One miligram of thorium emits `22alpha` particles per minute per unit solid anlge. Calculate average life of thorium. Atomic weight of Thorium is 232.

Answer

`1.786xx10^(10)yers`

Explanation

Here, `m=1 "milligram" =10^(3)g`
`tau=? A=232`
Number of atoms in 1mg of Th
`N=(6.023xx10^(23))/232xx10^(-3)=2.595xx10^(18)`
As `alpha` particles are emitted by the source in all the directions, i.e., in a solid angle of `4pi` steradian,
therefore, `(dN)/(dt)=22xx4pi alpha` particles/minute
form `(dN)/(dt)=lambdaN`
`lambda=(dN//dt)/N=(22xx4pi)/(2.595xx10^(18))`
`tau=1/lambda=(2.595xx10^(18))/(22xx4pi) `minutes
`=(9.39xx10^(15))/(60xx24xx365)` yers
`tau=1.786xx10^(10)years`