10.7 Half-Thickness
167
10.7 Half-Thickness
Since the law of exponential absorption, as stated for β-particles, is applicable to any
radiation, it can also be used for γ -rays. In the equation
I = I 0 e
μx
log I = log I 0 − μx
If
I =
1
2
I 0
then
x 0.5 =
0.693
μ
(10.4)
This suggests that the value of x 0.5 is specific for the respective energy of radiation
because μ is the linear absorption coefficient (cm
−1 ) of the radiation. Thickness of
absorber for which count rate becomes half of the initial value is equal to x 0.5 .
This thickness is called Half-thickness. Tables giving the energy of radiation and its
corresponding half-thickness of β-particles and γ -rays are available. Therefore, once
the half-thickness is determined, the energy of β-particles or γ -rays can be observed
from the table, and hence, the radioactive isotope can be identified. Half-thickness,
therefore, can also be used to identify radioactive isotope.
For the determination of half-thickness, we normally plot an absorption curve
as described earlier, and by examining the curve, half-thickness is determined. It is
worth remembering that aluminum or mica sheet absorbers are used for β-particles
and lead sheet for γ -rays. This is because, γ -rays possessing more penetrating power
and being energetic, would require a very thick aluminum sheet to stop. Hence, to
keep the thickness to a minimum value and yet enough to stop γ -rays, absorber with
higher atomic weight element like lead is used. The unit of thickness (gcm
−2 ) for
this purpose is expressed by multiplying actual thickness (cm) and the density of the
material (gcm
−3 ).
10.8 Half-Life Determination
Although determination of the energy of β-particles gives some information about
the type of radioactive isotope present in the sample, the identity of the isotope is confirmed only after determining its half-life. Therefore, for the identification of radioactive nuclides, information regarding half-life should be obtained. The time required
to decay radioactive isotope to its half activity is known as half-life of the radioactive isotope. The half-life of radioactive isotopes ranges from a few microseconds
to millions of years. However, in the study of nuclear reactions or in radiochemical
167
10.7 Half-Thickness
Since the law of exponential absorption, as stated for β-particles, is applicable to any
radiation, it can also be used for γ -rays. In the equation
I = I 0 e
μx
log I = log I 0 − μx
If
I =
1
2
I 0
then
x 0.5 =
0.693
μ
(10.4)
This suggests that the value of x 0.5 is specific for the respective energy of radiation
because μ is the linear absorption coefficient (cm
−1 ) of the radiation. Thickness of
absorber for which count rate becomes half of the initial value is equal to x 0.5 .
This thickness is called Half-thickness. Tables giving the energy of radiation and its
corresponding half-thickness of β-particles and γ -rays are available. Therefore, once
the half-thickness is determined, the energy of β-particles or γ -rays can be observed
from the table, and hence, the radioactive isotope can be identified. Half-thickness,
therefore, can also be used to identify radioactive isotope.
For the determination of half-thickness, we normally plot an absorption curve
as described earlier, and by examining the curve, half-thickness is determined. It is
worth remembering that aluminum or mica sheet absorbers are used for β-particles
and lead sheet for γ -rays. This is because, γ -rays possessing more penetrating power
and being energetic, would require a very thick aluminum sheet to stop. Hence, to
keep the thickness to a minimum value and yet enough to stop γ -rays, absorber with
higher atomic weight element like lead is used. The unit of thickness (gcm
−2 ) for
this purpose is expressed by multiplying actual thickness (cm) and the density of the
material (gcm
−3 ).
10.8 Half-Life Determination
Although determination of the energy of β-particles gives some information about
the type of radioactive isotope present in the sample, the identity of the isotope is confirmed only after determining its half-life. Therefore, for the identification of radioactive nuclides, information regarding half-life should be obtained. The time required
to decay radioactive isotope to its half activity is known as half-life of the radioactive isotope. The half-life of radioactive isotopes ranges from a few microseconds
to millions of years. However, in the study of nuclear reactions or in radiochemical