11this is an iit q.
Given a sample pf Radium-2008 having half life of 4 days. Find the probability, nucleus disintegrates after 2 half lives.
A. 1
B. 1/2
C. 1.5
D. 3/4
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8 Answers
66Starting with N0 nuclei, the number of nuclei at the end of time t is
N=N_0e^{-\lambda t}
where \lambda = \dfrac{\ln 2}{T_{1/2}}
So the number of nuclei disintegrated till time t equals N_0(1-e^{\lambda t})
So the probability that a nucleus disintegrates after time t is
p(t)=\dfrac{N_0(1-e^{\lambda t})}{N_0}=1-e^{-\lambda t}
For the present problem, t = 2 T1/2
Thus,
p(2T_{1/2})=1-e^{-\lambda 2T_{1/2}}=1-e^{-2\ln 2}=1-\dfrac{1}{4}=\dfrac{3}{4}
So Nishant sir's answer is indeed correct.
