Answer to Question #200408 in General Chemistry for Jerry

Question

Suppose a piece of cloth was found to contain a third of its original C-14/C12

 ratio, what is the approximate age of the sample? State any assumptions you

 made during calculation.

Answer 1

answer; age of sample is 8844 years.

Let,

$C^{14'} \over C^{12'}$ be new ratio

sol.

${C^{14'}\over C12'}={1\over3}{C^{14}\over C12}$

but we know that $C^{12}$ is stable isotope,

therefore,

$C^{12'}=C^{12}$

we get,

$C^{14'}={1\over3}C^{14}$

$N={N_o\over3}$

we have half life of C¹⁴ as = 5580 years

$5580={ln2\over k}$ ..............................1

now using,

$N=N_o e^{-kt}$

we get,

${N_0\over3}=N_o e^{-kt}$ ...............................2

using 1 and 2 we get,

$t=8844 years$

therefore age of sample is 8844 years.