Question

Carbon-14 is a radioactive isotope of carbon with a nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating.
The half-life of carbon-14 is 5,730 years.

If a fossilised tree trunk originally contained 8 nanograms of C-14, how long will it take for the C-14 to decay to 1 nanogram

Answer 1

Solution :

Half life of Carbon - 14 is 5730 years.

So it takes 5730 years for Carbon to decay to its half of its amount.

Let Ci be the initial amount of the carbon.

and Cf be the final amount of carbon.

Cf = ($1/2^n$) * Ci

where n is the number of half lives.

  $1/2^n$ = Cf/Ci

  $1/2^n$ = 1/8

So number of half lives :

n = 3

so it will take 3 half lives or 3*5730 years to decay.

t = 17190 years.