Atoms And Nuclei Question 409
Question: A radioactive element decays by p emission. A detector records n beta particles in 2 second and in next 2 seconds it records $ 0.75n $ beta particles. Find mean life corrected to nearest whole number. Given $ \ell n2=0.6931 $ and $ \ell n3=1.0986. $ .
Options:
A) $ 6.9sec $
B) $ 9.9sec $
C) $ 10.1sec $
D) $ 12.2sec $
Show Answer
Answer:
Correct Answer: A
Solution:
- We know that, $ N=N_{0}{{e}^{-\lambda t}} $
After 2 second, $ N_{1}=N_{0}{{e}^{-\lambda \times 2}} $ After $ (2+2) $ second, $ N_{2}=N_{0}{{e}^{-\lambda \times 4}} $ According to given conditions, $ N_{0}-N_{1}=n $ or $ N_{0}-N_{0}{{e}^{-2\lambda }}=n $ …(i) and
$ N_{0}{{e}^{-2\lambda }}-N_{0}{{e}^{-4\lambda }}=0.75,n $ … (ii)
After solving above equations, we get $ \lambda =0.145,s $ Mean life $ T=1/\lambda =6.9s $ .
