IB Physics SL E.3.12 Half-Life Changes

Practise applying integer half-lives to nuclei, activity or corrected count rate and identifying how repeated halving differs from a linear decrease over elapsed time.

Syllabus
First assessment 2025
Objective
—
Level
SL

Exam points

  • calculate the number of elapsed half-lives as t/T½ before applying the factor (1/2)ⁿ
  • apply repeated halving to undecayed nuclei, activity or background-corrected count rate
  • work backwards through half-lives by doubling rather than subtracting a fixed amount

E.3.12—Half-life changes question 1

[Maximum number: 2]

This question is in two parts. Part 1 is about renewable energy. Part 2 is about nuclear energy and radioactivity.

A small coastal community decides to use a wind farm consisting of five identical wind turbines to generate part of its energy. At the proposed site, the average wind speed is 8.5 m s−18.5 \mathrm{~m} \mathrm{~s}^{-1} and the density of air is 1.3 kg m−31.3 \mathrm{~kg} \mathrm{~m}^{-3}. The maximum power required from the wind farm is 0.75 MW . Each turbine has an efficiency of 30 %.

U-235 (92235U)\left({ }_{92}^{235} \mathrm{U}\right) can undergo alpha decay to form an isotope of thorium (Th).

A sample of rock contains a mass of 5.6 mg of U-235 at the present day.

The half-life of U-235 is 7.0×1087.0 \times 10^{8} years. Calculate the initial mass of the U-235 if the rock sample was formed 2.1×1092.1 \times 10^{9} years ago.

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