Prove that the instantaneous rate of change of activity of a radioactive substance in inversely proportional to the square of its half life
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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)2N /(T1/2)2 (since λ =0.693/ T1/2)
thus...
dA /dt is directly proportional to T1/2
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)2N /(T1/2)2 (since λ =0.693/ T1/2)
thus...
dA /dt is directly proportional to T1/2
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