Answer: 243 hours
Explanation:
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant
t = age of sample
a = initial amount of the reactant = [tex]5.000\mu g[/tex]
a - x = amount left after decay process = [tex]\frac{10}{100}\times 5.000\mu g=0.5\mu g[/tex]
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.
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]k=\frac{0.693}{73.00hours}=9.49\times 10^{-3}hours^{-1}[/tex]
b) for reducing the mass to 10.00 % of its original mass
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
[tex]t=\frac{2.303}{9.49\times 10^{-3}}\log\frac{5.000}{0.5}[/tex]
[tex]t=243hours[/tex]
The time taken to reach 10.00 % of its original mass is 243 hours
