to the sample

same material for the sample     activity of the sample

Using variables from the list, state

(i)
the independent variable
[1]
(ii)
the dependent variable
[1]
(iii)
the control variables for the experiment
[3]
2c
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4 marks

The experiment uses a variety of apparatus. 

Draw lines on Table 1.1 below to match the apparatus with its correct use.

 

Table 1.1
7-1-q5c-question-sl-sq-easy-phy

2d
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3 marks

Fig. 1.1 shows the graph that the student obtains from their results.

7-1-q5d-question-sl-sq-easy-phy

Fig. 1.1

Using Fig. 1.1, determine the half−life of the sample.

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3a
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3 marks

An isotope of polonium-213 (Po presubscript 84 presuperscript 213) first decays into an isotope of lead-209 (Pb presubscript 82 presuperscript 209) and then decays into the stable isotope of bismuth (Bi).

Fig. 1.1 shows two arrows on a neutron number N against proton number Z chart to illustrate these two decays.

23-2-3a-e-23-2-e-a-z-neutron-proton-number-graph-cie-ial-sq

Fig. 1.1

Use Fig. 1.1 to complete the nuclear decay equations for

(i)
the polonium isotope

Po presubscript 84 presuperscript 213 space rightwards arrow space Pb presubscript 82 presuperscript 209 space plus space.....................


[1]
 
(ii)
the lead isotope

Pb presubscript 82 presuperscript 209 space rightwards arrow space Bi presubscript 83 presuperscript..... end presuperscript space plus space straight e presubscript negative 1 end presubscript presuperscript 0 space plus space.....................

 [2]

3b
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5 marks

A pure sample of polonium-213 is produced in a research laboratory.

The half-life of Po presubscript 84 presuperscript 213 is very small compared with the half-life of Pb presubscript 82 presuperscript 209. After a very short time, the ionising radiation detected from the sample is mainly from the beta-minus decay of the lead-209 nuclei.

The half-life of Pb presubscript 82 presuperscript 209 is 3.3 hours.

(i)
State what is meant by the decay constant of a radioactive isotope.
[2]
(ii)
Calculate the decay constant, in s−1, of lead-209.
[3]

3c
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2 marks

The activity of the sample of Pb presubscript 82 presuperscript 209 after 7.0 hours is 12 kBq.

Calculate the initial activity of the sample of polonium-213.

3d
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3 marks
(i)
State the relation between the activity A of a sample of a radioactive isotope containing N atoms and the decay constant λ of the isotope.
[1]
(ii)
Determine the number of lead-209 nuclei in the sample initially.
[2]

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1a
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4 marks

A student sets up a radioactive source and a Geiger counter to investigate how the count rate of the source varies with time.

State and explain how the student could demonstrate

 
(i)
the spontaneous nature of radioactive decay,
[2]
(i)
the random nature of radioactive decay.
[2]
1b
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2 marks

Technetium-101 open parentheses Tc presubscript 43 presuperscript 101 close parentheses decays by beta-minus emission to form a stable isotope of Ruthenium open parentheses Ru close parentheses.

Complete the equation for this decay.

 

Tc presubscript 43 presuperscript 101 space rightwards arrow space Ru presubscript...... end presubscript presuperscript...... end presuperscript space plus space straight beta presubscript...... end presubscript presuperscript...... end presuperscript

1c
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8 marks

The variation with time t of the number N of technetium-101 nuclei in a sample of radioactive material is shown in Fig. 1.1.

23-2-1c-m-23-2-technetium-decay-curve-cie-ial-sq

Fig. 1.1

(i)
Use Fig. 1.1 to determine the activity, in Bq, of the sample of technetium-101 at time t = 14.0 minutes.
[4]
 
(ii)
Use your answer in (c)(i) to calculate the decay constant λ of technetium-101.
[2]
 
(iii)
On Fig. 1.1, sketch a line to show the variation with t of the number of ruthenium nuclei in the sample.
[2]
1d
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4 marks

Each decay releases a beta particle with energy 487 keV. 

(i)
Calculate, in J, the total amount of energy given to beta particles that are emitted between time t = 10 min and time t = 30 min.
[3]
(ii)
Suggest why the total amount of energy released by the decay process between time t = 10 min and time t = 30 min is actually greater than your answer in (d)(i).
[1]

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2a
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2 marks

A source of water is found to be contaminated with the radioactive isotope radium-228 open parentheses Ra presubscript 88 presuperscript 228 close parentheses.

This isotope of radium has a half-life of 5.75 years.

Explain the meaning of half-life in this context.

2b
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2 marks

Calculate the decay constant, in s–1, of radium-228.

2c
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4 marks

A sample is taken of the contaminated water. The activity of radium-228 in a sample of 1.0 kg of water is found to be 20 mBq.

The mass of water in 1.0 mol is 18 g.

Calculate

(i)
the number of radium-228 atoms in 1.0 kg of the contaminated water
[2]
(ii)
the ratio 

fraction numerator number space of space molecules space of space water space in space 1.0 space kg space of space water over denominator number space of space Ra presuperscript 228 space atoms space in space 1.0 space kg space of space water end fraction

[2]

2d
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3 marks

The maximum safe limit for the activity of radium-228 in water has been set as 18.5 mBq kg−1. 

Calculate the time, in days, for the activity of the contaminated water to be reduced to the safe limit.

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3a
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2 marks

State what is meant by radioactive decay.

3b
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4 marks

A radioactive sample consists of an isotope with a half-life T that decays to form a stable product. Only the isotope and the stable product are present in the sample. 

At time t = 0, the sample has an activity of A0 and contains N0 nuclei of the isotope. 

(i)
On Fig. 1.1, sketch the variation with t of the number N of nuclei of the isotope present in the sample from time t = 0 to time t = 3T.
[3]

23-2-3b-m-23-2-number-of-nuclei-time-graph-blank-cie-ial-sq

Fig. 1.1

(ii)
State the name of the quantity represented by the gradient of the graph in Fig. 1.1.
[1]
3c
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3 marks
(i)
On Fig. 1.2, sketch the variation with N of the activity A of the sample for values of N between N = 0 and N = N0.
[2]

23-2-3c-m-23-2-activity-number-of-nuclei-graph-blank-cie-ial-sq

Fig. 1.2

(ii)
State the name of the quantity represented by the gradient in Fig. 1.2.
[1]
3d
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2 marks

Calculate the fraction of undecayed nuclei N remaining relative to N0 at time t = 1.25T.

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1a
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4 marks

The radioisotope uranium-238 open parentheses straight U presubscript 92 presuperscript 238 close parentheses decays through a decay chain to the radioisotope lead-206 open parentheses Pb presubscript 82 presuperscript 206 close parentheses, which is stable. 

During the decay chain, 8 alpha particles are emitted, and X beta particles are emitted. 

Calculate the value of X.

1b
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4 marks

The half-life of uranium-238 is so long in comparison to any of the isotopes in its decay chain that we can assume the number of lead-206 nuclei, N subscript P b end subscript at any time is equal to the number of uranium-238 that have decayed. 

            The number of uranium-238 nuclei begin mathsize 16px style N subscript U end style at time t is given by the equation: 

                  N subscript U equals N subscript 0 e to the power of negative lambda t end exponent 

            where begin mathsize 16px style N subscript 0 end style is the number of uranium-238 nuclei at t = 0. 

Show that the ratio N subscript P b end subscript over N subscript U is given by: 

                  N subscript P b end subscript over N subscript U equals e to the power of lambda t end exponent minus 1

1c
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3 marks

Enriched uranium fuel is a mixture of the fissionable uranium-235 with the more naturally abundant uranium-238. Mixtures of radioactive nuclides such as this are very common in the nuclear power industry.  

Two samples of radioactive nuclides X and Y each have an activity of A0 at t = 0. They are subsequently mixed together. 

Show that the total activity of the mixture at time t = 48 years is equal to 9 over 64A0.  

The half-life of X and Y are 16 and 8 years respectively.

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2a
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2 marks

Rubidium (Rb) was found in samples of moon rock which were retrieved from the Apollo missions. The isotope R presubscript 37 presuperscript 87 b is known to have a half-life of 4.90 × 1010years.

One of the moon rock samples contains 1.2 mg of R presubscript 37 presuperscript 87 b. 

Show that the mass of R presubscript 37 presuperscript 87 b that the rock sample contained when the moon was formed 4.47 ×109 years ago was about 1.3 mg.

2b
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3 marks

Calculate the activity of 1.2 mg of R presubscript 37 presuperscript 87 b.

2c
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4 marks

Radioactive carbon dating is a method for determining the age of samples containing organic material. This is a commonly used method for terrestrial objects. 

Pieces of ancient wood found in a fireplace at an archaeological site can be dated by measuring the activity of carbon-14. A sample contains one carbon-14 atom per 8.0 × 1010 carbon-12 atoms. In living wood, the concentration of carbon-14 atoms is greater at one carbon-14 atom per 3.0 × 1010 carbon-12 atoms.

The half-life of carbon-14 is 1.8 × 1011 s. 

Explain why the concentration of carbon-14 is greater in living wood and calculate the age, in years, of the sample taken from the archaeological site.

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