Band gaps/ conductivity metals and insulators Flashcards
what is the “free electron” model
Metals release valence electrons to create a sea of free electrons
What are the pros to the free electron model
Can use the “particle in the box” model
What are the cons the free electron model
cannot explain insulators and semiconductors.
what is band theory
Molecular orbital (MO) can be extended to solids, which are just large “molecules” with, effectively, an infinite number of atoms.
how many electrons can an orbital accomodate for?
each orbital in the band can accommodate two electrons.
what is created in a band from the orbitals
If we have N s-orbitals then there are N molecular orbitals and these are so close together they form a band.
Effectively we then have a continuous range of energies.
what is a metal
can conductive electricity
what type of material is Solid Li and explain why.
In solid Li the valence 2s orbitals form a 2s-band. there are N atoms, then there are N 2s orbitals. To fill the band needs 2N electrons to fill the band.
But there is N 2s electrons.
The 2s-band is half-filled. Electrons are readily promoted into the empty orbitals in the band electrons can move through the solid
what is the fermi level?
energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature.
what is an insulator ?
all orbitals filled in the valence band, which is full. The conduction band is empty. There is a large gap between the valence band and the conduction band.
what is a Semiconductor?
The gap between the bands is smaller. As the temperature is increased electrons are excited from the valence band to the conduction band – we have a semiconductor
what type of molecule is NaCl can you explain why it is?
Valence band comprised of Cl 3p orbitals - is full.
Conduction band is made up of empty Na 3s orbitals. The band gap is 7 eV – an insulator
why is lithium is a metal?
The 2s orbitals overlap to form a band. Just as the 2s orbitals in the Li atom is half-full, in the solid the 2s band is half-full.
: Mg metal. Mg atom has electron configuration [Ne] 3s2. So here we have a filled orbital, so we would expect the 3s band to be full, and Mg to be an insulator. Why is Mg a metal?
3s and 3p orbitals are close in energy for Mg. So the 3s and 3p bands overlap and the result is a partially filled s-p band.
are all things metal at high pressures?
yes
