The `beta-` activity of a sample of `CO_(2)` prepared forma contemporarty wood gave a count rate of `25.5` counts per minute `(cp m)`. The same of `CO_(2)` form an ancient wooden stratue gave a count rate of `20.5 cp m`, in the same counter condition. Calculate its age to the nearest 50 year taking `t_(1//2)` for `.^(14)C` as 5770 year. What would be the expected count rate of an identical mass of `CO_(2)` form a sample which is 4000 year old?

Explanation

`r = 20.5 cp m, r_(0) = 25.5 cp m`
`:' r_(0) prop N_(0)` and `r prop N :' (r_(0))/(r) = (N_(0))/(N)`
Also `t = (2.303)/(lambda)` log `(r_(0))/(r)`
`t = (2.303xx5770)/(0.693)` log `(25.5)/(20.5) = 1817` year
Also, if `t = 4000 yr`, then
`4000 = (2.303xx5770)/(0.693)` log `(25.5)/(r)`
`r = 15.77 cpm`