Determine the age of ancient wooden item if it is known that the specific activity of `C^(14)` nuclide in them amounts to `3//5` of that in lately felled trees. The hlaf-life of `c^(14)` nuclei is `5570 years`

Explanation

In old wooden atoms the number of `C^(14)` nuclei steadily decreases because of radioactive decay. (In live trees biological process keep replenshing `C^(14)` nuclei maintaining a balance. This balance starts getting disrupeted as soon as the tree is felled.)
If `T_(1//2)` is the half life of `C^(14)` then `e^(-txx(In 2)/(T_(1//2)))=(3)/(5)`
Hence `t=T_(1//2)(In 5//3)/(In 2)= 4105 years ~~ 4.1 xx10^(3)years`