Question #200408

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.

Expert's answer

answer; * age of sample is 8844 years.*

Let,

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

sol.

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 C*^{14}* 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.*

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