Schroedinger's energy levels - potential wells

[lntz]

maybe this question has more to do with chemistry, but it's physical chemistry at the very least.

so, in physics class we have been learning about schroedingers equations for the H atom electron energy levels, and discussing bound electrons in a potential well. for these electrons to move up an energy level they must be given a certain amount of energy, and each level the electron moves up, behaves like a standing wave with certain harmonics. at least this is how we think about them at my level of physics. so these electrons must be given an amount of energy greater than or equal to the electrical potential of the nucleus to be 'free' or unbound. so how does this apply to metals? metals have a certain number of bound electrons, but also have some 'free' electrons, so they exist as cations. i understand the kind of answer i get about this from my chemistry teachers, but i'd really like to know how the 2 ideas of energy levels, and metallic bonding link together.

thanks in advance for any help you can give.
lntz

 

[LightHero]

The concept of energy levels and metallic bonding are linked together through the idea of delocalized electrons. In metals, the outermost electrons of the atoms are not tightly bound to any particular atom, but instead can be thought of as being shared amongst all the atoms in the metal lattice. This means that they form a 'sea' of delocalized electrons which are free to move around the lattice and effectively separate the positive ions from one another. The energy levels of these electrons correspond to the energy needed to be able to move between different lattice sites. As each electron moves up an energy level, it behaves like a standing wave, with certain harmonics. This is what allows for the electrons to move freely about the lattice and form metallic bonds.