The half-life T1/2 and the disintegration constant λ of a radioactive substance are related as
λT1/2=1
λT1/2=0.693
T1/2λ=0.693
By using N=N0e-λt, we get
N02=N0e-λT1/2⇒2=eλT12
By taking loge both the side
loge2=λT1/2⇒λT1/2=0.693