Question

${}^{222}Rn(half-life=4days)\to B$
Starting with one mol of A in a closed vessel at S.T.P, if the volume of helium gas collected after 8 days is 33.6 L, then what is the mass number of B?

Answer 1

Since it is given in STP,
$33.6LofHe=\frac{33.6}{22.4}=1.5mol$
So, moles of He = 1.5 mol
Again, ${}^{222}Rn$ has half life of 4 days
Since it is given a time period of 8 days, and thus the examiner is talking about 2 half-lives.
So, moles of ${}^{222}Rn$ reacted = 0.75 mol
So, effectively each ${}^{222}Rn$ produces 2 $\alpha$ particles.
So, the mass number of B = 222 - 8 = 214.