Carbon `-14` decays with half-life of about `5, 800` years. In a sample of bone, the ratio of carbon `-14` to carbon `-12` is found to be `(1)/(4)` of what it is in free air. This bone may belong to a period about `x` centuries ago. Where `x` nearest to

Options

A. `2 xx 58`
B. 58
C. `58//2`
D. `3 xx 58`

Answer

A

Explanation

`T_("Half") = 5,800yr`.
`(C^(14))/(C^(12)) = (1)/(4)`
`(N)/(N_(0)) = (C^(14))/(C^(14)+C^(12)) = (1)/(5) =(1)/(2^(n))`
`5 = 2^(n) = 2^(x//5800)`
n is about 2
`x = 2 xx 5800 yr. = 2xx 58` centuries
`{100 yr. =1` centuries)