Find the half life time period for first order reaction.

Explanation

The first order rate equation for reaction
`kt = 2.303 "log" ([A]_0)/([A])`
`t = (2.303)/k "log"([A]_0)/([A])`
half life time means that concentration decrease to half if its initial concentration
`[A] = ([A]_0)/(2) " and " t = (t_(1/2))`
`t_(1/2) = (2.303)/(k) "log" ([A]_0)/([A]_0) 2`
`t_(1/2) = (2.303)/(k) xx log 2 " " [log 2 = 0.3010]`
`t_(1/2) = (2.303)/(k) xx 0.3010`
`t_(1/2) = (0.693)/(k)`
It shows that half life period of a first order reaction independent of Initial concentration of its reactant.