Question

Prove that the instantaneous rate of change of activity of a radioactive substance is inversely proportional to the square of its half life

Answer 1

Activity or decay rate at any instant of time is

A= -N λ
differentiating w.r.t time we get instantaneous rate of change of activity of radioactive substance..
dA / dt= (-dN /dt) λ
Again dN / dt= -N λ
thus dA/ dt= N λ2

dA / dt
= ( 0.693 /(T1/2))^2 × N
(since λ =0.693/ T1/2)
thus...
dA /dt is inversely proportionaltional to T1/2