The hyperfine structure splitting of the ground state of hydrogen-like
Bi-209 is calculated for an extended nuclear charge distribution. The
probability density of the odd proton in Bi-209 is taken into account
explicitly in order to compute the effect of an extended magnetizatio
n distribution on the energy splitting. The probability density of the
odd proton is deduced from a mean-field model and the magnetization c
orrection is evaluated within the Bohr-Weisskopf formalism. We obtaine
d a transition wavelength of DELTAlambda = 242.3 nm. An estimate for t
he QED corrections is provided.