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.
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