Question

State whether each statement is true or false, and why. (a) A typical band gap energy for an insulator is $400\mathrm{kJ}/\mathrm{mol}$ (b) The conduction band is higher in energy than the valence band. (c) Electrons can conduct well if they are in a filled valence band. (d) Holes refer to empty atomic sites in a solid crystal.

Short answer

(a) False, as a typical band gap energy for an insulator is on the order of $1-10\mathrm{eV}$, which corresponds to roughly 100-1000 kJ/mol, and the given value is too high. (b) True, the conduction band is higher in energy than the valence band, allowing electrons to move freely and carry charge once excited. (c) False, electrons in a filled valence band are bound to atoms and cannot move freely to conduct charge. (d) False, holes represent the absence of an electron in a filled valence band and are not empty atomic sites.

Step-by-step solution

(a) A typical band gap energy for an insulator is $400\mathrm{kJ}/\mathrm{mol}$

: This statement is false. A typical band gap energy for an insulator is on the order of $1-10\mathrm{eV}$, which corresponds to roughly 100-1000 kJ/mol. The given value of $400\mathrm{kJ}/\mathrm{mol}$ is too high and is not typical for an insulator.

(b) The conduction band is higher in energy than the valence band.

: This statement is true. In solid materials, the valence band is the range of energy levels that are normally filled with electrons, while the conduction band is the range of energy levels that are normally empty. Conduction occurs when some electrons are excited to the conduction band, enabling them to move freely and carry charge. Therefore, the conduction band must be at a higher energy level than the valence band.

(c) Electrons can conduct well if they are in a filled valence band.

: This statement is false. Electrons in a filled valence band are bound to their respective atoms and cannot move freely to conduct charge. Electrical conduction occurs when electrons are excited from the valence band to the conduction band, which has empty energy levels allowing electrons to move freely.

(d) Holes refer to empty atomic sites in a solid crystal.

: This statement is false. Holes are not empty atomic sites, but rather they represent the absence of an electron in an otherwise filled valence band. When an electron is excited from the valence band to the conduction band, it leaves behind a hole in the valence band. Holes effectively act as positive charge carriers, as electrons can move to fill the hole, leaving behind an empty state that effectively moves in the opposite direction of the electron.