# You have 100g of radioactive plutonium-239 with a half-life of 24,000 years. how much will remain after (a) 12,000 years, (b) 24,000 years, and (c) 96,000 years?

## also, can you explain the answer and how you solved to get that. thanks

Nov 3, 2017

(a)$75 g$
(b)$50 g$
(c)$1.6 g$

#### Explanation:

A half life is the number of years it takes for a radioactive substance to decay to half its original mass or weight.

So for radioactive plutonium-239 with a half-life of 24,000 years, it will take 24,000 years to decay to 1/2 its weight so $100 g$ will become only $50 g$ in that time $\rightarrow$ (b)

In 12,000 years, it has only had time to decay $\frac{1}{2}$ of its $\frac{1}{2}$ life.
That means it has decayed only $\frac{1}{2} \ast \frac{1}{2} = \frac{1}{4}$ of its weight, so $1 - \frac{1}{4} = \frac{3}{4}$ still remains.

$\frac{3}{4} \ast 100 g = 75 g \to$ (a)

96,000 years is equal to $\frac{\cancel{96000} 6}{\cancel{24000}} = 6$ half life time periods.

At half-life time 0 we have 100g
At half-life time 1 we have 50g
At half-life time 2 we have 25g
At half-life time 3 we have 12.5g
At half-life time 4 we have 6.25g
At half-life time 5 we have 3.125g
At half-life time 6 we have 1.625g $\rightarrow$ (c)

There is a formula, but this tells you how to figure it out.