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
$\frac{D_{A} N_{A}}{D_{B}}$
B
$\frac{D_{B} N_{A}}{D_{A}}$
C
$\frac{(D_{A} + D_{B}) N_{A}}{D_{B}}$
D
$\frac{D_{B}}{(D_{A} + D_{B})} N_{A}$

Solution:

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

$A c t i v i t y = R = λ N w h e r e λ i s d e c a y c o n s \tan t I f R i s s a m e t h e n {λ_{1} N}_{1} = {λ_{2} N}_{2}$
[Step 1]: i.e. $D_{A} N_{A} = D_{B} N_{B}$
[Step 2]: $∴ N_{B} = \frac{D_{A} N_{A}}{D_{B}}$

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

Solution:

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