A) \[{{\log }_{e}}2/5\]
B) \[\frac{5}{{{\log }_{e}}2}\]
C) \[5{{\log }_{10}}2\]
D) \[5{{\log }_{e}}2\]
Correct Answer: D
Solution :
[d] \[N={{N}_{0}}{{e}^{-\lambda t}}\] Here, \[t=5\]minutes \[\frac{{{N}_{0}}}{e}={{N}_{0}}.{{e}^{-5\lambda }}\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\,5\lambda =1,\,\,\,\lambda =\frac{1}{5},\] Now, \[{{T}_{1/2}}=\frac{\ell n2.}{\lambda }=5\,\,\ell n2\]
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