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

Question 4.14: The half-life for radioactive decay of ¹⁴C is 5730 years. An archaeological artifact containing wood had only 80% of the ¹⁴C found in a living tree. Estimate the age of the sample.
Answer
If initial concentration [R]_{o =}100 g
Then final concentration, [R] = 80 % of 100 = 80 g
Given that half life t_1/2 = 5730 year
Use the formula

Plug the value of t _½ in this formula we get
k = 0.693/ 5730 years^-1 = 1.21 x 10 ^-4 years ^-1
Use the formula of first order reaction

Plug the values in this formula we get

t = 1845 years