The impurity induced charge density is calculated in jellium by solving the Schrödinger equation self-consistently following the procedure of Manninen and Nieminen and using Kohn-Sham density functional formalism. The host-ion contribution is included through the spherical solid model potential (SSMP). The calculated activation energy 0.27 eV is found in good agreement with experimental value 0.28±0.02 eV. The estimated residual resistivity 1.02 µΩ cm/at% for Lu-H system using the resulting phase shifts agrees reasonably well with the observed value 1.75±0.10 µΩ cm/at%. The calculated configurational energy shows that hydrogen prefers tetrahedral(T)-sites over octahedral(O)-sites in Lu matrix. This has been confirmed by Bonnet experimentally. A very shallow value ofs-type bound state of energy −0.00316 Ryd predicts that there is no formation of lutetium hydride solution and H⁺ exists as a free ion in Lu matrix.