Interaction of Radiation with Matter - Heavy Charged Particles

Atomic nuclei from particle accelerators, alpha particles and hadrons (mesons and baryons, protons included) are heavy charged particles, their masses are much more than leptons. However, the mass of tau, a heavy lepton, is twice as heavy as a proton.

Velocity of 1 MeV
alpha particles
Let v = velocity.
Mass = 4x1.66e-27 kg

Thus,
1 MeV = 1.60e-13 J
= (1/2)(4x1.66e-27 kg) v2

v = 6.9e6 m/s

Charged particles interact with electrons and nuclei via Coulomb interaction. These particles move at high speed. For example, an alpha particle with 1 MeV kinetic energy is moving with a speed of 6.9x106 m/s, almost 2% the speed of light. At higher energy, Einstein's theory of relativity should be applied to estimate the speed.

Because of the high molecular density, the number of ion pairs per unit volume or per unit length on the path produced by an alpha particle is very high. Multiple ionization also takes place,

A ® An+ + n e- where A is an atom or a molecule, and n is an integer. In this ionization process, secondary electrons are also produced by primary electrons.

Due to Coulomb interaction, alpha particles may excite an electron to a higher energy state, rather than knocking it off the molecule. Ionization and excitation break chemical bonds, and generate reactive species that cause further chemical reactions.

Stopping Power and Ion Pair Density on the Path of Alpha Particles

The Born-Bethe formula for
energy loss per unit length
(dE/dx) of charged particles,
dE     K M Z2
---- = --------
dx
        E     
K - proportional constant
M, Z - mass and atomic
    number of the atom
E - energy of alpha particle
The stopping power of a medium is the rate of energy loss per unit distance along the path. Born and Bethe have shown that the stopping power of a medium is proportional to the mass M, and to the square of atomic number, Z2, of the atoms in the medium. Thus, a medium consisting of heavy atoms have high stopping power. However, the stopping power is inversely proportional to the energy of the particle. A fast moving particle deposit less energy per unit length on its track. High stopping power results in generating high ion pair density.

As an alpha particle losses its energy, the stopping power increases. At the end of its path, the stopping power is the highest. Thus, along the path, the ion-pair density is the highest at the path end.

Heavy particles lose energy in a medium at a faster rate than light particles. They generate higher ion-pair densities. Thus, the tracks of alpha particles are different from those of fast moving protons.

Ranges of Heavy Particles

Heavy particles such as protons and alpha particles of certain energy will lose all their energies in a definite distance in a medium, and this distance is called the range. The range is the distance travelled by the particle.

The range depends on the energy and mass of the particles. The higher the energy, the larger is the range. When two particles have the same kinetic energy, the heavier one has a shorter range.

A graph showing the relationship between the range and energy such as the one shown here can be constructed from measurements of some standard sources. If the range of a charged particle source is measured, the energy of the particles can be determined against the chart. The range in aluminium is often used.

The range is a distance or thickness traveled by the particles, but the thickness is often measured in mass per unit area, which is the density times the distance.

Units of range,
cm or g cm-2
distance * density
    ~ cm * g cm-3
    ~ g cm-2

Example 1

On average, 35 eV is required to produce an ion pair. How many ion pairs are produced by a alpha particle with a 5.0 MeV kinetic energy? If the range of the alpha particle is 10 cm, what is the average ion-pair density?

Solution

The number of pairs and the ion-pair densityare estimated as follows:

5.0e6 eV
---------
35 eV
= 142900 pairs.
142900 pairs
---------
10 cm
= 14290 ion pairs / cm
The number of ion pairs is very high, although the total charge is little.

©cchieh@uwaterloo.ca