Radioactive decay and half-lifeAQA A-Level Physics: Subtopic test

1. 1
   A freshly prepared sample contains 4.0 × 10⁶ nuclei of a radioisotope. The decay constant of the isotope is 2.0 × 10⁻³ s⁻¹.

   (a)

   What is the initial activity of the sample?

   [1 mark]

   • A8.0 × 10³ Bq
   • B2.0 × 10⁹ Bq
   • C8.0 × 10⁶ Bq
   • D4.0 × 10⁶ Bq

   (b)

   What is the half-life of the isotope?

   [1 mark]

   • A2.9 × 10⁻³ s
   • B500 s
   • C1.0 × 10³ s
   • D3.5 × 10² s

   (c)

   Calculate the number of undecayed nuclei remaining after 600 s.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student measures the activity A of a sample of a radioisotope at regular intervals. She plots a graph of ln(A / Bq) against time t in minutes and obtains a straight line with a gradient of −0.080 min⁻¹ and an intercept of 8.0 on the ln(A / Bq) axis.

   (a)

   What does the gradient of the graph represent?

   [1 mark]

   • AThe half-life of the isotope
   • BThe initial activity of the sample
   • CThe negative of the decay constant
   • DThe number of undecayed nuclei

   (b)

   What is the initial activity of the sample?

   [1 mark]

   • A8.0 Bq
   • B3.0 × 10³ Bq
   • C55 Bq
   • D0.080 Bq

   (c)

   Determine the half-life of the isotope.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Carbon-14 has a half-life of 5730 years. Living wood contains carbon-14 and gives an activity of 0.230 Bq per gram of carbon, a value that stays constant while the tree is alive. A sample of carbon from an ancient wooden bowl gives an activity of 0.160 Bq per gram.

   (a)

   Calculate the decay constant of carbon-14 in year⁻¹.

   [3 marks]

   (b)

   Calculate the age of the wooden bowl, and state an assumption made in this method of dating.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A nuclear facility stores waste containing plutonium-239, which has a half-life of 2.4 × 10⁴ years, and also handles iodine-131, which has a half-life of 8.0 days. The Avogadro constant is 6.02 × 10²³ mol⁻¹.

   (a)

   Compare the problems of storing waste containing plutonium-239 with those of handling iodine-131, and discuss how the half-life affects the type of storage required.

   [6 marks]

   (b)

   A sample contains 1.0 mg of pure iodine-131, which has a molar mass of 131 g mol⁻¹. Calculate the initial activity of the sample and the time taken for its activity to fall to 1.0 × 10⁹ Bq.

   [6 marks]

   Total for question 4: 12 marks

End of questions