Answer: A. one-fourth
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{0.69}{t_{\frac{1}{2}}}=\frac{0.693}{30}=0.0231[/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 = age of sample = 60 sec
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process =
[tex]60=\frac{2.303}{0.0231}\log\frac{100}{a-x}[/tex]
[tex]\frac{100}{a-x}=4[/tex]
[tex]{a-x}=25[/tex]
Thus as 25 g of radioactive substance would be left after 60 seconds, which is [tex]\frac{25}{10}=\frac{1}{4}[/tex] of the initial amount.
