Prove that the instantaneous rate of change of activity of a radioactive substance is inversely proportional to the square of half life.
Text Solution
Verified by Experts
Activity `R=-(dN)/(dt)=lambdaN` The instantaneous rate of change of activity `(dR)/(dt)=d/(dt)(lambdaN)=lambda (dN)/(dt)=lambda(-lambdaN)=-lambda^2N` `=((0.693)/T)^2N=(0.693^2N)/(T^2)` Clearly, `(dR)/(dt) prop1/(T^2)`, which was to be proved.
Topper's Solved these Questions
ATOMS AND NUCLEI
PRADEEP|Exercise (II) very short answer 16|1 Videos
ATOMS AND NUCLEI
PRADEEP|Exercise (I) Short Answer questions 1|1 Videos
COMMUNICATION SYSTEMS
PRADEEP|Exercise MODEL TEST PAPER-2|9 Videos
Similar Questions
Explore conceptually related problems
The activity of a radioactive substance is readuced by 80% in 100 days. Its half life is
The half-life of a radioactive substance is 10 days. This means that
Show that the rate constant in a zero order reaction is inversely proportional of its half life period.
Rate of diffusion is directly proportional to the square root of molecular mass of substance.
The half life of radioactive substance is T. Then the fraction of the substance that has decayed in time t is-
PRADEEP-ATOMS AND NUCLEI-Assertion- Reason type question 12
