1.

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

Answer»

8,500 years
9,200 years
10,000 years
11,000 years

SOLUTION :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).


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