Respuesta :
Answer: 96.34%
Explanation:
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}{5715}=0.00012years^{-1}[/tex]
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 = time for decomposition = 300 years
a = let initial amount of the reactant = 100
a - x = amount left after decay process = ?
[tex]300=\frac{2.303}{0.00012}\log\frac{100}{100-x}[/tex]
[tex]x=3.66[/tex]
[tex](a-x)=100-3.66=96.34[/tex]
Thus 96.34 percent of a given amount remains after 300 years.
