An ancient piece of wood shows an activity of 7.8 disintegration per second, per gram of 14C. What is the age of piece of the wood if fresh 14C, shows an activity of 31.2 disintegration per second per gram? Half life of 14C is 5570 years.

Question

An ancient piece of wood shows an activity of 7.8 disintegration per second, per gram of 14C. What is the age of piece of the wood if fresh 14C, shows an activity of 31.2 disintegration per second per gram? Half life of 14C is 5570 years. (A) 16710 years (B) 33420 years (C) 11140 years (D) 22280 years

Tardigrade Admin · Accepted Answer

A=A0e- λ t 7.8=31.2e- (ℓ n 2/5570) t ⇒ -2ℓ n2=-(ℓ n 2/5570)t Solving, t=11140 years

Q. An ancient piece of wood shows an activity of $7.8$ disintegration per second, per gram of $_^{14} C .$ What is the age of piece of the wood if fresh $_^{14} C,$ shows an activity of $31.2$ disintegration per second per gram? Half life of $_^{14} C$ is $5570$ years.

$16710$ years

$33420$ years

$11140$ years

$22280$ years

$A = A_{0} e^{- λ t}$
$7.8 = 31.2 e^{- \frac{ℓ n 2}{5570} t}$
$\Rightarrow - 2 ℓ n 2 = - \frac{ℓ n 2}{5570} t$
Solving, $t = 11140$ years

Q. An ancient piece of wood shows an activity of 7.8 disintegration per second, per gram of _14C. What is the age of piece of the wood if fresh _14C, shows an activity of 31.2 disintegration per second per gram? Half life of _14C is 5570 years.

16710 years

33420 years

11140 years

22280 years