- Home
- Standard 12
- Physics
13.Nuclei
medium
Two radioactive nuclei $A$ and $B$ both convert into a stable nucleus $C$. At time $t = 0$ nuclei of $A$ are $4N_0$ and that of $B$ are $N_0$. Half life of $A$ is $1\, min$ and that of $B$ is $2\, min$. initially number of nuclei of $C$ are zero. At what time rate of disintegrations of $A$ and $B$ are equal .......... $min$
A
$4$
B
$6$
C
$8$
D
$2$
Solution
$A \rightarrow C$
$B \rightarrow C$
First order decay:
$\frac{d A}{d t}=-\lambda_{A} A$
$\frac{d B}{d t}=-\lambda_{B} B$
$A=4 N_{o} e^{-\lambda_{A} t}$
$B=N_{o} e^{-\lambda_{B} t}$
Rates of disintegration equal:
$\frac{d A}{d t}=\frac{d B}{d t}$
$4 \lambda_{A} e^{-\lambda_{A} t}=\lambda_{B} e^{-\lambda_{B} t}$
$4 \frac{\ln 2}{1} e^{-\frac{ln}{1} t}=\frac{\ln 2}{2} e^{-\frac{ln2}{2} t}$
$t=6 \min$
Standard 12
Physics
