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

Explanation

Given R=12 dis`//`min per g, `R_(0) =16 dis//min`per g `T_(1//2) = 5760`yr
Let t be the span of the tree. ,
According to radioactive decay law
`R=R_(0)e^(-lambdat) " or " R/R_(0) =e^(-lambdat) " or " e^(lambdat) =(Re)/(R) `
Taking log on both the sides
`lambdat log_(e) e= log_(e). (R_(0))/R rArr lambdat=(log_(10) .(16)/(12)) xx 2.303`
`t=(2.303 (log 4 - log3))/(lambda)`
`=(2.303 (0.6020 - 4.771) xx 5760)/(0.6931)" "(":." lambda =(0.6931)/(T_(1//2)))`
`=2391 . 20 yr`