Thermoluminescence

If a sample of ancient material is heated, it glows slightly but measurably more than the normal radiation given out by hot objects.  This is called thermoluminescence.   It is only seen in insulating materials like tiles; it is not seen in metals.  The intensity of thermoluminescence is only slightly greater, so needs sensitive instruments.  However, the older the material, the greater the thermo-luminescence.

Thermoluminescence can be explained by the behaviour of electrons that interact with photons.  You will be familiar with the relationship:

E = hf

You have also looked at transitions, in which excited electrons drop through the various energy levels on the quantum ladder, emitting photons.  You have also seen how the energy levels are represented in line spectra.  If you need to review this, go to the Sound of Music.

The spectra resulted from transitions in isolated atoms, i.e. gases. 

In solid materials the situation is more complex.  The electrons are affected by nearby nuclei and other electrons.  This has the effect of smearing the levels so that electrons can be in a range of allowed levels.

Most electrons remain bound to the atoms in a range of levels called the valence band.  There is a higher energy level shared between atoms called the conduction band.  Between these two is the forbidden gap.

Electrons can get sufficient energy to jump the gap and go into the conduction band. 

In real crystals there are defects.  These might be impurities or missing atoms.  They can cause extra levels to be present in the forbidden gap.   These are the defect levels.   Electrons can rest there some time, until it is disturbed (for example, by heating).  Then it will jump down to the valence band, giving out a photon.  The longer the material is buried, the more electrons are trapped in the defect levels.

The electrons are raised to the defect levels due to the action of radioactivity.

Radioactivity

You will remember that there are three kinds of radiation denoted by the first three letters of the Greek alphabet.  They are emitted by isotopes of elements with unstable nuclei which decay to other nuclei.

When doing radiation experiments, we need to take into account the background radiation, which comes radioactive nuclei in the soil, or cosmic rays from the Sun.

The X-rays superpose to form regions of constructive interference which appear as dark bands on the photographic films.  Mathematical analysis allows the archeologist to determine what crystals are there.

Measuring Faint Light

This is done by the use of a photomultiplier, a diagram of which is seen below:

A single photon of light releases a single photoelectron from a piece of photosensitive material.  The released electron is accelerated to the  first dynode (positively charged electrode).  It has gained enough energy to release more electrons, which go on to the second dynode, and so on.  It causes a cascade of electrons which is picked up as a current.

The Photoelectric Effect

The photomultiplier works because of the photoelectric effect.  We can demonstrate the photoelectric effects by attaching a reactive metal plate to a charged-up electroscope, then shining dim UV light onto it.  The electroscope discharges.  We then charge the electroscope up again, and shine a red laser onto the electroscope.  This time nothing happens.  This shows us that what we see is not a wave effect, because the amplitude of the laser light would be very large compared to that of the UV light.  It must be to do with the frequency.

Further experiments show that:

• there is a threshold frequency below which no photoelectrons are released however intense the radiation;

• above the threshold frequency, photoelectrons are released, even if the radiation is very weak;

• one photon releases one photoelectron;

• the brighter the light, the more photoelectrons are released;

• the maximum kinetic energy of the photoelectrons depends entirely on the frequency, NOT the intensity.

Below the threshold frequency, photons will increase the energy of photoelectrons, but not sufficiently to release them.

This picture shows why photoelectrons have a range of energies.  We are interested only in the maximum kinetic energy.  We can now work out a relationship between the photon frequency and the maximum kinetic energy.

The energy is supplied by the photons.  One photon leads to the release of one photoelectron.  For the photoelectron to be released, a job of work has to be done.  We call this the work function.  The rest of the photon energy is kinetic.  Therefore, by the conservation of energy:

Photon energy = kinetic energy + work function

In Physics code we write:

Eph = Ek + f

The physics code for work function is f ('phi', a Greek letter 'f').

Now we know that:

Eph = hf

So we can write:

hf = Ek + f

At the threshold frequency, the kinetic energy is zero. So we can write:

f = hf0

So we can rewrite our equation yet again to:

hf = Ek + hf0

Measuring the maximum kinetic energy of electrons is not easy to do directly, but we can do an experiment in which we shine light onto a photocathode to emit electrons.  These would be attracted to an anode.  But we reverse the voltage and increase it to a level at which even the most energetic electrons are repelled.

We call the voltage the stopping voltage.  We can relate it to the kinetic energy since:

Kinetic energy = charge × stopping voltage

So we can write:

Ek = eVs

So we can rewrite our relationship yet again:

hf = eVs + hf0

The Electronvolt

Joules are far too big and clumsy to use at this level.  So physicists have developed the idea above to express all such small energies in terms of the electronvolt (eV).   The electronvolt is defined as:

energy transferred when unit electronic charge is moved through a potential difference of 1 volt.

So we can write:

1 eV = 1.6 × 10^-19 J