Question

Derive relationship between half life and rate constant for first order reaction

Answer 1

According to question 
Let the half life be t1/2

Thus
For as first order reaction, we have

ln A / A' = -kt
Also 
at t1/2     A = 1/2 A'

Thus
substituting
ln 1/2 = -k t12
t1/2 = 0.693 / K
Thus this the equation for half life for first order reaction

Answer 2

The half-life of a reaction is the time required for the reactant concentration to decrease to one-half its initial value. The half-life of a first-order reaction is a constant that is related to the rate constant for the reaction: t1/2 = 0.693/k. Radioactive decay reactions are first-order reactions