The hyperfine structure (hfs) of electron levels of U-238(92) ions with the
nucleus excited in the low-lying rotational 2(+) state with an energy E2= 44.91 keV is investigated. In hydrogenlike uranium, the hfs splitting for
the 1s(1/2) ground state of the electron constitutes 1.8 eV. The hyperfine
-quenched (hfq) lifetime of the 1s2p P-3(0) State has been calculated for h
eliumlike U-238(92) and was found to be 2 orders of magnitude smaller than
for the ion with the nucleus in the ground state. The possibility of a prec
ise determination of the nuclear g(r) factor for the rotational 2(+) state
by measurements of the hfq lifetime is discussed.