The half-life for the radioactive decay of C-14C-14 is 5730 years. You may want to reference (Pages 598 - 605) Section 14.5 while completing this problem. Part A How long will it take for 25% of the C-14C-14 atoms in a sample of C-14C-14 to decay

The sample of Carbon-14 isotope will take 2377.9 years to decay it to 25 %

Explanation:

The equation used to calculate rate constant from given half life for first order kinetics:

where,

= half life of the reaction = 5730 years

Putting values in above equation, we get:

Rate law expression for first order kinetics is given by the equation:

where,

k = rate constant  =

t = time taken for decay process = ? yr

= initial amount of the sample = 100 grams

[A] = amount left after decay process =  (100 - 25) = 75 grams

Putting values in above equation, we get:

Hence, the sample of Carbon-14 isotope will take 2377.9 years to decay it to 25 %