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A certain radio isotope .(Z)X^(A) (half ...

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 ?

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The correct Answer is:
16.8L
Decay of `._(Z)^(A)X " to " ._(Z-2)^(A-4)Y` produces one helium atom. Therefore, decay of 1.0g atom of `._(Z)^(A)X` will produce l.0g of atom of helium gas. Half-life of X=10days.
Therefore, the amount decayed in w0 days`=(1)/(2)+(1)/(4)=(3)/(4)g ` of atom
1.0 g atom of He `=22400cm^(3) "at " 0^(@)C` and atm
`3//4g` atom of He`=22,400xx(3)/(4)=16,800cm^(3)`
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