Explain Half Life of a reaction.

Question

$\begin{array}{1 1} (a)\;t_{\frac{1}{2}} = \frac{0.093}{k}\\ (b)\;t_{\frac{1}{2}} = \frac{0.693}{k^2} \\(c)\;t_{\frac{1}{2}} = \frac{0.793}{k} \\(d)\;t_{\frac{1}{2}} = \frac{0.693}{k} \end{array}$