Question

Half-life is defined as the amount of time that it takes for radioactive substance to loose half its radioactivity. If a substance has a half life of 58 years and starts with 500 g radioactive, how much remains radioactive after 30 years?

Answer 1

You can work out a yearly decay-factor, which is just a growth factor (known from exponential functions in maths or economy), but now it's below 1.

Explanation:

`N=BxxG^t`, where N=new value, B=start value, G=growth (or decay) factor, and t=number of periods (years in this case.

We know that `G^58=1//2`, so
`G=root 58 (1/2)=(1/2)^(1/58)`

After 30 years, activity will be:

`N=500xx(root 58 (1/2))^30=500xx(1/2)^(30/58)=500xx0.699=349g`

On your calculator you can set this up like:

0.5 ^ (30 : 58) x 500 = 349