Nucleus: Practice Problem & Solution
Two radioactive materials $X_1$ and $X_2$ have decay constants $5\lambda$ and $\lambda$ respectively. Initially they have the same number of nuclei, then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $1/e$ after a time: (2008)
Solution Explained:
To solve this problem, we apply the core principles of Nucleus. Understanding the underlying formula is key to arriving at the correct answer below:
The number of nuclei are $N_1 = N_0 e^{-5\lambda t}$ and $N_2 = N_0 e^{-\lambda t}$. Their ratio is $N_1/N_2 = e^{-4\lambda t} = e^{-1}$. Therefore, $4\lambda t = 1$, yielding $t = \frac{1}{4\lambda}$.
Leave a Reply