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The half-life for radioactive decay of "...

The half-life for radioactive decay of `""^(14)C` is 5730 yr. An archaeological artifact containing wood had only 80% of the `""^(14)C` found in a living tree. Calculate the age of the sample.

Text Solution

Verified by Experts

`t_(1//2) = (0.693)/( k) " (for first order reaction)"`
`therefore k = (0.693)/(t_(1//2)) = (0.693)/( 5730) yr^(-1)`
We know that,
`t= (2.303)/(k) log"" ([R]_0)/([R]) = (2.303)/( (0.693)/(5730) ) log"" (100)/(80) ( "As", = (0.693)/(t_1//2) )`
`= (2.303 xx 5730)/(0.693) log"" (100)/(80) = (2.303 xx 5730)/(0.693)log"" 1.25`
`= (2.303 xx 5730)/(0.693) xx 0.0969 = 1845` yr (approx.).
Therefore, the age of the given archaeological artifact containing wood is 1845 yr.
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