# What amount of plutonuim would be left after 5000 years if you initially have 14 kilo- grams? The half-life of plutonium 240 is 6500 years.

Oct 8, 2016

$\textsf{8.2 \textcolor{w h i t e}{x} \text{kg}}$

#### Explanation:

sf(M_t=M_0e^(-lambdat)

$\therefore$$\textsf{\ln {M}_{t} = \ln {M}_{0} - \lambda t}$

sf(lambda=0.693/t_(1/2)=0.693/6500=1.066xx10^(-4)color(white)(x)a^(-1)

So:

$\textsf{\ln {M}_{t} = \ln 14 - \left(1.066 \times {10}^{- 4} \times 5000\right) = 2.64 - 0.533 = 2.107}$

From which:

$\textsf{{M}_{t} = 8.2 \textcolor{w h i t e}{x} k g}$