Question

Calculate the number of nuclei of carbon -14 undecayed after 22,920 years if the initial

number of carbon -14 atoms is 10,000. The half life of carbon -14 is 5730 years.​

Answer 1

Given:

The half life of carbon -14 is 5730 years.

To find:

The number of nuclei of carbon -14 undecayed after 22,920 years if the initial number of carbon -14 atoms is 10,000 ?

Calculation:

Let the number of half life passed be n :

$\therefore \: t = t_{ \frac{1}{2} } \times n$

$\implies \: 22920 = 5730\times n$

$\implies \: n = \dfrac{22920}{5730}$

$\implies \: n = 4$

Now, the number of nucleus left undecayed be N:

$\therefore \: \dfrac{N}{10000} = {( \dfrac{1}{2}) }^{n}$

$\implies \: \dfrac{N}{10000} = {( \dfrac{1}{2}) }^{4}$

$\implies \: \dfrac{N}{10000} = \dfrac{1}{16}$

$\implies \: N = \dfrac{10000}{16}$

$\implies \: N = 625$

So, 625 nucleus are undecayed.