Question

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

Answer 1

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

Step-by-step explanation:

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

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant = 100

a - x = amount left after decay process =
`(0.200)/(100)* 100=0.200`

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.

`t_{(1)/(2)}=(0.693)/(k)`

`k=(0.693)/(5730)=0.00012years^(-1)`

b) for reduction to 0.200% of its original value

`t=(2.303)/(0.00012)\log(100)/(0.200)`

`t=51400years`

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