Worksheet: Free Electron Model of Metals

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 𝑛=𝑛=𝑛=4 state and the state with the next higher energy?

What is the percentage change in the energy between the 𝑛=𝑛=𝑛=400 state and the state with the next higher energy?

  • A2.9×10%
  • B4.0×10%
  • C3.2×10%
  • D3.6×10%
  • E4.2×10%

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.

  • A4.27×10
  • B4.55×10
  • C4.15×10
  • D4.40×10
  • E4.70×10

Q3:

Copper at 𝑇=0K has a conduction band electron density of 8.47×10 m−3.

What is the Fermi energy of the copper?

What is the Fermi temperature of the copper?

  • A8.20×10 K
  • B8.35×10 K
  • C8.02×10 K
  • D8.65×10 K
  • E8.49×10 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.

  • A2.56×10 J
  • B1.70×10 J
  • C1.61×10 J
  • D4.24×10 J
  • E8.48×10 J

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