Question

The rate at which a particular decay process occurs in a radioactive sample, is proportional to the number of radioactive nuclei present. If N is the number of radioactive nuclei present at some instant, the rate of change of N is $\frac{dN}{dt}=-\lambda N$.

At $t=\infty$, which of the following incorrect?

• A. $N_2=0$
• B. $N_3=\frac{2N_0{\lambda }_2}{{\lambda }_2+{\lambda }_3}$
• C. $N_4=\frac{2N_0{\lambda }_2}{{\lambda }_2+{\lambda }_3}$
• D. $N_3+N_4+N_1+N_2=2N_0$

Answer 1

The correct option is C $N_4=\frac{2N_0{\lambda }_2}{{\lambda }_2+{\lambda }_3}$

At $t=\infty$, A and B will have decayed completely. So total number of nuclei of X and Y will be $2N_0$ which will be distributed in the ratio of thier decay rate constant.
So, respective nuclei of A,B, X and Y can be written as,

Clearly, we can match that option C is incorrect.