  Relativistic effects strongly influence the electronic structures of the
heaviest elements, thereby shaping their chemical and physical properties.
Studying ion mobility within a noble gas environment reveals how the
ion-neutral interactions depend on the ion's electronic configurations, thus
providing an avenue for exploring these effects. An ion mobility spectrometer
with a cryogenic drift tube was developed to precisely measure the low-field
reduced mobility of heavy lanthanide and actinide cations. The apparatus was
characterized by optimizing the bunching operation of ions with a miniature RF
coulomb buncher and evaluating the chromatography performance of the drift tube
operated with helium buffer gas at a temperature of 298K. Systematic ion
mobility measurements of lutetium cations (Lu$^{+}$) drifting in helium gas
were carried out as a case study. The electronic state chromatography of
Lu$^{+}$ has been demonstrated. The low-field reduced ion mobility for the
ground and lowest meta-stable state of Lu$^{+}$ have been examined. In
addition, the variation of both states' reduced mobility and the quenching of
meta-stable population has been investigated under different reduced electric
fields ($E/n_0$), the ratio of an electric field to neutral gas number density.
