Nuclear radiationEdexcel A-Level Physics: Topic test

1. 1
   Radon-222 (proton number 86) is a radioactive gas that seeps out of some rocks into buildings. It decays by alpha emission. A later nuclide in its decay chain, bismuth-214 (proton number 83), decays by beta-minus emission to polonium (proton number 84).

   (a)

   Which nuclide is formed when a nucleus of radon-222 emits an alpha particle?

   [1 mark]

   • A${}^{222}_{87}\text{Fr}$
   • B${}^{218}_{84}\text{Po}$
   • C${}^{218}_{86}\text{Rn}$
   • D${}^{226}_{88}\text{Ra}$

   (b)

   Which statement best explains why radon gas is a health hazard when it is breathed in, even though alpha particles cannot penetrate the skin?

   [1 mark]

   • AAlpha particles are weakly ionising but they penetrate deep into the body
   • BAlpha particles are the most penetrating radiation and pass through the chest wall
   • CRadon is a gamma emitter, so its radiation passes through the body
   • DAlpha particles are strongly ionising and are absorbed in a short distance, so inside the lungs all their energy is delivered to nearby cells

   (c)

   Write a nuclear equation for the decay of bismuth-214 by beta-minus emission.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A sealed source of unknown type is tested with a detector at a fixed distance. The background radiation gives 24 counts per minute. The count rates recorded, in counts per minute, are: no absorber 840; with a sheet of paper 838; with 3.0 mm of aluminium 26.

   (a)

   What is the corrected count rate with no absorber?

   [1 mark]

   • A864 counts per minute
   • B840 counts per minute
   • C816 counts per minute
   • D838 counts per minute

   (b)

   Which type of radiation does the source emit?

   [1 mark]

   • ABeta only
   • BAlpha only
   • CGamma only
   • DAlpha and gamma

   (c)

   Calculate the percentage of the corrected count rate that is removed by the 3.0 mm of aluminium.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Data for a lithium-7 nucleus, which contains 3 protons and 4 neutrons: nuclear mass = 7.014358 u. Mass of a proton = 1.007276 u. Mass of a neutron = 1.008665 u. 1 u = 1.66 × 10⁻²⁷ kg. Speed of light, c = 3.00 × 10⁸ m s⁻¹. Elementary charge, e = 1.60 × 10⁻¹⁹ C.

   (a)

   Calculate the mass deficit of the lithium-7 nucleus in kg.

   [3 marks]

   (b)

   Calculate the binding energy of the lithium-7 nucleus in MeV and its binding energy per nucleon. State what the binding energy per nucleon shows.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Binding energy per nucleon values, in MeV: uranium-235 7.6; barium-141 8.3; krypton-92 8.5; iron-56 8.8. Iron-56 lies at the maximum of the binding energy per nucleon curve. Elementary charge, e = 1.60 × 10⁻¹⁹ C.

   (a)

   In the core of a massive star, nuclei lighter than iron-56 fuse together. Explain why fusion of lighter nuclei releases energy but fusion of iron-56 nuclei does not, and why fusion requires very high temperature and density.

   [6 marks]

   (b)

   One fission reaction is ${}^{1}_{0}\text{n} + {}^{235}_{92}\text{U} \rightarrow {}^{141}_{56}\text{Ba} + {}^{92}_{36}\text{Kr} + 3\,{}^{1}_{0}\text{n}$. Calculate the energy released in one fission in MeV and in J. A reactor has a thermal power of 1.2 GW; calculate the number of fissions per second. Explain why energy is released in this fission.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   Carbon-14 has a half-life of 5730 years. A 1.00 g sample of carbon from living wood has an activity of 0.230 Bq. A 1.00 g sample of carbon from a wooden artefact found at a dig has an activity of 0.0575 Bq. Take 1 year = 3.156 × 10⁷ s.

   (a)

   What is the decay constant of carbon-14?

   [1 mark]

   • A3.83 × 10⁻¹² s⁻¹
   • B1.21 × 10⁻⁴ s⁻¹
   • C5.53 × 10⁻¹² s⁻¹
   • D1.92 × 10⁻¹² s⁻¹

   (b)

   What is the age of the artefact?

   [1 mark]

   • A5 700 years
   • B17 200 years
   • C11 500 years
   • D23 000 years

   (c)

   Calculate the number of carbon-14 nuclei in the sample from the artefact.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   A radioactive isotope is prepared in a laboratory. Its initial activity is 2.56 × 10⁴ Bq. Forty-eight minutes later the activity has fallen to 1.60 × 10³ Bq. Background radiation may be ignored.

   (a)

   What is the half-life of the isotope?

   [1 mark]

   • A48 min
   • B24 min
   • C16 min
   • D12 min

   (b)

   What activity is expected a further 36 minutes later?

   [1 mark]

   • A4.0 × 10² Bq
   • B2.0 × 10² Bq
   • C5.3 × 10² Bq
   • D0 Bq

   (c)

   A student says: "The half-life is 12 minutes, so after 24 minutes the whole sample will have decayed." Explain why this statement is wrong.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A thickness gauge in a factory contains a sealed source of strontium-90, which has a half-life of 28.8 years. The initial activity of the source is 3.7 × 10⁶ Bq. Take 1 year = 3.156 × 10⁷ s.

   (a)

   Calculate the decay constant of strontium-90 in s⁻¹.

   [3 marks]

   (b)

   Calculate the number of strontium-90 nuclei in the source at the start and the activity of the source after 10 years.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   Iridium-192 is a beta-minus and gamma emitter with a half-life of 74 days. Small sealed wires of iridium-192 are placed temporarily inside tumours to treat cancer. One wire has an initial activity of 1.2 × 10⁹ Bq.

   (a)

   Evaluate the suitability of iridium-192 for this use, referring to the types of radiation it emits and to its half-life. Compare it with an alpha emitter and with a source of half-life 5 minutes.

   [6 marks]

   (b)

   The wire is to be stored until its activity has fallen to 5.0% of its initial value. Calculate the activity at which it can be disposed of and the time this takes. Explain why the activity measured with a detector must be corrected for background radiation.

   [6 marks]

   Total for question 8: 12 marks

End of questions