10.4 β-Spectrometry
163
point for maximum thickness (known as R max ) corresponding to E max . This point can
be taken as the maximum range of the β-particles, provided the radioactive nuclide
is a pure β-emitter. Other method is by Feather Analysis, which is discussed here.
10.4.2 Feather Analysis
Most of β-emitters decay along with γ -rays (see Decay Scheme, Chaps. 7 and 8).
Due to the presence of γ -rays, it becomes difficult to decide the exact thickness
corresponding to the E max value. Like Bremsstrahlung radiation, γ -rays are also not
absorbed by the aluminum absorber, as a result, constant count rate is observed even
after the R max value. Moreover, count rate is also higher than that observed with
Bremsstrahlung radiation. For such cases, a Feather analysis is preferred, where the
relationship between R max and E max is derived by comparison of β-absorption curve
of the sample with that of a pure β-emitter, like
32 P. An absorption curve is plotted as
stated earlier and approximate value of R max is calculated from the method discussed
earlier. From approximate R max value calculated, the exact E max value is obtained,
with the help of empirical Feather’s Eqs. (10.2) and (10.3).
R(mgcm
−2
) = 543E max (MeV) − 160
(10.2)
or
E max (MeV) =
R
543
+ 294
(10.3)
10.4.3 Graphical Absolute Method
There are a number of difficulties in determining the accurate E max , by either of the
methods discussed earlier, especially if the source is a weak β-emitter and associated with γ -rays. In Feather analysis, it is frequently necessary to extrapolate the line
with pronounced curvature (Fig. 10.1 inset), forms of which depend strongly on the
geometrical counting conditions, and the accuracy of comparing the data with the
standard sample. This technique has not been discussed here, but the final equation
obtained from the analysis known as Feather analysis is mentioned earlier. A graphical absolute method for determining E max of β-particle developed by Barreira and
Laranjeira in 1957, is preferred and discussed here.
As discussed earlier, an absorption graph is plotted between the thickness of
the absorber on a semi-log graph paper, after subtracting the normal background
(Fig. 10.2). A tangent, M N (Fig. 10.2) is drawn at a suitable curvature (K ) of the
absorption plot. Then the absorption curve is projected on to this tangent M N with
horizontal lines ( AB, C D etc.) at the various thickness of the absorber. To every
163
point for maximum thickness (known as R max ) corresponding to E max . This point can
be taken as the maximum range of the β-particles, provided the radioactive nuclide
is a pure β-emitter. Other method is by Feather Analysis, which is discussed here.
10.4.2 Feather Analysis
Most of β-emitters decay along with γ -rays (see Decay Scheme, Chaps. 7 and 8).
Due to the presence of γ -rays, it becomes difficult to decide the exact thickness
corresponding to the E max value. Like Bremsstrahlung radiation, γ -rays are also not
absorbed by the aluminum absorber, as a result, constant count rate is observed even
after the R max value. Moreover, count rate is also higher than that observed with
Bremsstrahlung radiation. For such cases, a Feather analysis is preferred, where the
relationship between R max and E max is derived by comparison of β-absorption curve
of the sample with that of a pure β-emitter, like
32 P. An absorption curve is plotted as
stated earlier and approximate value of R max is calculated from the method discussed
earlier. From approximate R max value calculated, the exact E max value is obtained,
with the help of empirical Feather’s Eqs. (10.2) and (10.3).
R(mgcm
−2
) = 543E max (MeV) − 160
(10.2)
or
E max (MeV) =
R
543
+ 294
(10.3)
10.4.3 Graphical Absolute Method
There are a number of difficulties in determining the accurate E max , by either of the
methods discussed earlier, especially if the source is a weak β-emitter and associated with γ -rays. In Feather analysis, it is frequently necessary to extrapolate the line
with pronounced curvature (Fig. 10.1 inset), forms of which depend strongly on the
geometrical counting conditions, and the accuracy of comparing the data with the
standard sample. This technique has not been discussed here, but the final equation
obtained from the analysis known as Feather analysis is mentioned earlier. A graphical absolute method for determining E max of β-particle developed by Barreira and
Laranjeira in 1957, is preferred and discussed here.
As discussed earlier, an absorption graph is plotted between the thickness of
the absorber on a semi-log graph paper, after subtracting the normal background
(Fig. 10.2). A tangent, M N (Fig. 10.2) is drawn at a suitable curvature (K ) of the
absorption plot. Then the absorption curve is projected on to this tangent M N with
horizontal lines ( AB, C D etc.) at the various thickness of the absorber. To every