The half-life of carbon-14 is 5730 years. What percentage of carbon-14 remains in a sample after 12 half lives?

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The half-life of carbon-14 is 5730 years. What percentage of carbon-14 remains in a sample after 12 half lives?

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Answer 1 · 2016-06-24T20:57:45

0.024%

Explanation:

The equation for half life is:

$N(t) = N(0) * 0.5^(t/(T))$

In which $N(0)$ is the number of atoms you start with, and $N(t)$ the number of atoms left after a certain time $t$ for a nuclide with a half life of $T$ .

From this you can deduce that:

$0.5^(t/(T))$ = the fraction of C-14 left after a certain period of decay
$t/T$ is the number of half lifes that have passed

In the example $12$ half lifes have passed so the equation is:
$0.5^(12) = 0.00024$ (fraction) $* 100% = 0.024%$

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The half-life of carbon-14 is 5730 years. What percentage of carbon-14 remains in a sample after 12 half lives?

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