# 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?

May 13, 2018

$\text{60.63 mg}$ 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")

$\text{N = 80 mg" × e^-"0.4 ln(2)" = "60.63 mg}$