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# work function

The work function is the energy required to liberate an electron from a material. It is important in the photoelectric effect and in thermionics.

When a kettle of water is heated to its boiling point, water molecules leave the surface and pass into the air above the liquid. When a piece of metal is heated, electrons leave the surface of the metal and pass into the space above the metal surface. This property, called thermionic emission, is used in devices such as the cathode-ray tube.

Both water molecules and electrons need heat energy to drive them away from the surfaces, because they are normally held there by forces of attraction. All particles exert a force of attraction on their neighbors – this is a consequence of the law of gravitation, and applies equally to molecules in a liquid, solid or a gas, or to the planets and the Sun. But electron are held in a solid by an additional set of powerful electrical forces.

In a solid metal the vast numbers of positively charged nuclei are surrounded by just enough negatively charged electrons for all the positive charges to be neutralized. If there were, say, 10,000,000 positive nuclei each carrying 65 units of positive charge, then there would normally be 650,000,000 electrons present in the metal to produce a neutral lump of metal.

What happens if some of the electrons are 'boiled off' when the metal is heated? Some of the positive charges on nuclei are no longer neutralized by electrons; so the metal is no longer electrically neutral but is positively charged. It is a basic law of electricity that unlike charges attract each other. On the escaping electrons therefore a force of attraction acts and tries to stop them for leaving. This force is there only because the positive charge left behind them draws them back.

In the solid, this effect is called the image effect because each escaping electron leaves behind an 'image' charge equal in size but of opposite charge.

## Potential wells in solid

Both water molecules in the liquid, and electrons in the solid are 'trapped' because they need to be given energy to escape. This is often represented by thinking of the electrons as being in potential well. The electrons are at the bottom of the well, and need to be lifted out by the energy they receive. But the electrons do not fill the well like water does. They can occupy only certain energy bands. At absolute zero the electrons occupy only lower bands of the well. as the temperature is increased the electrons receive more energy and pass into higher bands further up the well, and if they receive still more energy they leave the well altogether. Some electrons are then emitted although the actual number that leaves is a very small proportion of all the electrons in the metal.

 The electrons in the metal are trapped in a potential well due to the force of attraction on them. If they are given sufficient energy they can clear the well and leave the metal. The work done in leaving the well is the work function.

The amount of work that has to be done to lift an electron up the sides of the potential well and clear of the metal is called the work function. Each different material has its own work function.

## Photoelectric and secondary emission

Energy can be given to the electrons in the wells by light waves or by electrons that strike the surface of the metal. In photocells an electric current is released by light waves striking a photocathode, which is an electrode coated with material of low work function. In a photomultiplier cell a single electron hits an electrode (dynode) that is coated with material of low work function and releases more than one electron. These electrons released pass on to another dynode and release an even greater number of electrons. The process is repeated many times and the result is that the single initial electron has led to an avalanche of electrons. The release of electrons by an electron at the surface is called secondary emission.