Answer to Question #136050 in Chemistry for Carl

Question

It is believed that humans first arrived in the Western Hemisphere during the
last Ice Age, presumably by traveling over an exposed land bridge between
Siberia and Alaska. Archaeologists have estimated that this occurred about
11,000 yr ago, but some argue that recent discoveries in several sites in North
and South America suggest a much earlier arrival. Analysis of a sample of
charcoal from a fire in one such site gave a 14C decay rate of 0.4 dpm/g of
carbon. What is the approximate age of the sample?

Answer 1

¹⁴C has half-life (t_1/2 = 5730 years).

Decay rate of ¹⁴C in fresh wood today is 13.6 dpm/g.

1) Determine decimal fraction of ¹⁴C remaining:

0.4 / 13.6 = 0.03

2) Determine how many half-lives have elapsed:

(1/2)ⁿ = 0.03

n log 0.5 = log 0.03

n = 5.06

3) Determine length of time elapsed:

5730 yr x 5.06 = 29000 yr