# The half-life of cobalt-60 is 5.2 years. Find the time it would take for a sample of 0.5 grams to decay to 0.1 gram?

Aug 24, 2016

Just over 12 years

#### Explanation:

The half life is the time taken for the mass of the substance to decrease by a half.

In this case, the amount of substance remaining is 20% of the initial amount (0.1 g out of initial 0.5 g).

Therefore you can say: ${\left(\frac{1}{2}\right)}^{n} = 0.2$

Now rearrange for n:

$n . \log 0.5 = \log 0.2$

$n = \left(\log \frac{0.2}{\log} 0.5\right) = \frac{- 0.6989}{- 0.3010} = 2.32$

So it would take 2.32 half lives to decay this much, which is 2.32 x 5.2 which is 12.064 years.