A) \[\frac{\ln \,2}{k}\]
B) \[\frac{1}{k\times a}\]
C) \[\frac{0.693}{k\times a}\]
D) \[\frac{3}{2k{{a}^{2}}}\]
Correct Answer: A
Solution :
From the first order reaction \[k=\frac{{{\log }_{n}}}{t}\left( \frac{a}{a-x} \right)\] \[k=\frac{{{\log }_{n}}}{{{t}_{1/2}}}\left( \frac{a}{a-\frac{a}{2}} \right)\] \[\because \]\[x=\frac{a}{2},\] \[t={{t}_{1/2}}\] \[k=\frac{{{\log }_{n}}}{{{t}_{1/2}}}\frac{2a}{a},\] \[k=\frac{{{\log }_{n}}2}{{{t}_{1/2}}}\] or \[{{t}_{1/2}}=\frac{{{\log }_{n}}2}{k}\]
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