Answer: The carbon-14 left after 10 years is 25 g
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 rate constant
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]k=\frac{0.693}{5years}=0.139years^{-1}[/tex]
b) for amount left after 10 years
[tex]t=\frac{2.303}{k}\log\frac{a}{(a-x)}[/tex]
[tex]10=\frac{2.303}{0.139}\log\frac{100}{(a-x)}[/tex]
[tex](a-x)=25g[/tex]
Thus carbon-14 left after 10 years is 25 g
