Rankers Physics

Uncategorized: Practice Problem & Solution

52. A sample of radioactive element has a mass of 10 gm at an instant $t = 0$. The approximate mass of this element in the sample after two mean lives is: (2003)
1.35 gm
2.50 gm
3.70 gm
6.30 gm

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

Mean life is $\tau = 1/\lambda$. Mass remaining after time $t$ is $m = m_0 e^{-\lambda t}$. After two mean lives, $t = 2\tau = 2/\lambda$. So, $m = 10 e^{-2} = 10 / (2.718)^2 \approx 1.35$ gm.

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