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

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

Step-by-step 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* 41000)`

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

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