A) \[0.4\,ln\,2\]
B) \[0.2\,\ln \,2\]
C) \[0.1\,\ln \,2\]
D) \[0.8\,\ln \,2\]
Correct Answer: A
Solution :
Given, \[{{N}_{0}}\lambda =5000,\,N\lambda =12500\] \[N={{N}_{0}}{{e}^{-\lambda t}}={{N}_{0}}{{e}^{-5\lambda }}\] where, \[\lambda \] is decay constant per minute. \[N\lambda ={{N}_{0}}\,\lambda {{e}^{-5\lambda }}\] \[1250={{N}_{0}}\lambda {{e}^{-5\lambda }}\] \[\therefore \] \[\frac{{{N}_{0}}\,\lambda }{{{N}_{0}}\,\lambda {{e}^{-5\lambda }}}=\frac{5000}{1250}=4\] \[{{e}^{5\lambda }}=4\] \[5\lambda =2{{\log }_{e}}2\] \[\lambda =0.4\,\,\ln \,2\]
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