# Question 444dd

May 28, 2017

The half life is 10.7 h.

#### Explanation:

The integrated rate law for radioactive decay is

$\ln \left({A}_{0} / {A}_{t}\right) = k t$

where

${A}_{0}$ and ${A}_{t}$ are the activities at time $t = 0$ and at time $t$
$k$ is the decay constant
$t$ is the time

ln((9000 color(red)(cancel(color(black)("Bq"))))/(400 color(red)(cancel(color(black)("Bq"))))) = 3.114 = k × "2 days"#

$k = \frac{3.114}{\text{2 days" = "1.557 day"^"-1}}$

${t}_{\frac{1}{2}} = \ln \frac{2}{k} = \ln \frac{2}{\text{1.557 day"^"-1" = "0.4453 days" = "10.7 h}}$