A piece of charcoal from the ruins of a settlement in Japan was found to have `.^(14)C//``.^(14)C` ratio what was `0.617` times that found in living organisms. How old is the piece of charcol? (`t_(1//2)` for `.^(14)C` is 5770 year?)

Explanation

Given, `t_(1//2) = 5770 yr`
`(N_(C^(14)))/(N_(C^(12))) = 0.167xx (N_(OC^(14)))/(N_(OC^(12)))`
`:' C^(14)` undergoes decay and `C^(12)` does not,
`:. N_(C^(12)) = N_(OC^(12))`
`:. (N_(OC^(14)))/(N_(C^(14))) = (1)/(0.617)`
`t = (2.303)/(lambda) log (N_(0))/(N)`
`= (2.303xx5770)/(0.693) log (1)/(0.617) = 4021.29 yr`