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Radioactive Decay · Paper 2 — Free Physics SL Practice Questions

1MasterySAQ-SHalf-life and decay constant5 marksPaper 2~8 min

Data

1 year=3.16×107 s1\,\text{year} = 3.16 \times 10^{7}\,\text{s}
A sample of cobalt-60, used in radiotherapy machines, has a decay constant of λ=4.2×10−9 s−1\lambda = 4.2 \times 10^{-9}\,\text{s}^{-1}. The graph shows the activity of the sample over time. The curve starts at A0=8.0×1014 BqA_0 = 8.0 \times 10^{14}\,\text{Bq}; at t=5.3 yearst = 5.3\,\text{years} the activity is 4.0×1014 Bq4.0 \times 10^{14}\,\text{Bq}; at t=10.6 yearst = 10.6\,\text{years} the activity is 2.0×1014 Bq2.0 \times 10^{14}\,\text{Bq}.
(a)
Calculate the half-life of cobalt-60 in years using the decay constant. [2 marks]
(b)
Determine the initial number of cobalt-60 nuclei in the sample. [2 marks]
(c)
A medical physicist states that after three half-lives the sample is no longer suitable for radiotherapy because its activity has fallen below 1.0×1014 Bq1.0 \times 10^{14}\,\text{Bq}. Evaluate this statement. [1 mark]
diagram

Solutions

2ChallengeSAQ-LRadioactive decay and applications6 marksPaper 2~9 min

Data

- Initial activity of the sample: A0=800 MBqA_0 = 800\,\text{MBq} - Atomic mass of fluorine-18: m(F-18)=2.98850×10−26 kgm(\text{F-18}) = 2.98850 \times 10^{-26}\,\text{kg} - Atomic mass of oxygen-18: m(O-18)=2.98762×10−26 kgm(\text{O-18}) = 2.98762 \times 10^{-26}\,\text{kg} - Mass of a positron: me+=9.11×10−31 kgm_{e^+} = 9.11 \times 10^{-31}\,\text{kg} - Speed of light: c=3.00×108 m s−1c = 3.00 \times 10^{8}\,\text{m\,s}^{-1}
A medical cyclotron produces a pure sample of the radioisotope fluorine-18 (918F^{18}_{9}\text{F}) for use in PET scans. Fluorine-18 decays via positron emission to oxygen-18 (818O^{18}_{8}\text{O}) with a half-life of 110 minutes.
(a)
(i) Calculate the decay constant of fluorine-18. [1]
(ii) Determine the number of fluorine-18 atoms in the sample at the instant is produced. [2 marks]
(b)
(i) Explain why the energy released per decay cannot be calculated from the difference in atomic masses of fluorine-18 and oxygen-18 alone. [2]
(ii) Calculate the energy, in MeV, released in a single fluorine-18 decay. [2 marks]
(c)
Determine the time, in hours, after production at which the activity of the sample falls to 25 MBq25\,\text{MBq}. [2 marks]
diagram

Solutions

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