NEET Physics Nuclei Questions Solved

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In a radioactive material the activity at time t1 is R1 and at a later time t2, it is R2. If the decay constant of the material is λ, then

(a) R1=R2e-λt1-t2                                    (b) R1=R2eλt1-t2

(c) R1=R2t2t1                                          (d) R1=R2

(a) The decay rate R of a radioactive material is the number of decays per seconds.

From radioactive decaylaw,

      -dNdtN

or    -dNdt=λN

i.e. Rate of reaction is directly proportional to the initial concentration of reactants.

Thus,     R=-dNdt     or   RN

or         R=λN   or R=λN0e-λt                     ...(i)

where R0=λN0 is the activity of the radioactive material at time t=0.

At time t1,           R1=R0 e-λt1                      ...(ii)

At time t2,             R2=R0 e-λt2                      ...(iii)

Dividing Eq. (ii) by Eq. (iii), we have 

       R1R2=e-λt1e-λt2=e-λt1-t2

or    R1=R2 e-λt1-t2

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