For half-life period ($t_{1/2}$t1/2​), the general formulas

General formula for $n^{\text{th}}$nth order ($n \neq 1$)

$$\boxed{t_{1/2}=\frac{2^{\,n-1}-1}{(n-1)\,k\,[A]_0^{\,n-1}}}$$

This formula gives:

• Zero order (n=0): $\displaystyle t_{1/2}=\frac{[A]_0}{2k}$
• Second order (n=2): $\displaystyle t_{1/2}=\frac{1}{k[A]_0}$

For first order (n=1), use the separate formula:$$\boxed{t_{1/2}=\frac{0.693}{k}}$$

because the general $n^{\text{th}}$nth-order expression is not valid for n=1