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A LevelPhysicsCIEExam Questions23. Nuclear Physics23.2 Radioactive Decay

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First teaching 2020

Last exams 2024

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Radioactive Decay (CIE A Level Physics)

Exam Questions

1 hour6 questions
Easy
Medium
1a
Sme Calculator6 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]

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1b
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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]

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1c
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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]

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1d
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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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Define half−life.

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2b
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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]

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2c
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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

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2d
Sme Calculator3 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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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]

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3b
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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]

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3c
Sme Calculator2 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.

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3d
Sme Calculator3 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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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]

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1b
Sme Calculator2 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

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1c
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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]

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1d
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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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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.

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2b
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Calculate the decay constant, in s–1, of radium-228.

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2c
Sme Calculator4 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]

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2d
Sme Calculator3 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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State what is meant by radioactive decay.

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3b
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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]

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3c
Sme Calculator3 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]

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3d
Sme Calculator2 marks

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

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