Electrical- Conductors

Question 1

Charge of electron

Answer 1

1.6x10-19 C

Question 2

What limits mobility of electrons?

Answer 2

Can be trapped at lattice or framework sites in atomic bonds or particular orbitals.
They collide with atoms or defects in the channel system or at defect sites.
They interact with each other and photons

Question 3

Drift velocity

Answer 3

Average rate at which the carriers move

Symbol V bar

Question 4

Other formula for mobility

Answer 4

μ=Vbar/ε
Where V bar is drift velocity
ε is electric field gradient

Question 5

How to find mobility of free electrons in a material

Answer 5

See how many valence electrons there are per atom. Find number of atoms inside a unit cell. Divide the product of these by the volume of the unit cell to get n. Divide conductivity by n and charge of electron to get mobility.

Question 6

Conductivity ranges at 300K for conductors, semiconductors and insulators

Answer 6

Conductors over 100S/cm
Semiconductors between 100 and 10^-6 S/cm
Insulators below 10^-6 S/cm

Question 7

What determines whether an element conducts or not?

Answer 7

Depends on how the atomic orbitals which contain the valence electrons overlap and whether there is any for the electrons to be delocalised or whether the bonding is more covalent when the electrons are localised in particular orbitals.

Question 8

Assumptions and principles of molecular orbital theory MOT

Answer 8

Think of the solid as a giant molecule. Uses Pauli exclusion principle, degeneracy of each AO and its relative energy, Aufbau method for constructing the ground state electron configuration, Hund’s rule for partially filled degenerate set of orbitals.

Question 9

MOT for H2

Answer 9

The molecular orbitals (MO) form from linear combination of the 1s AO of the 2 H atoms. Forms a bonding MO (σ) and antibonding MO (σ*). The two electrons from the AOs of the H atoms go into the lower energy bonding MO.

Question 10

MOT for He2

Answer 10

There are 4 electrons to fit into the 2 MOs. So two go in the bonding MO and two go in the antibonding MO. σ* has a higher energy than the initial AOs so the diatomic molecule He2 is unstable.

Question 11

MOT for 2 elements A and B

Answer 11

If B has the AO of lower energy, on the diagram it is below the level of the AO for A and is closer to the σ. When this orbital is occupied by 2 electrons, there will be a net transfer of charge from A to B. B is the electronegative atom.

Question 12

Rules of MOT

Answer 12

n AOs produce n MOs. Need only consider valence AOs and the relative energy of the valence AOs on the atoms. Need to consider symmetry and overlap of AOs (crystal structure and ionic radii for solids, molecular shale and bond lengths for molecules). In polyatomic molecules, greater variety of MOs can be formed. Larger molecules has more numerous and closely spaced MOs.

Question 13

Describe the orbital energies in a solid

Answer 13

There is a conduction band of higher energy formed from empty orbitals in the ground state. There is a valence band of lower energy formed from occupied electron orbitals in the ground state. Between these is an energy gap where the density of orbitals is 0 (band gap)

Question 14

What determines the width of a band?

Answer 14

Related to interatomic separation and hence on the degree of overlap between orbitals on adjacent atoms. Strong overlap gives wide bands and small overlap gives narrow bands. S and p block metals are wide-band solids.

Question 15

How do orbitals overlap in metals?

Answer 15

Valence p and s orbitals overlap strongly to give bands many eV in width (6-8). Contracted core orbitals give very narrow bands (under 0.1eV) and retain their atomic identity in solid and don’t contribute to the bonding. If these bands are partially filled by valence electrons the electron delocalisation throughout the solid can occur and results in metallic conductivity.

Question 16

Fermi level Ef

Answer 16

Energy where the probability of electron occupation is 1/2 (half of the energy levels with this energy are empty). Only electrons close to Ef contribute to conductivity

Question 17

How do the velocities of electrons sum in a metal carrying a current and not?

Answer 17

When no current carried, average velocities sum to 0.
When electric field applied (Eapp), each electron experiences force -qEapp and a change in velocity which no longer sum to 0. They drift in direction opposite to Eapp. Current then flows.

Question 18

How does width of an energy band relate to interatomic separation?

Answer 18

At r0 (at STP) in Na, the 3s and 3p orbitals form braid bands that overlap. The others don’t and remain as discrete AOs on individual atoms. At r’ Na compressed using pressure to reduce interatomic separation, the 2s and 2p orbitals can overlap to form bands of energy levels.