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

The half-life for radioactive decay of `.^14C` is 5730 years. An archaeological artifact contented wood that has only 80% of the `.^14C` found in living tree. Estimate the age of the sample.

Text Solution

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Decay constant. `K = (0.693)/(t_(1/2)) `[Half life period equation]
`t_(1/2) = 5730 `years
`K = 1.209 xx 10^(-4)"year"^(-1)`
` N_0 = 100, N=80 `
`t = (2303)/(K) "log" ([A]_0)/([A])`
(First Order Equation)
`t = 2.303 log ([N_0])/(N)`
`= (2.303)/(1.209 xx 10^(-4)) xx "log" (100)/(80)`
`= (2.303)/(1.209 xx 10^(-4)) xx 0.693 `
` 1846 `years.
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