The ratio of in a piece of wood is part that of atmosphere. If half life of is 5730 years, the age of wood sample is ______ years.

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Solution

Q.
The ratio of $\frac{{}^{14}C}{{}^{12}C}$ in a piece of wood is $\frac{1}{8}$ part that of atmosphere. If half life of ${}^{14}C$ is 5730 years, the age of wood sample is ______ years. [2024]

Ans.
(17190)

${}^{14}C$ is radioactive and undergoes first order decay. In a piece of wood amount of ${}^{14}C$ decreases because of radioactive decay but amount of ${}^{12}C$ remains same. So if ratio of $\frac{{}^{14}C}{{}^{12}C}$ in a piece of wood is $\frac{1}{8}$ , this implies ratio of amount ${}^{14}C$ remained in the wood to the initial amount is $\frac{1}{8}$ .

  In first order reaction equal percentage of reaction is completed in equal time interval. Thus concentration gets halved after every $t_{1 / 2}$ .

   $1 \overset{t_{1 / 2}}{\to} \frac{1}{2} \overset{t_{1 / 2}}{\to} \frac{1}{4} \overset{t_{1 / 2}}{\to} \frac{1}{8}$

  To get to ${(\frac{1}{8})}^{th}$ value of initial amount, it takes $3 t_{1 / 2}$ time i.e.

   $3 \times 5730 years = 17190 years$

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