Question

Radioactive manganese-52 decays with a half-life of 5.6 days. A chemist obtains a fresh sample of manganese-52 and measures its radioactivity. She then determines that to do an experiment, the radioactivity cannot fall below 25% of the initial measured value. How long does she have to perform the experiment?

Answer 1

Answer: 11.2 days

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

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.

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

$k=\frac{0.693}{5.6days}=0.124days^{-1}$

b) for completion of 75% of reaction

$t=\frac{2.303}{0.124}\log\frac{100}{100-75}$

$t=\frac{2.303}{0.124}\log\frac{100}{25}$

$t=11.2days$

The time for which she has to perform the experiment is 11.2 days