Scientist can determine the age of ancient objects by a method called radiocarbo

Question

Scientist can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen isotope of carbon, ^14C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates ^14C through food chains. When a plant or animal dies. It stops replacing its carbon and the amount of ^14C begins to decrease through radioactive decay. Therefore, the level of radioactive must also decay exponentially. A parchment fragment was discovered that had about 67% as much ^14C radioactivity as does not plant material on Earth today. Estimate the age of the parchment.

Explanation / Answer

We knoe that the decay equation; N = No e^ (-kt)
Given N = 0.61No
and k = 0.6931/T where T is half life cycle
Here given - half-life period of C-14 =T= 5730 years
So, 0.61No=Noe^(-kt)

Or, e^(-kt)=0.61

Or, e^(kt)=1/0.61
k t = ln (100/61)
or required time, t = 1/k * ln (100/61)
Or t = T/0.6931* ln(100/61) =5730/ 0.6931 * ln(100/61)
And t=4086.4 years
So Age of parchment is nearly 4086 years

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