For a first order reaction half life period `t(1/2)`is independent of initial concentration of its reacting species. By deriving the equation for `t(1/2)`of first order reaction, prove that `t_(1/2)`is independent of initial concentration of its reacting species.

Explanation

For a first order reaction,`k=2.303/tlog[[R_0]]/[[R]]`When t=`t_(1/2)[R]=[[R_0]]/2,`
`t_(1/2)=2.303/k log([[R_0]]/[[R_0]])/2 `
`2.303/klog2=(2.303xx0.3010)/k
thereforet^(1/2)=0.693/k`