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 A₀ is the initial activity of the sample. and A_t is the activity of sample at any time t.

T = 0.18 × 10⁴ years.

Age of given sample is 0.18 × 10⁴ years.