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

The decay equation is, `._(Z)X^(A) rarr ._(Z-2)Y^(A-4) + ._(2)He^(4)`
`t_(1//2) = 10` day, `N_(0) = 1g` atom, `T = 20` day
`:. N = 2, (:' n = T//t_(1//2))`
`:.' Amount of `X` left after 2 halves `= (1)/(2^(2)) g` atom
`:.` Amount of `X` used in 2 halves `= 1- (1)/(2^(2)) = (3)/(4)g` atom
`:' 1g` atom of `X` give 1 mole of `He` or `22400 ml He`
`:. (3)/(4)g` atom of `X` gives `(3)/(4)` mole of `He`
or `(22400xx3)/(4) = 16800 mL He`.