What is the age of an ancient wooden piece if it is known that the specific activity of `C^(14)` nuclide in it amounts to `3//5` of that in fresh trees? Given: the half of `C` nuclide is `5570 years` and `log_(e)(5//3)=0.5` .

Options

A. `1000 years`
B. `2000 years`
C. `3000 years`
D. `4000 years`

Answer

D

Explanation

`(3)/(5)N_(0) =N_(0) e^(- lambda t)`
`rArr e^(lambda t) =(5)/(3)`
`log_(e) e^(lambda t) =log_(e).(5)/(3)` or `lambda t=log_(e) .(5)/(3)`
or `t=(1)/(lambda) log_(e).(5)/(3)`
`=(T)/(0.693) xx0.5 [:. T=(0.693)/(lambda)]`
`=(5570xx0.5)/(0.693) years =4018.7 years`

`4000 years`