RadioactivityAQA A-Level Physics: Topic test

20 questions, 54 marks

AQA A-Level Physics

Radioactivity topic test

Total 54 marks

Name

Class

Date

1
The radius R of a nucleus of nucleon number A is given by R = R₀A^(1/3), where R₀ = 1.2 fm (1 fm = 10⁻¹⁵ m). Take the mass of a nucleon to be 1.67×10⁻²⁷ kg.
(a)
What is the radius of a nucleus of nucleon number 64?
[1 mark]
A77 fm
B4.8 fm
C9.6 fm
D19 fm
(b)
What does the relationship R = R₀A^(1/3) suggest about nuclear matter?
[1 mark]
AThe density is approximately the same for all nuclei.
BThe density increases as the nucleon number increases.
CThe density decreases as the nucleon number increases.
DThe density depends only on the number of protons.
(c)
Calculate the density of nuclear matter.
[2 marks]
Total for question 1: 4 marks
2
A sealed source is placed at a fixed distance from a Geiger–Müller tube. With the source removed, the tube records a background count rate of 25 counts per minute. With the source in place the count rate is 460 counts per minute with no absorber, 395 counts per minute with a sheet of paper in front of the tube, 95 counts per minute with 3 mm of aluminium, and 25 counts per minute with 10 cm of lead.
(a)
Which row lists alpha, beta and gamma radiation in order of increasing penetrating power?
[1 mark]
Agamma, beta, alpha
Bbeta, alpha, gamma
Calpha, beta, gamma
Dalpha, gamma, beta
(b)
What is the count rate due to the source alone when the sheet of paper is in place?
[1 mark]
A395 counts per minute
B420 counts per minute
C65 counts per minute
D370 counts per minute
(c)
Deduce, using corrected count rates, whether the source emits alpha radiation and whether it emits beta radiation.
[2 marks]
Total for question 2: 4 marks
3
Phosphorus-32 is a radioisotope with a half-life of 14.3 days. A sample has an initial activity of 8.0×10⁶ Bq.
(a)
Calculate the decay constant of phosphorus-32 in s⁻¹.
[3 marks]
(b)
Calculate the activity of the sample after 30 days.
[4 marks]
Total for question 3: 7 marks
4
Americium-241 is an alpha emitter with a half-life of 432 years. It is used in ionisation smoke detectors. One detector contains 0.30 µg of americium-241. The molar mass of americium-241 is 241 g mol⁻¹, the Avogadro constant is 6.02×10²³ mol⁻¹ and 1 year = 3.16×10⁷ s.
(a)
Show that the activity of the americium-241 in the detector is about 3.8×10⁴ Bq.
[6 marks]
(b)
Explain why an alpha emitter with a long half-life is suitable for use in a smoke detector, and calculate the activity of the americium-241 after 10 years.
[6 marks]
Total for question 4: 12 marks
5
Caesium-137 (¹³⁷₅₅Cs) decays by β⁻ emission to an excited state of barium-137. The excited barium nucleus then emits a single gamma photon of energy 0.662 MeV and falls to its ground state. Use e = 1.60×10⁻¹⁹ C.
(a)
What is the composition of the barium-137 nucleus formed in the β⁻ decay?
[1 mark]
A56 protons and 81 neutrons
B54 protons and 83 neutrons
C53 protons and 80 neutrons
D55 protons and 82 neutrons
(b)
A different unstable nucleus decays by β⁺ emission. Which row shows the changes to its proton number Z and neutron number N?
[1 mark]
AZ increases by 1, N decreases by 1
BZ decreases by 2, N decreases by 2
CZ decreases by 1, N increases by 1
DZ and N unchanged
(c)
Calculate the energy of the gamma photon in joules and explain what its single, definite value shows about the nuclei that emit it.
[2 marks]
Total for question 5: 4 marks
6
Use e = 1.60×10⁻¹⁹ C and 1/(4πε₀) = 8.99×10⁹ N m² C⁻². In an investigation of the structure of the atom, alpha particles of kinetic energy 5.0 MeV are fired directly at the nucleus of a copper atom (proton number 29).
(a)
Which observation in the alpha particle scattering experiment showed that the nucleus is both very dense and positively charged?
[1 mark]
AMost alpha particles passed through the foil with little or no deflection.
BA very small proportion of alpha particles were deflected through angles greater than 90°.
CThe alpha particles lost kinetic energy when passing through the foil.
DThe alpha particles were stopped completely by a thin sheet of paper.
(b)
What is the kinetic energy of an alpha particle at its point of closest approach to the nucleus, in a head-on approach?
[1 mark]
A5.0 MeV
B2.5 MeV
Cgreater than 5.0 MeV
Dzero
(c)
Calculate the distance of closest approach of the alpha particle to the nucleus.
[2 marks]
Total for question 6: 4 marks
7
A sealed flask contains radon-222, an alpha emitter with a half-life of 3.82 days. The initial activity of the radon is 6.4×10⁴ Bq.
(a)
Calculate the decay constant of radon-222 in s⁻¹ and the number of radon nuclei in the flask at the start.
[3 marks]
(b)
The flask may be opened safely once the activity has fallen to 1.0% of its initial value. Calculate how long this takes, in days.
[4 marks]
Total for question 7: 7 marks
8
Fluorine-18 (¹⁸₉F) is a β⁺ emitter with a half-life of 110 minutes, used in medical diagnosis. The only stable isotope of fluorine is fluorine-19. An injection requires an activity of 3.0×10⁸ Bq at the moment of injection. The fluorine-18 is made in a cyclotron 4.0 hours before the injection.
(a)
Write a decay equation for fluorine-18 and state the changes in proton number and neutron number. Explain why fluorine-18 is unstable and how β⁺ decay brings the nucleus closer to stability.
[6 marks]
(b)
Calculate the activity of the fluorine-18 at the moment it was made. Explain one advantage and one disadvantage of using a source with such a short half-life.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).