2003 AIPMT NucleiRadioactive Decay Law and Mean Life Medium Question 63 of 77 in Nuclei

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 :

A 1.35 gm
B 2.50 gm
C 3.70 gm
D 6.30 gm

The answer is A.

Solution

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.

Concept Decay after two mean lives

Nuclei in past papers

77 questions from this chapter have appeared across 26 exam years.