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

1 Answer
Jun 24, 2016

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%