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