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One mole of radioactive nuclide , X with...

One mole of radioactive nuclide , X with half life of ten days decays as `""_(Z)^(A) X to ""_(Z- 4) ^(A - 8) Y + 2 ""_(2) ^(4) He` . If the no. of moles of Helium formed in 20 days is 0.25 x then x = …..

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The correct Answer is:
6
`1 (""_(Z) X^(A)) to ( Z- A) Y ^((A - 8)) + 2 ( ""_(2) He^(4)) `, 1 mole of `X overset(10 "days")(to) (1)/(2)` mole of X `overset(10 "days")(to)`
t = 20 days , `n_x` consumed = `(1 - (1)/(4)) = (3)/(4)` mole of X , 1 mole of .X. from `to` 2 mole of He gas `(3)/(4)` mole of .X. from `to 2 xx (3)/(4)` mole of He gas , `V_(He) = 2 xx (3)/(4) xx 22.4 = 33.6I`,
`n_(He "gas") to 2 xx (3)/(4) = (3)/(2)` moles , `0.25 xx = (3)/(2) , x = (3)/(2 xx 0.25)= (3)/(0.50) = 6`
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