Question

An archaeological specimen containing ${}^{14}C$ 40 counts in 5 min per gram of carbon. A specimen of freshly cut wood gives 20.3 counts per gram of carbon per minute. The counter used recorded a background count of 5 counts per minute in absence of any ${}^{14}C$- containing sample. What is the age of the specimen?
$[T_{50}o{f}^{14}C=5668a]$

• A. $13328$ yr
• B. $17321$ yr
• C. $14328$ yr
• D. None of these

Answer 1

The correct option is A $13328$ yr

Counter has zero-error of 5 counts per min(cpm)
$\therefore Initialactivity=20.3-5=15.3$ cpm
Activity after time $t=(\frac{40}{5}-5)=3.0$ cpm
$\therefore \lambda =\frac{2.303}{t}log\frac{15.3}{3.0}$
$\frac{0.693}{5668}=\frac{2.303}{t}log\frac{15.3}{3.0}$
$t=13328$ yr