Answer: 2.5 grams
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) to calculate the rate constant:
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}{2years}=0.346years^{-1}[/tex]
b) to find amount left after 4 years
[tex]4=\frac{2.303}{0.346}\log\frac{10}{a-x}[/tex]
[tex](a-x)=2.5g[/tex]
Thus 2.5 g of cesium would remain from a 10 g sample after 4 years
