How old is a mammoth's tusk if 25 percent of the original C-14 remains in the sample, if the half-life of C-14 is 5730 years?

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Answer 1 · 2016-04-10T15:05:07

The tusk would be 11 460 years old.

You calculate the number of half-lives and multiply by the length of one half-life.

The number of half-lives is $n = \frac{t}{t_{\frac{1}{2}}}$ $n = t/t_(1/2)$ , so $t = n t_{\frac{1}{2}}$ $t = nt_(1/2)$ .

For each half-life, you divide the total amount of the isotope by 2, so

$Amount remaining = \frac{original amount}{2^{n}}$ $"Amount remaining" = "original amount"/2^n$ or

$A = \frac{A_{0}}{2^{n}}$ $A = A_0/2^n$

You can rearrange this to

$\frac{A_{0}}{A} = 2^{n}$ $A_0/A = 2^n$

If the original amount was 100 %, and 25 % of the nuclide remains undecayed, we have

$\frac{100}{25} = 2^{n}$ $100/25 = 2^n$

$4 = 2^{n}$ $4 = 2^n$

$n = 2$ $n = 2$

$t = n t_{\frac{1}{2}} = 2 \times 5730 yr = 11 460 yr$ $t = nt_(1/2) = "2 × 5730 yr" = "11 460 yr""$