A) 2 hr
B) 4 hr
C) 1/2 hr
D) 1/4 hr
Correct Answer: C
Solution :
For first order reaction, \[k=\frac{2.303}{{{t}_{1/2}}}\log \frac{a}{\left( a-\frac{a}{2} \right)}=\frac{2.303}{t}\log \frac{a}{(a-x)}\] \[\therefore \] \[\frac{2.303}{{{t}_{1/2}}}\log 2=\frac{2.303}{1}\log \frac{a}{a/4}\] \[\frac{2.303\times 0.3010}{{{t}_{1/2}}}=2.303\times \log 4\] \[\therefore \] \[{{t}_{1/2}}=\frac{0.3010}{\log 4}\] \[=\frac{0.3010}{0.6020}\] \[=\frac{1}{2}hour\]
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