Question

A radioactive substance has a half-life of 125 years - if there were originally 80 radioactive milligrams 50 years ago, how much is still radioactive today?

Answer 1

`"60.63 mg"` is still radioactive today.

Explanation:

Radioactive decay constant (`λ`)

`λ = "ln(2)"/("T"_"1/2") = "ln(2)"/"125 years"`

Amount of radioactive substance left after time `t` is

`"N = N"_0 e^-(λt)`

`"N = 80 mg" × e^-( "ln(2)"/("125 years") × "50 years")`

`"N = 80 mg" × e^-"0.4 ln(2)" = "60.63 mg"`