Hello Altamash Dhalait ,

Quantum mechanics cannot provide, from first principles (ab initio), the values of material parameters such as electrical conductivity, i.e., why silver is the element, of the 92 naturally occurring elements, with the highest electrical conductivity at room temperature. If you measured the conductivity of all the elements beforehand, quantum mechanics can provide some justification and some rationalization for the trends you observe; the most obvious exceptions seem to be transition group metals, i.e., Group IIB to IIB in the Periodic Chart, although, even nontransition group elements such as beryllium are also hard to explain. Note, according to Charles Kittel, E. M. McMillan observed that the resistivity (1/conductivity) of insulators and metals covers an observed range of 1032, perhaps the widest range of any physical parameters, see [1]. What about the fact that 86 of the 109 natural and manmade elements are metals, see [2]. How does quantum mechanics explain that fact? As to your two example metals: copper and nickel, they are both transition group metals, and have extremely complicated Fermi surfaces depending on their crystal form, see [3].

[1] Charles Kittel; Introduction to Solid State Physics, Fourth Edition; John Wiley & Sons, Inc.; 1971; pp. 260 (chart of the electrical conductivity and resistivity of metal elements) & 295 (McMillan's observation).

[2] P. W. Atkins; Periodic Kingdom; Basic Books; 1995; p. 4.

[3] J. M. Zisman; Electrons in Metals; Taylor & Francis Ltd.; 1970; 76 pp.

Regards,

Tom Cuff

By the property that the fraction of the conduction band of copper that contains available states is larger than for nickel. The calculation can be quite involved in practice, but one shouldn't conflate principle with practice.

What quantum mechanics allows to understand is that the energy spectrum for electrons in any crystal is described by bands, that, given a certain number of electric charges, their states have a certain structure and this implies that their energy can't be arbitrary-in particular it can't be greater than a certain value, known as the Fermi level. The electrons that contribute to the conductivity, i.e. to the electric current, that an external electric field can give rise to, have energies that belong in the ``conduction'' band. Therefore the Fermi level must be in this band, for conductivity to be possible and the question then becomes what fraction of the states in the conduction band has energy less than the Fermi level. So the greater this filling factor is, the better a conductor the material is.

Altamash Dhalait I can't answer the question directly but I can point you in the direction of an alternative model of the structure of the atom. This is referenced in the discussion of the hydrogen bond:

Preprint The Hydrogen Bond (June 2022)

Richard