Question

Scientists found a fossilized bone from an organism at an excavation site in North Dakota. When they took the bone back to the lab, they realized that the bone had only 12.5% of the total carbon-14 left. Based on the amount of carbon-14 left in the bone how old is the bone if the half-life of carbon-14 is 5730 years?

Answer 1

Answer: 17328.7 years

Explanation:

Half-life of sample of carbon-14 = 5730 years

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{5730}=1.2\times 10^{-4} years^{-1}$

$N=N_o\times e^{-\lambda t}$

N = amount left = 12.5 g

$N_0$= initial amount = 100 g

$\lambda$= disintegration constant= $1.2\times 10^{-4} years^{-1}$

t= ?

$12.5=100\times e^{-1.2\times 10^{-4}\times t}$

$t=17328.7years$

Thus the bone is 17328.7 years old.

Answer 2

T = 3⋅5,730 = 17,190 years