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  • A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half lif

A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of C14 is 5730 years, then age of the wooden piece placed in the museum is approximately :

 

Option: 1

 10439 years
 


Option: 2

13094 years


Option: 3

 19039 years

 


Option: 4

39049 years


Answers (1)

best_answer

Given

A_{0}=20 decays/min

After some time t

A_{t}=2 decays/min

\because A_{t}= A_{o}. e^{-xt} \ \ or 2=20.e^{-\lambda t}

\Rightarrow e^{-\lambda t}= \frac{1}{10} \ or \ \lambda t= ln (10)

t= \frac{ln10}{\lambda } =(\frac{ ln10}{ln2}) t_\frac{1}{2}\cong 19039\ years

\because t_\frac{1}{2}=5730\ years

Posted by

Suraj Bhandari

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