  Thorium-229 possesses the lowest nuclear first excited state with an energy
of about 8 eV. The extremely narrow linewidth of the nuclear first excited
state with the uncertainty of 53 THz prevents the direct laser excitation and
the realization of the nuclear clock. We present a proposal using the Coulomb
crystal of a linear chain formed by the $^{229}$Th$^{3+}$ ions, the nuclei of
$^{229}$Th$^{3+}$ ions in the ion trap are excited by the electronic bridge
(EB) process. The 7$P_{1/2}$ state of the thorium-229 nuclear ground state is
chosen for the EB excitation. Using the two-level optical Bloch equation under
experimental conditions, we calculate that 2 out of 36 prepared thorium ions in
the Coulomb crystal can be excited to the nuclear first excited state, and it
takes about 2 hours to scan over the uncertainty of 0.22 eV. Taking the
advantage of transition enhancement of the EB and the long stability of the
Coulomb crystal, the energy uncertainty of the first excited state can be
limited to the order of 1 GHz.
