Q1. A student attempted to determine the half-life of a radioactive substance, which emits particles, by placing it near a suitable counter. He recorded C, the number of counts in 30 s, at various times, t, after the start of the experiment. The results given in the table were obtained.

(a) Explain what is meant by half-life. (1 mark)

(b) Complete the table. (1 mark)

(c) On the graph paper

(i) plot ln C against t,

(ii) draw the best straight line through your points,

(iii) determine the gradient of your graph. (5 marks)

(d)

(i) Show that the decay constant of the substance is equal to the magnitude of the gradient of your graph.

(ii) Calculate the half-life of the substance. (3 marks)

(e) This particular experiment is likely to lead to an inaccurate value for the half-life. Suggest two ways in which the accuracy of the experiment could be improved. (2 marks)

(f) The age of a piece of bone recovered from an archaeological site may be estimated by ¹⁴C dating. All living organisms absorb ¹⁴C but there is no further intake after death. The proportion of ¹⁴C is constant in living organisms.

• A 1 g sample of bone from an archaeological site has an average rate of decay of 5.2 Bq due to ¹⁴C.
• A 1 g sample of bone from a modern skeleton has a rate of decay of 6.5 Bq.

(The counts are corrected for background radiation).

Calculate the age, in years, of the archaeological samples of bone.

Half life of ¹⁴C = 5730 years

(4 marks)

(Total 16 marks)

Q2.

(a) In a radioactivity experiment, background radiation is taken into account when taking corrected count rate readings in a laboratory. One source of background radiation is the rocks on which the laboratory is built. Give two other sources of background radiation.

(1 mark)

(b) A γ ray detector with a cross-sectional area of 1.5 × 10^–3m² when facing the source is placed 0.18 m from the source. A corrected count rate of 0.62 counts s^–1 is recorded.

(i) Assume the source emits γ rays uniformly in all directions. Show that the ratio number of γ photons incident on detector to the number of γ photons produced by source is about 4 × 10^–3.

(2 marks)

(ii) The γ ray detector detects 1 in 400 of the γ photons incident on the facing surface of the detector. Calculate the activity of the source. Give an appropriate unit.

(3 marks)

(c) Calculate the corrected count rate when the detector is moved 0.10 m further away from the source.

(3 marks)

(Total 9 marks)

Q3.

A radioactive source used in a school laboratory is thought to emit α particles and γ radiation.

Describe an experiment that may be used to verify the types of radiation emitted by the source.

The experiment described should allow you to determine how the intensity of radiation varies with distance in air or with the thickness of suitable absorbers.

Your answer should include:

the apparatus you would use and any safety precautions you would take
the measurements you would make
how the measurements would be used to reach a final decision about the emitted radiation.

(Total 6 marks)

Q4.

(a) In a radioactivity experiment, background radiation is taken into account when taking corrected count rate readings in a laboratory.

One source of background radiation is the rocks on which the laboratory is built.

Give two other sources of background radiation.

(1 mark)

(b) A γ ray detector with a cross-sectional area of 1.5 × 10^–3 m² when facing the source is placed 0.18 m from the source. A corrected count rate of 0.62 counts s^–1 is recorded.

(i) Assume the source emits γ rays uniformly in all directions.

Show that the ratio is about 4 × 10^–3

(2 marks)

(ii) The γ ray detector detects 1 in 400 of the γ photons incident on the facing surface of the detector.

Calculate the activity of the source.

State an appropriate unit.

(3 marks)

(c) Calculate the corrected count rate when the detector is moved 0.10 m further from the source.

(3 marks)

(Total 9 marks)

Q5. Potassium-42 decays with a half-life of 12 hours. When potassium-42 decays, it emits β– particles and gamma rays. One freshly prepared source has an activity of 3.0 × 10⁷ Bq.

(a) To determine the radiation dose absorbed by the scientist working with the source, the number of gamma rays photons incident on each cm² of the body has to be known.

One in every five of the decaying nuclei produces a gamma ray photon.

A scientist is initially working 1.50 m from the fresh source with no shielding. Show that at this time approximately 21 gamma photons per second are incident on each cm² of the scientist's body.

(3 marks)

(b) The scientist returns 6 hours later and works at the same distance from the source.

(i) Calculate the new number of gamma ray photons incident per second on each cm² of the scientist's body.

(ii) Explain why it is not necessary to consider the beta particle emissions when determining the radiation dose the scientist receives.

(5 marks)

(Total 8 marks)

 

 

You may also want to try 'carbon dating' questions

or general radioactivity questions