Question

What is half life period? Derive its derivation.

Answer 1

It is the time in which concentration of reactant is reduced to one half of the initial concentration. It is denoted by $t_{1/2}$.
Derivation of half life period:
We know that for first order reaction
$K=\frac{2.303}{t}\log \frac{a}{(a-x)}$
or $t=\frac{2.303}{K}\log \frac{a}{(a-x)}$
If $t=t_{1/2}$ and $x=\frac{a}{2}$
then $t_{1/2}=\frac{2.303}{K}\log \frac{a}{(a-\frac{a}{2})}$
$t_{1/2}=\frac{2.303}{K}\log 2$
$t_{1/2}=\frac{2.303}{K}\times 0.3010$ $(\because \log 2=0.3010)$
$t_{1/2}=\frac{0.693}{K}$
Above equation is the derivation of half life period.