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Question

A radioactive isotope is being produced at a constant rate dNdt = R in an experiment. The isotope has a half-life t12. Show that after a times t>> t12, the number of active nuclei will become constant. Find the value of this constant. 


Solution

Given : Half life period = t12

Rate of Radio active decay 

= dNdt = R 

R=dNdt

After time t>>t12 the number of active nuclei will become constant 

i.e. (dNdt)present=R=(DNDt)decay

R=(DNDt)decay

R=λN

[Where, λ = Radioactive decay constant, N= constant number]

R=0.693t12(N)

Rt12 = 0.693 N

N=Rt120.693


Physics
Concepts of Physics
Standard XII

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