The half-life for radioactive decay of 14C is 5730 years. An archeological artifact containing wood had only 80%of the 14C found in a living tree. Estimate the age of the sample.

Radio active decay occurs via first order rate law,

t_{1/2} = 5730 years. rate constant(k) of given decay is 0.693/t_{1/2}

⇒ 0.693/5730 = 1.2 × 10^{-4} year^{-1}

By first order integrated rate law age of sample will be,

where T is the age of sample A_{0} is the initial activity of the sample. and A_{t} is the activity of sample at any time t.

T = 0.18 × 10^{4} years.

__Age of given sample is 0.18 × 10 ^{4} years.__

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