Physics and Engineering of Radiation Detection

2.5. Interaction of Electrons with Matter 135

Re

Thickness

L

og

(C

ounts

)

Log(Background Counts)

Figure 2.5.6: Typical absorp-

tion curve for electrons passing

through a material. The curve

deviates from the ideal straight

line with increasing thickness.

Since the extrapolation of the

straight line overestimates the

range, therefore normally the end

of the curve is extrapolated to the

background level to determine the

true range. This corresponds to

the electrons of endpoint energy.

higher energies. This can be seen from Fig.2.5.7, where we have plotted the ESTAR
data for water and air along with the values computed from the above expressions.
It should be noted that the spectrum of electrons emitted from a radioactive
source is continuous with an endpoint energy. In such a case generally one is inter-
ested in determining the range of the most energetic electrons. This can simply be
done by substituting the endpoint energy of the spectrum into the above expression.
Such computations are important, for example to determine the shielding necessary
for a particular source in the laboratory.
The specific range as computed from the expressions 2.5.28 or obtained from some
other data source (such as ESTAR) can be divided by the density of the material to
determine the range in units of distance, such as

Re=

Rspe

ρ

, (2.5.29)

whereρdenotes the density of the material.

Example:

Compute the thickness of aluminum shielding required to completely stop

electrons having an endpoint energy of 5MeV.