Question

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

Answer 1

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

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 `100g` will become only `50g` in that time `rarr` (b)

In 12,000 years, it has only had time to decay `1/2` of its `1/2` life.
That means it has decayed only `1/2**1/2=1/4` of its weight, so `1-1/4=3/4` still remains.

`3/4**100g=75g to` (a)

96,000 years is equal to `(cancel(96000)6)/cancel24000=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 `rarr` (c)

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