  Alpha decays in the EXO-200 detector are used to measure the fraction of
charged $^{218}\mathrm{Po}$ and $^{214}\mathrm{Bi}$ daughters created from
alpha and beta decays, respectively. $^{222}\mathrm{Rn}$ alpha decays in liquid
xenon (LXe) are found to produce $^{218}\mathrm{Po}^{+}$ ions $50.3 \pm 3.0\%$
of the time, while the remainder of the $^{218}\mathrm{Po}$ atoms are neutral.
The fraction of $^{214}\mathrm{Bi}^{+}$ from $^{214}\mathrm{Pb}$ beta decays in
LXe is found to be $76.4 \pm 5.7\%$, inferred from the relative rates of
$^{218}\mathrm{Po}$ and $^{214}\mathrm{Po}$ alpha decays in the LXe. The
average velocity of $^{218}\mathrm{Po}$ ions is observed to decrease for longer
drift times. Initially the ions have a mobility of $0.390 \pm
0.006~\mathrm{cm}^2/(\mathrm{kV}~\mathrm{s})$, and at long drift times the
mobility is $0.219 \pm 0.004~\mathrm{cm}^2/(\mathrm{kV}~\mathrm{s})$. Time
constants associated with the change in mobility during drift of the
$^{218}\mathrm{Po}^{+}$ ions are found to be proportional to the electron
lifetime in the LXe.
