A certain radioisotope `""_(Z)^(A)X` (`t_((1)/(2))=10` days) decays to give `""_(Z-2)^(A-4)Y`. If 1 mole of `""_(Z)^(A)X` is kept in a sealed vessel, what volume of helium will accumulate in 20 days at NTP?

Explanation

`""_(Z)^(A)X rarr ""_(Z-2)^(A-4)Y+ ""_(2)^(4)He`
Suppose that x moles of X give x moles of He after 20 days.
`therefore` moles of X after 20 days `=1-x`
Now, we have, `lamda= (2.303)/(t) "log" (N^(0))/(N)= (0.6932)/(t_((1)/(2)))`
or `(2.303)/(20) "log" (1)/(1-x) = (0.6932)/(10)`
x=0.75 mole
`therefore` volume of He at NTP= `0.75 xx 22.4`
=16.8 litres