Nucleus: Practice Problem & Solution
The half life of a radioactive nucleus is 50 days. The time interval $(t_2 - t_1)$ between the time $t_2$ when 2 / 3 of it has decayed and the time $t_1$ when 1 / 3 of it had decayed is: (2012 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:
At $t_1$, fraction remaining is $1 - 1/3 = 2/3$. At $t_2$, fraction remaining is $1 - 2/3 = 1/3$. The ratio of remaining nuclei is $(1/3)/(2/3) = 1/2$. This represents exactly one half-life, which is 50 days.
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