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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".)

User Ivo San
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1 Answer

3 votes

Answer:

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 %

User Krohrbaugh
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