In this worksheet, we will practice finding the density of a free electron model and electron quantum states of metals and defining metals' Fermi energy and temperature.

Q1:

In the free electron model of metals.

What is the percentage change in the energy between the
state and the state with the next higher energy?

What is the percentage change in the energy between the
state and the state with the next higher energy?

A

B

C

D

E

Q2:

A cube of copper has edges 1.50 mm
long. Calculate the number of electron quantum states in this cube whose energies are in the
range 3.75 eV to
3.77 eV.

A

B

C

D

E

Q3:

Copper at has a conduction band electron density of
m^{−3}.

What is the Fermi energy of the copper?

What is the Fermi temperature of the copper?

A
K

B
K

C
K

D
K

E
K

Q4:

What is the ratio of the density of states for electrons at
2.7 eV and at
0.27 eV?

Q5:

Find the average energy of an electron in a Zn wire, consisting of one mole of zinc. Use a value of 266.49 pm for the lattice spacing of zinc.

A
J

B
J

C
J

D
J

E
J

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