IB Physics SL E.3.12 Half-life changes Question Bank

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 $8.5 \mathrm{~m} \mathrm{~s}^{-1}$ and the density of air is $1.3 \mathrm{~kg} \mathrm{~m}^{-3}$. The maximum power required from the wind farm is 0.75 MW . Each turbine has an efficiency of 30 %.

U-235 $\left({ }_{92}^{235} \mathrm{U}\right)$ 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 $7.0 \times 10^{8}$ years. Calculate the initial mass of the U-235 if the rock sample was formed $2.1 \times 10^{9}$ years ago.