# Question db7d8

Apr 30, 2017

The amount left is $= 22.5 g$

#### Explanation:

In the first $8 h$, 50% is left, that is $\frac{360}{2} = 180 g$

In $16 h$, 25% is left, that is $\frac{360}{4} = 90 g$

In $24 h$, 12.5% is left, that is $\frac{360}{8} = 45 g$

In $32 h$, 6.25%# is left, that is $\frac{360}{16} = 22.5 g$

The radioactive decay is an exponential function.

$m = {m}_{0} \cdot {e}^{- \lambda t}$

Where $\lambda$ is the radioactive decay constant

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

Here, we have

$\lambda = \ln \frac{2}{8} {h}^{-} 1$

So,

$m = 360 \cdot {e}^{- \ln \frac{2}{8} \cdot 32}$

$= 360 \cdot 0.0625$

$= 22.5 g$