Scientists can determine the age of ancient objects by a method called radiocarb

Question

Scientists can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive 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 radioactivity must also decay exponentially. A parchment fragment was discovered that had about 74% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment.

Explanation / Answer

N = No e^ -kt
Given N = 0.74No
and k = 0.6931/T
Here T - half-life period of C-14 = 5730 y
So e^kt = 1/ 0.74
k t = ln 4/3
or required time t = 1/k * ln (1/ 0.74 )
Or t = 5730/ 0.6931 * ln (1/ 0.74)
And t = 2378.3 y
So Age of parchment is nearly 2489.3 years

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