Answer: C) 28.8
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 = initial amount of the reactant = 1.000 g
a - x = amount left after decay process = 0.908 g
a) to find rate constant
[tex]4.00yr=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
[tex]k=\frac{2.303}{4.00}\log\frac{1.000}{0.908}[/tex]
[tex]k=0.024yr^{-1}[/tex]
b) 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}{0.024yr^{-1}}=28.8yr[/tex]
The half-life of strontium-90 is 28.8 yr.
