* Please keep in mind that all text is machine-generated, we do not bear any responsibility, and you should always get advice from professionals before taking any actions. Here C04e0R is the classical geometrical value, pR/l is the ratio of the particle radius R to the ThomasFermi screening length l, and e is the material dielectric constant. A generalized energy-density relation is obtained using the force-balance equation and taking into account the Chandrasekhars relativistic electron degeneracy pressure. The result is CTFC01p1 tanh p/1(1e1)p1 tanh p, with CTFC0. In this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide range of electron number-densities and the atomic-number of screened ions. Single-body electrostatic energy which has maximum relative error of < 2. We calculate the self-capacitance and charging energy of a spherical nanoparticle in the ThomasFermi approximation. This result is obtained through a compari-son with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. Ext and ind are associated with external and charge induced in metal, respectively. We prove that in Thomas-Fermi-Dirac-von Weizs¨acker the-ory, a nucleus of charge Z>0 can bind at most Z+C electrons, where C is a universal constant. Integrals represent relative magnitude with regard to U at ideal limit TF = 0. Dependence of integrals on dimensionless distance to surface / TF = TF TF metal behaves like metal at long distances and like insulator at short distances.