Solution:
$$
t_{1 / 2}=\frac{0.693}{k} ; N=N_{0^{-(-k)}}
$$
$$
\begin{aligned}
&\ln \frac{N}{N_{0}}=-k t \\
&\Rightarrow k t=\ln \left(\frac{N_{0}}{N}\right) \\
&\therefore \frac{1}{N}-\frac{1}{N_{0}}
\end{aligned}
$$
\(=\ln k t_{1 / 2}\) is not correct