The electrical current in ionic solutions

Another point of interest is that not all but only about one electron per atom is free to carry the current. Only the electrons in levels near the top of the filled part of the partially filled band are free to move under the application of a field. As we saw in Section 28.4, to carry a current the electrons must be able to shift from one set of levels to another set vacant levels that are not very much different in energy must be available. Vacant levels are available only near the top of the filled part of a partially filled band and so only these electrons contribute to the conductivity. 

Finally, there is the curious result that if the electrons that carry the current are in levels near the top of a band, then the field pushes the electrons in the wrong direction wrong in the sense that they are accelerated in the direction opposite to the usual one. These electrons behave as if they were positively charged. This happens with zinc and cadmium as well as a number of other metals. The effect is detected in the Hall experiment the Hall potential for these metals has the opposite sign when compared with a metal such as copper. 

Measurement of the magnitude and sign of the Hall potential in semiconductors enables us to distinguish experimentally between p- and n-type semiconductors, and to determine, knowing k, the number and mobility of the carriers. 

If a direct current is passed between two electrodes in an electrolytic solution, a chemical reaction, electrolysis, occurs at the electrodes. After a study of various types of electrolytic reactions, Faraday (1834) discovered two simple and fundamental rules of behavior, now called Faraday s laws of electrolysis. Faraday s first law states that the amount of chemical reaction that occurs at any electrode is proportional to the quantity Q of electricity passed Q is the product of the current and the time, Q = It. The second law states that the passage of a fixed quantity of electricity produces amounts of two different substances in proportion to their chemical equivalent weights. Faraday s experiments showed that these rules were followed with great accuracy. So far as we know these laws are exact. 

The equation has been balanced so that one mole of electrons is either consumed at the cathode (Vg = — 1) or produced at the anode (Vg = + 1). This equation states that for each mole of electrons that passes, moles of are produced or consumed. If a quantity of electricity, Q = It, is passed, then the number of moles of produced or consumed is 

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