Question

A hospital prepares a 100 mg supply of technetium-99m which has a half-life of 6 hours. How much technetium-99m will remain after 72 hours

Answer 1

Notice that 72 hours is 12 times the half-life of 6 hours. So, the starting amount of 100 mg will decay to half, 12 times. In other words

• after 1 hour, 100 mg decays to 50 mg

• after a total 2 hours, 100 mg decays to 25 mg

• after a total 3 hours, 100 mg decays to 12.5 mg

and so on, so that after a total of 72 hours, the hospital is left with

$\dfrac{100\,\rm mg}{2^{12}} = \boxed{0.0244140625 \, \mathrm{mg}}$