When charcoal is prepared from a living tree, it shows a disintergration rate of 15.3 disintergrations of ``^14C` per gram per minute. A sample form an ancient piece of charcoal shows ``^14C`activity to be 12.3 disintergrations per gram per minute. How old is this sample ? Half-life of ``^14C` is 5730 y.

Answer

A

Explanation

Given ` A_(0) = 15.3,A = 12.3, `
`t_(1/2) = 5730 year `
` lambda = (0.6931)/(t_(1/2) ) = (0.6931)/(5730) yr_(_1) `
Let the time passed be t,
` We know A = A_(0 e) ^(0.6991)/(2780) xx t ` Brgt ` rArr in (123)/(153) = (-06931)/(5730) t )`
`rArr t = 1804.3 xx t ` .