A piece of wood was found to have `""^(14)C//^(12)C` ratio 0.7 times that in a living plant. Calculate the period (in years) when the plant died. (`t_((1)/(2)) " for " C^(14)= 5760yr`)

Options

A. 2770 yr
B. 2966 yr
C. 2980 yr
D. 3070 yr

Answer

B

Explanation

Given, `N_(0) = 1N, N_(t) = 0.70 and t_(1//2) = 57600 yr`
`k = (0.693)/(t_(1//2)) = (0.693)(5760)`
We also know, `k = (2.303)(t) "log" (N_(0))/(N_(t)) = (0.693)/(5760)`
or `t = (2.303 xx 5760 xx 0.155)/(0.693) = 2966yr`