Answer to Question #128841 in Atomic and Nuclear Physics for Aimee

Question

Radon has a half life of 56 seconds after what time will it’s activity be reduced to 90 percent

Answer 1

The notion of half-life means that after 56 seconds the activity will decrease by 2.

$\dfrac{N(t)}{N_0} = 2^{-\lambda t},$ here $0.5 = 2^{-t/56} \Rightarrow \lambda = 1/56.$

$\dfrac{N(t)}{N_0} = 2^{- t/56},$ so $\; 0.90 = 2^{-t/56} , \; 0.90 = e^{-(\ln 2)\cdot t/56} \Rightarrow t \approx 8.5\,\mathrm{s}.$