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?

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Answer 1 · 2016-08-24T10:18:59

Just over 12 years

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: ${(\frac{1}{2})}^{n} = 0.2$ $(1/2)^n = 0.2$

Now rearrange for n:

$n . log 0.5 = log 0.2$ $n.log 0.5 = log 0.2$

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

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