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

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

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Decay constant (k) = `0.693/(t_1//2) = (0.693/5730yr^(-1))`
Radio active dacays follow first order kinetics
`t=2.303 / k log""([A]_0)/([A])`
`k = 0.693/ 5730 yr^1[A]_0= 100%, [A] = 80%`
`:.t = ((2.303 xx 5730)/0.693) xx log"" 100/80`
`=((2.303 xx 5730 xx0.0969)/0.693)= 18 45` years.
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