What is the disintegration constant of radon if the number of its atoms diminishes by `18%` in 24 h? `["Take ln "(0.82)~~-0.2]`

Options

A. `2.1 xx 10^(-3) s^(-1)`
B. `2.1 xx 10^(-4) s^(-1)`
C. `2.1 xx 10^(-5)s^(-1)`
D. `2.1 xx 10^(-6) s^(-1)`

Answer

D

Explanation

Given `(1- (N)/(N_(0))) = 0.18 rArr (N)/(N_(0)) = 0.82 = 82%`
Now, `(82)/(100) = e^(- lamda t)`
`rArr (82)/(100) = e^(-lamda(24 xx 60 xx 60)) rArr lamda xx 24 xx 3600 = ln ((100)/(82))`
`rArr lamda = 2.1 xx 10^(-6) sec^(-1)`