Question

Wooden article and freshly cut tree show activity of 7.6 and 15.2 min${}^{-1}$g${}^{-1}$ of carbon $(t_{1/2}=5760year)$ respectively. The age of the article is:

• A. $5760year$
• B. $5760\times \frac{15.2}{7.6}year$
• C. $5760\times \frac{7.6}{15.2}year$
• D. $5760\times (15.2-7.6)year$

Answer 1

Answer: (A)

$5760year$

$N\left(t\right)=No(\frac{1}{2}{)}^{\frac{t}{t_{1/2}}}$

Given, $N\left(t\right)=$7.6 Min and $t_{1/2}=$5760 years

$N_o=$15.2 min

$\therefore 7.6=15.2(\frac{1}{2}{)}^{\frac{t}{t_{1/2}}}$

$0.5={\frac{1}{2}}^{\frac{t}{t_{1/2}}}$

$t=t_{1/2}$

$\therefore t=5760years$