# What is the half-life of 20 g of a radioactive sample if 5 g remain after 8 minutes?

May 31, 2016

$4 \min .$

#### Explanation:

${m}_{i} = {m}_{r} \times {2}^{n}$

${m}_{i} = \text{ is the initial mass}$

${m}_{r} = \text{ is the remaining mass after n periods}$

$n \text{ is the number of periods }$

${2}^{n} = {m}_{i} / {m}_{r}$

${2}^{n} = \frac{20}{5}$

${2}^{n} = 4$

${2}^{n} = {2}^{2} \text{ } \implies n = 2$

$n = \frac{t i m e}{\text{half-life}}$

$\text{half-life } = \frac{t i m e}{n}$

$\text{half-life} = \frac{8 \min}{2} = 4 \min$

$20 \setminus g \to 10 \setminus g \to 5 \setminus g$