Velocity of 1 MeV alpha particles |
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Let v = velocity. Mass = 4x1.66e-27 kg
Thus, v = 6.9e6 m/s |
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,
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.
The Born-Bethe formula for energy loss per unit length (dE/dx) of charged particles, |
dE K M Z^{2}
---- = -------- dx E |
K - proportional constant M, Z - mass and atomic number of the atom E - energy of alpha particle |
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.
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} |
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distance * density
~ cm * g cm^{-3} ~ g cm^{-2} |
Example 1
Solution
The number of pairs and the ion-pair densityare estimated as follows:
5.0e6 eV --------- 35 eV | = 142900 pairs. |
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142900 pairs --------- 10 cm | = 14290 ion pairs / cm |