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

Explanation:

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

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant = 100

a - x = amount left after decay process = $\frac{0.200}{100}\times 100=0.200$

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.

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$k=\frac{0.693}{5730}=0.00012years^{-1}$

b) for reduction to 0.200% of its original value

$t=\frac{2.303}{0.00012}\log\frac{100}{0.200}$

$t=51400years$

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