  Time evolution of radial wave packets built from the eigenstates of Dirac
equation for a hydrogenic systems is considered. Radial wave packets are
constructed from the states of different $n$ quantum number and the same lowest
angular momentum. In general they exhibit a kind of breathing motion with
dispersion and (partial) revivals. Calculations show that for some particular
preparations of the wave packet one can observe interesting effects in spin
motion, coming from inherent entanglement of spin and orbital degrees of
freedom. These effects manifest themselves through some oscillations in the
mean values of spin operators and through changes of spatial probability
density carried by upper and lower components of the wave function. It is also
shown that the characteristic time scale of predicted effects (called
$T_{\mathrm{ls}}$) is for radial wave packets much smaller than in other cases,
reaching values comparable to (or even less than) the time scale for the wave
packet revival.
