Question

For which of the following elements the valence band will be full? Explain how you arrive at your answer:

sodium, magnesium, aluminum and silicon

Based on the answer, predict which of these elements will be metal, and which may not be metal. Then compare your prediction with the actual observations.

Answer 1

Bands are essentially closed spaced orbitals.

For Sodium, Na, which has an atomic number 11, has one valence electron in the 3s band. This shows that the 3s band is half filled as there is a vacancy for one more electron.

For Magnesium, (12), 3s band has 2 electrons and is full. Thus the 3s band is full.

Aluminum, has 13 electrons and thus 3 valence electrons. Thus the 3s band is full while 3p band has one electron.

As can be seen from the above, all the three elements, Na, Al, Mg, show partially filled valence bands.

Correlating the electronic configuration to energy band gap using the band theory, we obtain that the conduction band and the valence band overlap for these three elements. Thus they are metals.

Silicon, on the other hand, has completely filled valence band. However, the energy gap between the conduction band and the valence band is not very high. Thus, silicon acts as a semiconductor.