Q. 18

# A piece of wood from the ruins of an ancient building was found to have a ^{14}C activity of 12 disintegrations per minute per gram of its carbon content. The ^{14}C activity of the living wood is 16 disintegrations per minute per gram. How long ago did the tree, from which the wooden sample came, die? Given half-life of ^{14}C is 5760 years.

Answer :

The time from which the wooden sample came died

Given

The rate the disintegration for ancient wood; = 12, rate the disintegration for living wood; = 16. The half live of = 5760 years. To find the time for the death of the sample find the relationship between rate of decay and time taken to decay.

Formula Used

Rutherford and Soddy Radioactive Decay Law: The law tells us that the chances of a radioactive decay of an atom with respect to time is constant in nature and is independent of time. The formula is

where

is the initial quantity of the substance, is the quantity that remained after initial decay, is called the decay constant can be written as , T is the time required for the decay.

Explanation

The rate of disintegration of Ancient wood (: = 12

The rate of disintegration of living wood or initial number of atom (): = 16

Shifting places to remove the negative power of the decay rate constant

The value of can be written as

After calculation we get the solution as

Therefore, the sample that died was 2391.2 years ago.

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