A) \[{{t}_{1/2}}\propto {{R}_{0}}\]
B) \[{{t}_{1/2}}\propto 1/{{R}_{0}}\]
C) \[{{t}_{1/2}}\propto R_{0}^{2}\]
D) \[{{t}_{1/2}}\propto 1/R_{0}^{2}\]
Correct Answer: A
Solution :
For a zero order reaction, rate, \[\frac{d[R]}{dt}=k\] On integrating, we get \[[R]=-kt+[C]\] When \[t=0,[R]=[{{R}_{0}}]\] \[\therefore \] \[[C]=[{{R}_{0}}]\] \[\therefore \] \[[R]=-kt+[{{R}_{0}}]\] When \[t={{t}_{1/2}},[R]=\frac{[{{R}_{0}}]}{2}\] \[\therefore \] \[\frac{[{{R}_{0}}]}{2}-[{{R}_{0}}]=k{{t}_{1/2}}\] \[\therefore \] \[{{t}_{1/2}}=\frac{[{{R}_{0}}]}{2k}\] \[{{t}_{1/2}}\propto [{{R}_{0}}]\]
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