Answer: Half-life of the substance is 16 years.
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 = 48 years
a = initial amount of the reactant = 240 micrograms
a - x = amount left after decay process = 30 microgarms
[tex]48=\frac{2.303}{k}\log\frac{240}{30}[/tex]
[tex]k=\frac{2.303}{48}\log\frac{240}{30}[/tex]
[tex]k=0.0433years^{-1}[/tex]
b) [tex]t_{\frac{1}{2}}[/tex] of reaction
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}=\frac{0.693}{0.0433}=16years[/tex]
Thus half-life of the substance is 16 years.
