Question

The half life of 226/88 Ra is 1620 years. How much of a 220 g sample of 226/88 Ra will be left after 10 half lives?

Answer 1

Given:
Half-life = 1620 years
Original mass, m₀ = 220 g

The decay equation is of the form

`m(t) = m_(0) e^(-kt)`
where
t = time, years
k = constant

At half-life, m = 0.5m₀ and t = 1620. Therefore

`e^(-1620k) = 0.5 \\\\ -1620k = ln(0.5) \\\\ k = - (ln(0.5))/(1620) =4.2787 * 10^(-4)`

When t = 10 half-lives = 16200 years, obtain

`m = (220 \, g) e^{-4.2787 * 10^(-4)*16200}=0.2148 \, g`

Answer: 0.215 g (nearest thousandth)