Dual Nature of Radiation and MatterElectron Emission

Metals have free electrons; they carry the current in a wire. But a free electron cannot simply leave the metal. If it tries, the surface it leaves behind becomes positively charged and pulls it back: the positive ions hold the free electrons in. An electron gets out only if it is given enough energy to overcome this pull. The minimum energy needed is the work function of the metal, written φ₀ and measured in electron volts (eV). Below, the energies are drawn as heights: the electron sits at the top of the sea of free electrons, and has to climb φ₀ to reach the escape level.

The height of the step is the work function. Any energy beyond it stays with the electron as kinetic energy, and with less than φ₀ the electron is pulled back. One electron volt is the energy an electron gains when it is accelerated through a potential difference of 1 volt: 1 eV = 1.602 × 10⁻¹⁹ J, a handy unit in atomic and nuclear physics. The work function depends on the metal and on the state of its surface. For caesium, φ₀ = 2.14 eV = × 10⁻¹⁹ J.

Three Ways Out

The energy can be supplied to the free electrons in three ways.

• Thermionic emission. Heating the metal gives its free electrons enough thermal energy to come out.
• Field emission. A very strong electric field, of the order of 10⁸ V/m, pulls electrons out of the metal, as in a spark plug.
• Photoelectric emission. Light of suitable frequency falling on the metal frees electrons from its surface. These light-generated electrons are called photoelectrons.

Sort each example by where the electrons get their energy.

Speed Round: Getting Electrons Out

1 eV = 1.6 × 10⁻¹⁹ J, and an electron accelerated through V volts gains V electron volts. Get five right to move on.