Question

A piece of wood from an archaeological sample has $5.0counts{min}^{-1}$ per gram of C-14, while a fresh sample of wood has a count of $15.0{min}^{-1}{g}^{-1}$. If half-life of C-14 is $5770$ yrs, the age of the archaeological sample is:

• A. 8,500 yr
• B. 9,200 yr
• C. 10,000 yr
• D. 11,000 yr

Answer 1

The correct option is B 9,200 yr

Age of archaeological sample,

$t=\frac{2.303}{k}\log \left(\frac{N_0}{N}\right)$

(Here, $N_0=$ initial activity, $N=$ remaining activity)

and $k=\frac{0.693}{t_{1/2}}$ (where $t_{1/2}=$ half-life)

$=\frac{0.693}{5770}{yr}^{-1}$

$\therefore t=\frac{2.303\times 5770}{0.693}\log \left(\frac{15}{5}\right)$

$=19175.0\log 3yr$

$=9148yr\approx 9200yr$