Question

9. C-14 decays to N-14 by beta emission with a half-life of 5730 years. What is the age of an artifact that has a ratio of N-14 to C-14 of 15:1?

10. Refer to question 9 above: If an artifact is found to be 34,380 years old, what fraction of the original amount of C-14 isotope in the artifact has decayed?

Answer 1

rate constant(k) = 0.693/T1/2

                  = 0.693/5730

                  = 1.21*10^-4 y-1

first order kinetics

k = (1/t)ln(a0/a)

k = rate constant = 1.21*10^-4 y-1

t = time taken = ? years

a0 = initial concentration of C-14 = (15+1)= 16

a = final concentration of c-14 = 1

(1.21*10^-4) = (1/t)ln(16/1)

age of an artifact = t = 22913.96 years

10. (1.21*10^-4) = (1/34380)ln(16/a)

   a = final concentration of C-14 = 0.25

amount of C-14 isotope decayed = 16-0.25 = 15.75