A certain radio isotope `._(Z)X^(A)` (half life `= 10 ` days) decays to give `._(Z-2)Y^(A-4)` . If `1.0 g` atom of `X` is kept in a sealed vessel, find the volume of helium accumulated at `STP` in `20` days ?

Explanation

Since `1.0 g` atm of `X = 1 mol` of `X = a_(0)`
`._(Z)X^(A) rarr ._(Z-2) X^(A-4) + ._(2)He^(4)`
`{:("Initial",1,0,0,),("Final",1-x,x,x,):}`
`n =` Number of half lives `= (20)/(10) = 2`
Moles of `X` left `= ((1)/(2))^(n) xx a_(0)`
`= ((1)/(2))^(2) xx 1 = (1)/(4)mol rArr (1-x) mol`
Moles of helium formed `= 1 - (1)/(4) = (3)/(4) mol rArr x mol`
`= (3)/(4) xx 22.4L = 16.8L` at `STP`