# Exam-style Questions: Radioactive Decay Equations

1. a) Define the bequerel.

(1 mark)

b) Write down an equation that relates the activity (A) of a source to the number of atoms it contains (N). Identify any new symbols you introduce.

(1 mark)

(Marks available: 2)

Answer outline and marking scheme for question: 1

a) 1 Bq = 1 decay per second

(1 mark)

b) A = lN l is the decay constant

(1 mark)

(Marks available: 2)

2. A sample of radioactive material contains 1 x 1018 atoms and its activity is measured as 9 x 1012 Bq. Calculate the decay constant for the sample.

(Marks available: 2)

Answer outline and marking scheme for question: 2

Use A = lN

(1 mark)

l = 1 x 105 per second

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(Marks available: 2)

3. A piece of wood from an ancient spear has a mass of 1kg. An activity of 7.5 disintegrations per minute is recorded from it (assume due to be from the decay of the isotope carbon 14). A similar modern replica made from the same wood but with a mass of 2kg has an activity of 30 disintegrations per minute. If the half-life of carbon 14 is 5730 years calculate the age of the ancient spear.

(Marks available: 2)

Answer outline and marking scheme for question: 3

5730 years

4. Cobalt 60 is used in many applications where gamma radiation is required. The half-life of cobalt 60 is 5.26 years. If a sample has an initial activity of 2 x 1015 Bq what will its activity be after 3 years?

(Marks available: 2)

Answer outline and marking scheme for question: 4

1.35 x 1015 Bq

5. Living matter has an activity of 260 BqKg-1 due to carbon 14. If a sample of wood from a burial site has an activity of 155 Bq Kg-1 estimate the age of the site. Half-life of carbon 14 is 5730 years.

(Marks available: 2)

Answer outline and marking scheme for question: 5

Around 4280 years

6. Geiger counter placed 20cm from a point source of gamma radiation registers a count rate of 6000s-1. Calculate the count rate 1 metre away.

(Marks available: 2)

Answer outline and marking scheme for question: 6

1200 s-1