Answer: The amount left after 4.94 days is [tex]0.875\mu g[/tex]
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
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.
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]k=\frac{0.693}{3.8}=0.18days^{-1}[/tex]
b) to calculate amount left after 4.94 days
[tex]t=\frac{2.303}{0.18}\log\frac{2.1\mu g}{a-x}[/tex]
[tex]4.94=\frac{2.303}{0.18}\log\frac{2.1\mu g}{a-x}[/tex]
[tex]\log\frac{2.1\mu g}{a-x}=0.39[/tex]
[tex]\frac{2.1\mu g}{a-x}=2.4[/tex]
[tex]{a-x}=0.875\mu g[/tex]
The amount left after 4.94 days is [tex]0.875\mu g[/tex]
