Question

A carbon sample from the frame of picture gives 7 counts of $C^{14}$ per minute per gram of carbon. If freshly cut wood gives 15.3 counts of $C^{14}$ per minute, calculate the age of frame. ($t_{1/2}of{C}^{14}$ = 5570 years)

• A. 6286 years
• B. 5527 years
• C. 5570 years
• D. 4570 years

Answer 1

The correct option is A 6286 years

For $1^{st}$ order radio active disintegration,

$K=\frac{1}{t}ln\frac{a_{\circ }}{a_t}$

here, $a_{\circ }=15.3$ counts per minute,

$a_t=7$ counts per minute, $K=\frac{ln2}{t_{\frac{1}{2}}}$

$\therefore \frac{ln2}{5570}=\frac{1}{t}ln\frac{15.3}{7}$

$\therefore t=$age of frame$\approx 6286$ years.