Nucleus: Practice Problem & Solution
The decay constant of a radio isotope is $\lambda$. If $A_1$ and $A_2$ are its activities at times $t_1$ and $t_2$ respectively, the number of nuclei which have decayed during the time $(t_1 - t_2)$: (2010 Mains)
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:
Activity is related to the number of nuclei by $A = \lambda N$. The number of nuclei at $t_1$ is $N_1 = A_1/\lambda$ and at $t_2$ is $N_2 = A_2/\lambda$. Number of nuclei decayed is $N_1 - N_2 = \frac{A_1 - A_2}{\lambda}$.
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