23.2 Radioactive Decay | CIE A Level Physics Topic Questions 2025

1a

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]

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1b

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]

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1c

6 marks

The element neptunium has at least 24 isotopes. One of the isotopes is neptunium-231 $({}_{93}^{231}{Np})$ , which has a half-life of 49 minutes.

(i)

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

${}_{93}^{239}{Np}$ ${}_{94}^{231}{Np}$ ${}_{93}^{219}{Np}$ ${}_{90}^{231}{Np}$ ${}_{93}^{244}{Np}$

[3]

(ii)

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

$\frac{49}{0.693}$ $\frac{0.693}{49}$ $\frac{0.693}{49 \times 60}$ $\frac{49 \times 60}{0.693}$

[3]

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1d

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

${}_{. . .}^{. . .}{Np} \to {}_{. . .}^{. . .}{Pu} + . . . . . . . . . . . . . . . . . . . . .$

${}_{. . .}^{. . .}{Np} \to {}_{. . .}^{. . .}U + . . . . . . . . . . . . . . . . . . . . .$

${}_{. . .}^{. . .}{Np} \to {}_{. . .}^{. . .}{Pa} + . . . . . . . . . . . . . . . . . . . . .$

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1a

4 marks

The radioisotope uranium-238 $({}_{92}^{238}U)$ decays through a decay chain to the radioisotope lead-206 $({}_{82}^{206}{Pb})$ , which is stable.

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

Calculate the value of X.

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1b

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, $N_{P b}$ at any time is equal to the number of uranium-238 that have decayed.

The number of uranium-238 nuclei $N_{U}$ at time t is given by the equation:

$N_{U} = N_{0} e^{- λ t}$

where $N_{0}$ is the number of uranium-238 nuclei at t = 0.

Show that the ratio $\frac{N_{P b}}{N_{U}}$ is given by:

$\frac{N_{P b}}{N_{U}} = e^{λ t} - 1$

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1c

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 $\frac{9}{64}$ A₀.

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

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1a

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]

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1b

2 marks

Technetium-101 $({}_{43}^{101}{Tc})$ decays by beta-minus emission to form a stable isotope of Ruthenium $(Ru)$ .

Complete the equation for this decay.

${}_{43}^{101}{Tc} \to {}_{. . . . . .}^{. . . . . .}{Ru} + {}_{. . . . . .}^{. . . . . .}β$

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1c

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]

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1d

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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Radioactive Decay (CIE A Level Physics)

Topic Questions