A) \[\frac{In\,\,2}{k}\]
B) \[\frac{0.693}{0.5}\]
C) \[\frac{\log \,2}{2k}\]
D) \[\frac{\log \,2}{k\sqrt{0.5}}\]
Correct Answer: A
Solution :
For first order reaction \[k=\frac{2.303}{t}\log \frac{a}{(a-x)}\] \[\Rightarrow \] \[{{t}_{1/2}}=\frac{2.303}{k}\log \frac{a}{(a-a/2)}\] \[\Rightarrow \] \[{{t}_{1/2}}=\frac{2.303}{k}\log \,2\] \[\therefore \] \[{{t}_{1/2}}=\frac{\operatorname{In}\,2}{k}\]
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