A piece of wood from an archaeological source shows a `.^(14)C` activity which is `60%` of the activity found in fresh wood today. Calculate the age of the archaeological sample. (`t_(1//2)` for `.^(14)C = 5570` year)

Answer

4252 years

Explanation

`((a)/(a-x))=(N_(0))/(N)=(100)/(60)`
`K=(0.693)/(t_(1//2))=(0.693)/(57770)`
`:.t=(2.303)/(K)log((N_(0))/(N))`
`=(2.303xx5770year)/(0.693)log((100)/(60))`
`:.t=(2.303)/(K)log((N_(0))/(N))`
`=(2.303xx5770year)//(0.693)(2-1.7781)`
`=4252 years`