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%#