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 = t/t_(1/2)#, so #t = nt_(1/2)#.

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

#"Amount remaining" = "original amount"/2^n# or

#A = A_0/2^n#

You can rearrange this to

#A_0/A = 2^n#

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

#100/25 = 2^n#

#4 = 2^n#

#n = 2#

#t = nt_(1/2) = "2 × 5730 yr" = "11 460 yr""#