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?

Mar 10, 2017

It will take $325.1$days

Explanation:

We use

$N \left(t\right) = {N}_{0} {e}^{- \lambda t}$

$\lambda$ is the radioactive decay constant

$N \left(t\right) = 0.2 {N}_{0}$

${t}_{\frac{1}{2}}$ is the radioactive half life

${t}_{\frac{1}{2}} = 140 d$

$\lambda = \ln \frac{2}{t} _ \left(\frac{1}{2}\right)$

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

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

$\ln 0.2 = - 0.00495 t$

$t = \ln \frac{0.2}{-} 0.00495 = 325.1 \mathrm{da} y s$