Question

If the half life is 5700 years, how do you find the percentage of original carbon-14 that remains in a sample after 2476 years have passed?

Answer 1

I get `74.1%` of the original amount remaining.

Explanation:

Well, if the half-life of `""14^C` is `5700` years, then that means after `5700` years have happened, there will be half of the original amount, i.e. `50%` of the original amount of `""14^C` left.

So, after `2476` years, the sample of `""14^C` has evolved:

`2476/5700~~43.4%` of a half-life

A rule to remember is that if `n` is the number of half-lives elapsed, there will be `100/(2^n)%` of the original amount of substance remaining. For the source of this information, click here.

So here, `n=43.4%=0.434`. Therefore, there will be

`100/(2^0.434)`

`~~100/1.35`

`~~74.1%` of the original amount remaining.