Looking for classes? Ksquare Career Institute, Bengaluru →
Nuclei
Radioactive Decay Law and Mean Life
1 question from 1 paper, each with its answer.
- question
- 1
- paper
- 1
- of Nuclei
- 1.3%
Concepts tested
- Decay after two mean lives
All Questions
2003 AIPMT 1 question
-
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 :Radioactive decay law: $N = N_0e^{-\lambda t}$, so the mass $m = m_0e^{-\lambda t}$.
Mean life $\tau = \dfrac{1}{\lambda}$, so two mean lives means $t = \dfrac{2}{\lambda}$.
$m = m_0e^{-\lambda(2/\lambda)} = m_0e^{-2}$
$m = \dfrac{10}{e^2} = \dfrac{10}{7.39} \approx 1.35$ gm
So about 1.35 gm of the element remains after two mean lives.