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 $\frac{dN}{dt}=-\lambda N$.

The number of nuclei of B will first increase then after a maximum value, it will decreases, if

• A. ${\lambda }_1>{\lambda }_2+{\lambda }_3$
• B. ${\lambda }_1={\lambda }_2={\lambda }_3$
• C. ${\lambda }_1={\lambda }_2+{\lambda }_3$
• D. For any values of ${\lambda }_1,{\lambda }_2$ and ${\lambda }_3$

Answer 1

The correct option is A ${\lambda }_1>{\lambda }_2+{\lambda }_3$

If we assume option C to be correct, then rate of decay of A to B is same as rate of decay of B to X plus rate of decay from B to Y which means number of nuclei of B will not increase and rather remain same. So clearly option C is correct.

If we assume option B to be correct, then rate of decay of A to B is same as rate of decay of B to X and rate of decay from B to Y which means in due time course number of nuclei of B will decrease.

Now, clearly when ${\lambda }_1>{\lambda }_2+{\lambda }_3$, number of nuclei of B will first increase but after a maximum value when A is decayed completely, B will start decreasing. So, option A is correct.