A parent radioactive nucleus A (decay constant  DA) converts into a radioactive nucleus B of decay constant  DB. Initially number of atoms of B is zero. At any time NA, NB  are number of atoms of nuclei A and B respectively. Then maximum value of  NB is

# A parent radioactive nucleus A (decay constant  ${\text{D}}_{\text{A}}$) converts into a radioactive nucleus B of decay constant  ${\text{D}}_{\text{B}}$. Initially number of atoms of B is zero. At any time   are number of atoms of nuclei A and B respectively. Then maximum value of  ${\text{N}}_{\text{B}}$ is

1. A

$\frac{{D}_{A}{N}_{A}}{{D}_{B}}$

2. B

$\frac{{D}_{B}{N}_{A}}{{D}_{A}}$

3. C

$\frac{\left({D}_{A}+{D}_{B}\right){N}_{A}}{{D}_{B}}$

4. D

$\frac{{D}_{B}}{\left({D}_{A}+{D}_{B}\right)}{N}_{A}$

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### Solution:

[Concept]: NB reaches maximum when activity of A and B will be same

[Step 1]: i.e.  ${D}_{A}{N}_{A}={D}_{B}{N}_{B}$
[Step 2]:  $\therefore {N}_{B}=\frac{{D}_{A}{N}_{A}}{{D}_{B}}$

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