Answer: 5 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
a = let initial amount of the reactant = x
a - x = amount left after decay process = [tex]\frac{x}{16}[/tex]
a) for calculating k
[tex]20=\frac{2.303}{k}\log\frac{x}{\frac{x}{16}}[/tex]
[tex]k=\frac{2.303}{20}\log{16}[/tex]
[tex]k=0.138years^{-1}[/tex]
b) for calculating 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}{0.138years^{-1}}[/tex]
[tex]t_{\frac{1}{2}}=5years[/tex]
Thus its half life is 5 years
