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By use of classical mechanics, Bohr developed an equation of stopping power, -dE/dx, given as the product of a kinematic factor and a stopping number.
Incorporating this effect, the stopping number of an electron is given by a complicated expression that involves a different arrangement of the parameters found in the stopping number of heavy charged particles; i.e., This stopping-power formula has a wide range of validity, from approximately a few hundred electron volts to a few million electron volts in materials of low atomic number.
The most important nontrivial quantity in the equation for stopping number is the mean excitation potential, I. Experimental values of this parameter, or quantity, are known for most atoms, but no single theory gives it over the whole range of atomic numbers because the calculation would require knowledge of the ground states and all excited states.
Even though the basic stopping-power theory has been developed for atoms, it is readily applied to molecules by virtue of Bragg's rule (named for the British physicist William H. Bragg), which states that the stopping number of a molecule is the sum of the stopping numbers of all the atoms composing the molecule.
The stopping number includes the atomic number and the natural logarithm of a term that includes the velocity of the incident particle as well as its charge, a typical transition energy in the system (see Figure 1; a crude estimate is adequate because the quantity appears within the logarithm), and Planck's constant, h.
The theory by which Bethe derived a stopping number is generally accepted as providing the framework for understanding the variation of range with energy, though in practice the mean excitation potential, I, must be obtained in many cases by experimental curve fitting.
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