Q: Plutonium decays with a half life of 24,000 years. If plutonium is stored for 72,000 years, what fraction of if remains ?

Sol: T_{1/2} = 24,000 years

Duration of time(t) = 72,000 years

Number of half lifes , $\large n = \frac{t}{T_{1/2}} $

n = 72000/24000 = 3

$\large 1 g \rightarrow \frac{1}{2}g \rightarrow \frac{1}{4}g \rightarrow \frac{1}{8}g $

Fraction of plutonium remains = 1/8 g