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

Question

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

Infinity Learn · Accepted Answer

The decay rate R of a radioactive material is the number of decays per second.From radioactive decay law,$$-dNdt$$∝N or $$-dNdt=$$λN Thus,$$R=-$$ dNdt or R∝N or $$R=$$λN or $$R=$$λ$$N0e-$$λt    .....(i)Where$$ $$R0=$$λ$$N0$$ is the activity of the radioactive material at time t $$=$$ $$0$$.At time $$t1$$, $$R1=R0e-$$λ$$t1$$    ......$$(ii)At$$ time $$t2$$, $$R2=R0e-$$λ$$t2$$      ......$$(iii)Dividing$$ Eq.$$(ii) by (iii) , we have $$R1R2=e-$$λ$$t1e-$$λ$$t2=e-$$λ(t1-t2) or $$R1=R2e-$$λ(t1-t2)

In a radioactive material the activity at time $t_{1} is R_{1}$ and at a later time $t_{2}, it is R_{2}$ . If the decay constant of the material is $λ$ ,then

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

In a radioactive material the activity at time $t_{1} is R_{1}$ and at a later time $t_{2}, it is R_{2}$ . If the decay constant of the material is $λ$ ,then