Question

A piece of bone from an archaeological site is found to give a count rate of $15$ counts per minute. A similar sample of fresh bone gives a count rate of $19$ counts per minute. Calculate the age of the specimen. Given $T_{1/2}=5570years$

Answer 1

Count rate of fresh sample $N_0=19$ counts/minute

Count rate of bone $N=15$ counts/minute

$T_{1/2}=5570$ years, Age of the sample, $t=?$

$N=N_0{e}^{-\lambda }t$

$\lambda =\frac{0.6931}{5570}$

$15=19e^{-\lambda t}$ (or) $e^{\lambda t}=\frac{19}{15}$

$\log e\frac{19}{15}=\lambda t$ (or) $t=\log e\frac{19}{15}\times \frac{1}{\lambda }$

$t=\frac{5570}{0.6931}\times 2.3026\times {\log }_{10}\frac{19}{15}$

$=\frac{5570}{0.6931}\times 2.3026\times 0.1026$

$t=1899years$.