Question

A piece of wood was burned and 7.32 g of $C{O}_2$ was collected. The total radioactivity in $C{O}_2$ was 7.6 dpm. How old was the wood sample ? Given $t_{\frac{1}{2}}$ of C - 14 = 5730 years, specific activity of carbon obtained from a fresh wood sample is 15.2 dpm.

• A. 5730 years
• B. 11460 years
• C. 22920 years
• D. None of these

Answer 1

The correct option is B

11460 years

Mass of carbon in $7.32gC{O}_2=\frac{12}{44}\times 7.32=2g;$
Activity per g(specific activity)$=\frac{7.6}{2}=3.8dpm$
Fraction of activity remaining $=\frac{3.8}{15.2}=\frac{1}{4}=(\frac{1}{2}{)}^2$
No. of half - lives clapsed = 2;
Age of the sample $=2\times 5730years$