Calculate the time required for 60% of a sample of radon undergo decay. Given `T_(1//2)` of radon = 3.8 days.

Explanation

Here consider `R_(n) - 222` with a half life of 3.823 days.
From decay equation,
Current amount = `"Initial amount" xx (2)^(-n)`
`N = N_(0) (2)^(-n)`
`(N)/(N_(0)) = (2) ^(-t)/(T_(1/2))`
`log((N)/(N_(0)) = log (2) xx (-(t)/(T_(1/2)))`
`log((N)/(N_(0)))/(log(2)) = (-(t)/(T_(1/2)))`
`t = (log(0.4))/(log(2)) xx (-3.823)`
Time t = `5.05` days.