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

Explanation

Half life period of radon = `T_(1//2)` = 3.8 days
Amount of sample undergo decay = 60%
Time required = ?
`lamda=0.6931/3.8` days.
Amount of sample disintegrated = 60%
Amount of sample present/Remaining amount = 100 - 60 = 40%
Let initial amount of the sample present = `N_(0)`
According to law of disintegration
Sub. for `N=N_(0)e^(-lamdat)`
`thereforee^(-lamdat)=10/4`
`loge^(2.5)=lamdaxxt`
`thereforet=3.8/(0.6931)xxlog_(10)^(2.5)xx2.3026` = 5.022 days.