# The half-life of an isotope of tritium is 4500 days. How many days will it take an amount of tritium to fall to a quarter of its initial mass?

## year 9 question

Apr 29, 2018

9000 days.

#### Explanation:

Decay can be described by the following equation:

${M}_{0} = \text{initial mass}$

$n$=number of half lives

$M = {M}_{0} \times {\left(\frac{1}{2}\right)}^{n}$

$\left(\frac{1}{4}\right) = 1 \times {\left(\frac{1}{2}\right)}^{n}$

$\left(\frac{1}{4}\right) = \left({1}^{2} / {2}^{2}\right)$

So $n = 2$, which means 2 half-lives must have passed.

1 half-life is 4500 days, so it must take $2 \times 4500 = 9000$ days for the sample of tritium to decay to a quarter of its initial mass.