A piece of wood from an aechaeological sample has 5.0 counts `"min"^(-1)` per gram of C - 14, while a fresh sample of wood has a count of `15.0 "min"^(-1)`. If half-life of C-14 is 5770 years, the age of the archaeological sample is

Options

A. 8,500 years
B. 9,200 years
C. 10,000 years
D. 11,000 years

Answer

B

Explanation

Radioactive decay follows first order kinetics.
Now, `t_(1//2) = 5770` years
`lambda = (0.693)/(t_(1//2)) = (0.693)/(5770) "years"^(-1)`
where , `lambda` = decay constant
If age is t years, then
`t = (2.303)/(lambda) log_(10) ("activity of the fresh sample")/("activity of archaecological sample")`
`implies t = 2.303 xx (5770)/(0.693) xx log_(10) 15/5`
`implies t = 9149` years `~~ 9200` years (approx).