Question

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

Answer 1

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%`