Use the exponential decay model, A=Aoe^(kt), to solve this exercise. The half-life of polonium-210 is 140 days. How long will it take for a sample of this substance to decay to 20% of its original amount?

Question

33976 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-10T15:29:19

It will take $325.1$ $325.1$ days

We use

$N (t) = N_{0} e^{- λ t}$ $N(t)=N_0e^(-lambda t)$

$λ$ $lambda$ is the radioactive decay constant

$N (t) = 0.2 N_{0}$ $N(t)=0.2N_0$

$t_{\frac{1}{2}}$ $t_(1/2)$ is the radioactive half life

$t_{\frac{1}{2}} = 140 d$ $t_(1/2)=140d$

$λ = \frac{ln 2}{t_{\frac{1}{2}}}$ $lambda=ln2/t_(1/2)$

$= \frac{ln 2}{140} = 0.00495 d^{- 1}$ $=ln2/140=0.00495d^-1$

$0.2 = e^{- 0.00495 t}$ $0.2=e^(-0.00495t)$

$ln 0.2 = - 0.00495 t$ $ln0.2=-0.00495t$

$t = \frac{ln 0.2}{- 0.00495} = 325.1 d a y s$ $t=ln0.2/-0.00495=325.1days$