Question

An archaeologist graduate student found a leg bone of a large animal during the building of a new science building. The bone had a carbon-14 decay rate of 14.8 disintegrations per minute per gram of carbon. Living organisms have a decay rate of 15.3 disintegrations per minute. How old is the bone?

Answer 1

Answer:

The answer to the question is 275 years

Explanation:

Here we have

The decay rate is given by

dN/dt = -λN

or dN/N = -λdt

Integrating the above equation with limits N and N₀ we have

㏑(N/N₀) = -λt

Note that the half life $t_{\frac{1}{2} }$ = (㏑ 2)/λ

From where λ = 0.693/5730 =  1.21 × 10⁻⁴

∴ ㏑(14.8/15/3) = -1.21 × 10⁻⁴ × t

or t =  275 years