Question

In a certain nuclear reactor, a radioactive nucleus is being produced at a constant rate $=1000/s$. The mean life of the radionuclide is $40$ minutes. At steady state, the number of radionuclide will be

• A. $4\times {10}^4$
• B. $24\times {10}^4$
• C. $24\times {10}^5$
• D. $24\times {10}^6$

Answer 1

The correct option is C $24\times {10}^5$

Mean life $T=40min=40\times 60s=2400s$

So decay constant $\lambda =\frac{1}{2400}/s$

At steady state $\frac{-dN}{dt}\text{(rate of decay) should be equal to rate of production}$

But rate of decay es equal to $N\lambda$ also.

so $N\lambda =1000/s$

So $N=\frac{1000}{\lambda }=2400\times 1000=24\times {10}^5$

Option C is correct.