1. Tardigrade
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  4. 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.

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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.

NTA AbhyasNTA Abhyas 2020

Solution:

$A=A_{0}e^{- \lambda t}$
$7.8=31.2e^{- \frac{\ell n 2}{5570} t}$
$\Rightarrow -2\ell n2=-\frac{\ell n 2}{5570}t$
Solving, $t=11140$ years