# Question #70676

Apr 16, 2017

The mass left is $= 6.39 g$

#### Explanation:

The half life of Cobalt 60 is ${t}_{\frac{1}{2}} = 5.27 y e a r s$

The radioactive decay constant is $\lambda = \ln \frac{2}{{t}_{\frac{1}{2}}}$

So,

$\lambda = \ln \frac{2}{5.27} = \frac{0.69}{5.27}$

$= 0.1309 \left(y e a r {s}^{-} 1\right)$

We apply the equation

$A = {A}_{0} \cdot {e}^{- l a m \mathrm{da} t}$

The activity is proportional to the mass.

$m = {m}_{0} \cdot {e}^{- l a m \mathrm{da} t}$

$m = 200 \cdot {e}^{-} \left(0.1309 \cdot 26.3\right)$

$m = 200 \cdot {e}^{-} 3.443$

$m = 200 \cdot 0.03195$

$m = 6.391 g$