Half life of a first order reaction and a zero order reaction are same. Then the ratio of the initial rate of the first order reaction to that of zero order reaction is

Options

A. `(1)/(0.693)`
B. `2 xx 0.693`
C. `0.693`
D. `2//0.693`

Answer

B

Explanation

`t_(1//2)` for 1st order reaction `= (0.693)/(k)`
`t_(1//2)` for zero reaction `= ([A_(0)])/(2k')`
Initial rate for 1st order reaction `(r_(1))=k[A_(0)]`
Initial rate for zero reaction `(r_(0))=k'`
`:. (r_(1))/(r_(0))=(k[A_(0)])/(k')`
But (0.693)/(k)=([A_(0)])/(2k')`
`:. (k[A_(0)])/(k')=([A_(0)])/(2k')`
`:. (k[A_(0)])/(k')=2xx0.693`
i.e., `(r_(1))/(r_(0))=2xx0.693`.