Answer
Please see the work below.
Work Step by Step
We know that a half-life is actually the time required for the concentration of a reactant or the amount of a radioactive isotope to fall to one-half of its initial value.
Now we write the expression for the half-life of a zero-order reaction
$t_{\frac{1}{2}}=\frac{[A]_0}{2k}$
The half-life of a first-order reaction is given as
$t_{\frac{1}{2}}=\frac{\ln 2}{k}$
The half-life for a second order reaction is
$t_{\frac{1}{2}}=\frac{1}{k[A]_0}$
