Respuesta :
Answer: a) 3.85 days
b) 10.54 days
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 = time taken for decomposition = 3 days
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process = [tex]\frac{58}{100}\times 100=58g[/tex]
First we have to calculate the rate constant, we use the formula :
Now put all the given values in above equation, we get
[tex]k=\frac{2.303}{3}\log\frac{100}{58}[/tex]
[tex]k=0.18days^{-1}[/tex]
a) Half-life of radon-222:
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]t_{\frac{1}{2}}=\frac{0.693}{0.18}=3.85days[/tex]
Thus half-life of radon-222 is 3.85 days.
b) Time taken for the sample to decay to 15% of its original amount:
where,
k = rate constant = [tex]0.18days^{-1}[/tex]
t = time taken for decomposition = ?
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process = [tex]\frac{15}{100}\times 100=15g[/tex]
[tex]t=\frac{2.303}{0.18}\log\frac{100}{15}[/tex]
[tex]t=10.54days[/tex]
Thus it will take 10.54 days for the sample to decay to 15% of its original amount.
