The half-life of radioactive carbon-14 is 5730 years. If the 14C level in a sample of organic matter has been reduced to 0.200% of its original value, approximately how much time has passed? Radioactive decay follows first-order kinetics.

a. 1650 years
b. 51,400 years
c. 29,900 years
d 2,870,000 years
e. 9220 years

The time for organic matter has been reduced to 0.200% of its original value is 51400 years

Explanation:

Expression for rate law for first order kinetics is given by:

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant = 100

a - x = amount left after decay process =

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

b) for reduction to 0.200% of its original value

The time for organic matter has been reduced to 0.200% of its original value is 51400 years