Derive the relationship between the half-life of a first order reaction,t1/2 and the rate constant k.?

Answer 1

t1/2 = .693/k
k = t1/2/.693

That's the formula, as for deriving it, well I don't know why you would want to do that.

Answer 2

A = A0e^(-kt)

at half life A =A0/2 dividing two sites by A0

so 1/2 =e^(-kt)

2= e^kt

kt =ln2

t = ln2/k =0.693/k