A) \[6.9\text{ }sec\]
B) \[9.9\text{ }sec\]
C) \[10.1\text{ }sec\]
D) \[12.2\text{ }sec\]
Correct Answer: A
Solution :
[a] 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 \[T=1/\lambda =6.9s\].
You need to login to perform this action.
You will be redirected in
3 sec
