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

t = 3⋅5,730 = 17,190 years

Answer 2

Answer: 17328.7 years

Step-by-step explanation:

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

`\lambda =\frac{0.693}{t_{(1)/(2)}}=(0.693)/(5730)=1.2* 10^(-4) years^(-1)`

`N=N_o* e^(-\lambda t)`

N = amount left = 12.5 g

`N_0`= initial amount = 100 g

`\lambda`= disintegration constant=
`1.2* 10^(-4) years^(-1)`

t= ?

`12.5=100* e^{-1.2* 10^(-4)* t}`

`t=17328.7years`

Thus the bone is 17328.7 years old.