Electron emission
Electrons held inside a metal
Late in the nineteenth century, scientists passed electricity through gases at very low pressure, in discharge tubes. At a pressure of about 0.001 millimetre of mercury, a glow appeared on the glass opposite the cathode. Rays were streaming out of the cathode: cathode rays.
In 1897, J. J. Thomson bent these rays with electric and magnetic fields. They curved the way negative charges would. Cathode rays are streams of tiny, negatively charged particles, which we call electrons.
Thomson measured their charge-to-mass ratio, e over m. It came out the same, whatever metal the cathode was made of and whatever gas was in the tube. Electrons are a part of all matter.
A few years later, Millikan’s oil-drop experiment measured the electron’s charge itself: 1.602 × 10⁻¹⁹ coulomb. Every charge he found was a whole-number multiple of this value. Charge is quantised.
Now look inside a metal. Each atom gives up one or more of its outer electrons, and these wander freely through the whole piece of metal. They are the free electrons that carry current in a wire.
So why don’t they simply fly out of the surface? Watch one try. As it leaves, the positive ions it leaves behind pull it back. Free electrons can move inside the metal, but they cannot get out on their own.
To pull an electron out, we must give it a certain minimum energy. This minimum energy is called the work function of the metal, written φ₀.
Work functions are tiny amounts of energy, so we measure them in electron volts. One electron volt is the energy an electron gains when it is accelerated through a potential difference of 1 volt: 1.602 × 10⁻¹⁹ joule.
Here are some work functions. Caesium, 2.14 electron volt, is the easiest to free electrons from. Sodium, 2.75. Copper, 4.65. Platinum, 5.65, the highest in the table. The value also depends on how clean the surface is.
Three ways out
Think of the free electrons as sitting in a well. The top of the electron sea is a depth φ₀ below the level where an electron is free. To climb out, an electron needs at least φ₀ of extra energy. There are three ways to give it that energy.
The first is heat. The thermal energy of an electron is about k T. At room temperature, 300 kelvin, k T is only about 0.026 electron volt, far less than a work function of a few electron volts. No electrons escape.
Now heat a tungsten filament until it glows white, to about 2500 kelvin. k T rises to about 0.22 electron volt. Most electrons are still far short of φ₀, but a tiny fraction of the fastest ones have enough energy, and they boil off the surface.
This is thermionic emission: electrons emitted by a heated metal. A hot filament sends out a steady stream of electrons. This is how electrons were produced in old radio valves and in X-ray tubes.
The second way is a very strong electric field, of the order of 10⁸ volt per metre. Watch the energy picture: the field tilts the energy outside the surface downhill, and the barrier holding the electrons in becomes very thin.
Electrons are pulled straight out of the metal, even when it is cold. This is field emission. It happens at the sharp electrode of a spark plug, where the field is strongest.
The third way is light. When light of a suitable frequency falls on a metal surface, electrons are emitted. This is photoelectric emission, and the electrons are called photoelectrons.
Notice the words, a suitable frequency. Ultraviolet light pulls electrons out of zinc, but red light does not, however bright it is. That clue will lead us to the photon.
So: heat gives thermionic emission, a strong field gives field emission, and light gives photoelectric emission. In every case, the electron must get at least the work function φ₀ to escape.
Try it: getting electrons out
- Heat: lower the temperature to 300 K. Compare kT with φ₀ and watch the emission stop. Where does it start again?
- Try caesium (φ₀ = 2.14 eV) and platinum (5.65 eV) at the same temperature. A smaller work function makes emission enormously easier.
- Strong field: raise E and watch the barrier width w = φ₀/(eE) shrink. Electrons come out only when it is down to a couple of nanometres.
- Light: find the longest wavelength that frees electrons from sodium. Below it, the photon arrow does not reach the vacuum level.
Work function in joules
The work function of sodium is 2.75 eV. What is this in joules?
- 4.41 × 10⁻¹⁹ J
- 2.75 × 10⁻¹⁹ J
- 1.72 × 10¹⁹ J
- 4.41 × 10⁻¹⁸ J
Answer
A. 1 eV = 1.602 × 10⁻¹⁹ J, so φ₀ = 2.75 × 1.602 × 10⁻¹⁹ J = 4.41 × 10⁻¹⁹ J. Dividing by 1.602 × 10⁻¹⁹ instead of multiplying gives the absurd 1.72 × 10¹⁹ J; an electron volt is a tiny amount of energy.
Why not at room temperature?
A piece of tungsten at room temperature does not emit electrons, but a tungsten filament at 2500 K does. Why?
- At room temperature, tungsten has no free electrons
- The work function of tungsten becomes zero when it is hot
- At 300 K the thermal energy kT ≈ 0.026 eV is far below φ₀; at 2500 K a few of the fastest electrons have energy above φ₀
- Heat creates new electrons inside the metal
Answer
C. A metal always has free electrons; the surface holds them in. To escape, an electron needs at least φ₀ ≈ 4.5 eV for tungsten. At 300 K, kT ≈ 0.026 eV, so practically no electron has that much. At 2500 K, kT ≈ 0.22 eV: still much less than φ₀, but a tiny fraction of the electrons now have enough, and that is thermionic emission. The work function itself does not change.
Summary
- Electron volt:
1 eV = 1.602 × 10⁻¹⁹ J - Condition to escape:
energy given ≥ φ₀ - Thermal energy at 300 K:
kT ≈ 0.026 eV
- Cathode rays are streams of electrons (Thomson, 1897); Millikan measured the electron’s charge, e = 1.602 × 10⁻¹⁹ C.
- Free electrons move inside a metal but are held back at the surface by the positive ions.
- The work function φ₀ is the minimum energy needed to take an electron out of a metal. It depends on the metal and its surface: caesium 2.14 eV is the lowest and platinum 5.65 eV the highest in the NCERT table.
- Three ways to supply it: thermionic emission (heat), field emission (a field of about 10⁸ V/m) and photoelectric emission (light of suitable frequency).