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

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

Grade:Upto college level

1 Answers

Anshuman Chand
13 Points
3 years ago
A=-(lambda)*N; here A is activity of the substanceDifferentiating,dA/dt= -(dN/dt)*(lambda)or dA/dt= (lambda)* N* (lambda)Since dN/dt=(lambda)* NNow, lambda = 0.693/T(1/2); T(1/2) is half life.So, dA/dt= (N* (0.693*0.693))/(T(1/2)*T(1/2))Hence, proved

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