The half life of radon is 3.8 days . After how many days will only one twentieth of radon sample be left over ?

Options

A. 5
B. 10
C. 15
D. 17

Answer

D

Explanation

`lambda=(0.693)/(T_(1//2))`
`therefore lambda=(0.693)/(3.8)="0.182 per day"`
If initially at t = 0, the number of atoms present be `N_(0)`, then the number of atoms N left after a time t is given by
`N=N_(0)e^(-lambdat)`
`or (N)/(N_(0)) =e^(-lambdat) or (1)/(20)=e^(-lambdat)" "therefore" "e^(lambdat)=20`
Taking log on both sides we get,
`lambdat=log_(e)20=2.3026log_(10)""(20)/(0.182)~~"17 days."`