Nucleus: Practice Problem & Solution
Two radioactive substances A and B have decay constants $5\lambda$ and $\lambda$ respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be $(1/e)^2$ after a time interval: (2007)
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:
$N_A = N_0 e^{-5\lambda t}$ and $N_B = N_0 e^{-\lambda t}$. The ratio is $N_A/N_B = e^{-4\lambda t} = (1/e)^2 = e^{-2}$. This gives $4\lambda t = 2$, which implies $t = 1/2\lambda$.
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