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

Options

A. `6.9`
B. `1.5`
C. `0.105`
D. `9.2`

Answer

A

Explanation

Time required for `99.9%` reaction is `10` times of half-life period.
`T_(99.9) = 10T_(50)`
But `T_(50) = (0.693)/(k)`
`:. T_(av) = (1)/(k)`
and `T_(50) = 0.693 T_(av)`
`:. T_(99.9) = 10 xx 0.693 T_(av) = 6.93 T_(av)`