In a first order reaction $A \to B,$ if $k$ is the rate constant and the initial concentration of the reactant $A$ is $0.5 \ M,$ then the half-life is:

• A
  $\frac{\ln 2}{k}$
• B
  $\frac{0.693}{0.5 \ k}$
• C
  $\frac{\log 2}{k}$
• D
  $\frac{\log 2}{k \ \sqrt{0.5}}$