<u>Answer:</u> The sample of Carbon-14 isotope will take 2377.9 years to decay it to 25 %
<u>Explanation:</u>
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 %