The nucleus is treated as a source in Kerr-Newman geometry, under the assumption that the angular momentum of the source is equal to the intrinsic spin angular momentum of the nucleus. The spin radius a of the nucleus, which figures in the Kerr-Newman metric, is of the order of the Compton wavelength of the nucleus. The radial functions in Chandrasekhar's separated Dirac equation in Kerr geometry, are transformed so as to yield a pair of simultaneous first-order differential equations with real coefficients, as in flat space. The magnetic quantum number m appears explicitly in the differential equations, thus lifting the hyperfine splitting degeneracy of Dirac's equation in flat space.