Question

The half life of carbon is 5,730 years. What fraction of the original 14/6 C would be in a wooden axe handle that was 17,190 years old? (Plz explain how u got it step by step if u can T^T)

Answer 1

Answer:

$\frac{1}{8}$  

Explanation:

The half-life of carbon (5730 y) is the time it takes for half the carbon to decay.

After one half-life, half (50 %) of the original amount will remain.

After a second half-life, half of that amount (25 %) will remain, and so on.

$\text{17 190 y} \times \frac {\text {1 half-life}}{\text{5730 y}} = \text{3 half-lives}$  

We can construct a table.

No of half-lives  Fraction remaining

            1                       $\frac{1}{2}$  

            2                      $\frac{1}{4}$  

            3                      $\frac{1}{8}$  

The general formula is

$\text{Fraction remaining} = \frac{1}{2^{n}}$

where n = the number of half-lives.

Thus, $\frac{1}{8}$ of the original carbon remains after 17 190 y.