Number of natural life times `(T_(av))` required for a first order reaction to achieve `99.9%` level of comletion is

Options

A. `6.93`
B. `2.31`
C. `9.2`
D. infinite

Answer

A

Explanation

`t_(99.9) = 10 xx t_(1//2)`
`=10 xx (0*693)/(k) " "(because t_(1//2) = (0*693)/(k))`
`=10 xx 0*693 xx t_(av)" " (because t_(av) = (1)/(k))`
`= 6*93 xx t_(av), i.e., 6*93` natural life times.