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.
\(t_{\frac{1}{2}}=\frac{0.693}{k}\)
\(k=\frac{0.69}{t_{\frac{1}{2}}}=\frac{0.693}{30}=0.0231\)
Expression for rate law for first order kinetics is given by:
\(t=\frac{2.303}{k}\log\frac{a}{a-x}\)
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 =
\(60=\frac{2.303}{0.0231}\log\frac{100}{a-x}\)
\(\frac{100}{a-x}=4\)
\({a-x}=25\)
Thus as 25 g of radioactive substance would be left after 60 seconds, which is \(\frac{25}{10}=\frac{1}{4}\) of the initial amount.
