Explanation

(a) $N = N_{0}\left( \frac{1}{2} \right)^{t/T_{1/2}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ N_{A} = \ 10\ \left( \frac{1}{2} \right)^{t/1}and\ \ N_{B} = \ 1\left( \frac{1}{2} \right)^{t/2}$
Given $N_{A} = N_{B}$
$\Rightarrow \ \ \ \ 10\ \left( \frac{1}{2} \right)^{t}\ = \left( \frac{1}{2} \right)^{t/2} \Rightarrow \ 10\ = \left( \frac{1}{2} \right)^{- t/2}$
$\Rightarrow$ $\ \ \ \ \ \ \ \ \ \ \ \ \ 10\ = \ 2^{t/2}$
Taking log on both the sides
$\ \ \ \ \ \ {\ \log_{10}}{10\ }\ = \ \frac{t}{2}\ \log_{10}2\ \ \Rightarrow \ 1 = \ \frac{t}{2} \times \ 0.3010$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ t\ = \ 6.62\ yr$