Question

The practical limit to ages that can be determined by radiocarbon dating is about 41000-yr-old sample, what percentage of the original 614C atoms remains? (For percentage you can either enter the percentage with a percent sign "65.1%" or the percentage as a fraction "0.651".)

Answer 1

Answer:

In percentage, the sample of C-4 remains = 0.7015 %

Explanation:

The Half life  Carbon 14 =  5730 year

$t_{1/2}=\frac {ln\ 2}{k}$

Where, k is rate constant

So,  

$k=\frac {ln\ 2}{t_{1/2}}$

$k=\frac {ln\ 2}{5730}\ hour^{-1}$

The rate constant, k = 0.000120968 year⁻¹

Time = 41000 years

Using integrated rate law for first order kinetics as:

$[A_t]=[A_0]e^{-kt}$

Where,  

$[A_t]$ is the concentration at time t

$[A_0]$ is the initial concentration

So,  

$\frac {[A_t]}{[A_0]}=e^{-0.000120968\times 41000}$

$\frac {[A_t]}{[A_0]}=0.007015$

In percentage, the sample of C-4 remains = 0.7015 %