A wooden artifact sample gave activity 32- particles per second while the freshly cut wood gave activity of 64- particles per second in GM counter- Calculate the age of the wooden artifact t1-2 of 14 C -5670 years

The half-life for radioactive decay of $^{14} C$ is 5730 yr. An archaeological artifact containing wood had only $80 %$ of the $^{14} C$ found in a living tree. Estimate the age of the sample.

Q. Wooden artifact and freshly cut tree are

7.6

and

15.2

{m i n}^{- 1} g^{- 1}

of carbon

(t_{1 / 2} = 5760 y e a r s)

respectively. The age of the artifact is:

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A wooden artifact sample gave activity 32β particles per second while the freshly cut wood gave activity of 64β particles per second in GM counter. Calculate the age of the wooden artifact (t1/2 of 14C=5670 years )

The correct option is B 5670 yrsWe know,k=2.303t×logN0N Now, 0.693t1/2=2.303tagelog10(N0N)0.6935670=2.303tagelog10(6432)tage=5670 yrs

A wooden artifact sample gave activity $32 β$ particles per second while the freshly cut wood gave activity of $64 β$ particles per second in GM counter. Calculate the age of the wooden artifact ( $t_{1 / 2}$ of $^{14} C = 5670 y e a r s$ )

The correct option is B $5670$ yrs
We know,

$k = \frac{2.303}{t} \times l o g \frac{N_{0}}{N}$

Now,

$\frac{0.693}{t_{1 / 2}} = \frac{2.303}{t_{a g e}} {log}_{10} (\frac{N_{0}}{N})$

$\frac{0.693}{5670} = \frac{2.303}{t_{a g e}} {log}_{10} (\frac{64}{32})$

$t_{a g e} = 5670 y r s$