Physical Structure of Matter
Radioactivity
Law of distance and absorption of gamma or beta rays
5.2.41-01/11
What you can learn about …
Radioactive radiation
Beta-decay
Conservation of parity
Antineutrino
Gamma quanta
Half-value thickness
Absorption coefficient
Term diagram
Pair formation
Compton effect
Photoelectric effect
Conservation of angular
momentum
Forbidden transition
Weak interaction
Dead time
Principle:
The inverse square law of distance is
demonstrated with the gamma radiation from a 60Co preparation, the
half-value thickness and absorption
Set-up of experiment P2524111 with Cobra3
What you need:
µ
cm
Experiment P2524111 with Cobra3
Experiment P2524101 with GM Counter
Unit-construction plate for radioactivity
09200.00
1
1
Counter tube, magnet held
09201.00
1
1
Source holder, magnet held
09202.00
1
1
Plate holder for demo. board with magnet
09204.00
1
1
Counter tube, type A
09025.11
1
1
Screened cable, BNC, l = 750 mm
07542.11
1
1
Vernier caliper
03010.00
1
1
Radioactive sources, set
09047.50
1
1
Absorption plates for b-radiation
09024.00
1
1
Absorption material, lead
09029.01
1
1
Absorption material, iron
09029.02
1
1
Absorption material, aluminium
09029.03
1
1
Absorption material, Plexiglas®
09029.04
1
1
Absorption material, concrete
09029.05
1
1
Geiger-Müller Counter
13606.99
1
RS232 data cable
14602.00
1
Cobra3 Basic Unit
12150.00
1
Power supply, 12 V-
12151.99
1
Counter tube module
12106.00
1
Cobra3 Radioactivity Software
14506.61
1
PC, Windows® 95 or higher
Complete Equipment Set, Manual on CD-ROM included
Law of distance and absorption of gamma
or beta rays
P25241 01/11
PHYWE Systeme GmbH & Co. KG · D - 37070 Göttingen
g cm
Attenuation coefficient of different materials as a function of the material density (from left to right: Plexiglas®, concrete, aluminium, iron, lead).
coefficient of various materials
determined with the narrow beam
system and the corresponding mass
attenuation coefficient calculated.
Tasks:
1. To measure the impulse counting
rate as a function of the distance
between the source and the counter tube.
2. To determine the half-value thickness d1/2 and the absorption coefficient of a number of materials
by measuring the impulse count-
ing rate as a function of the thickness of the irradiated material.
Lead, iron, aluminium, concrete
and Plexiglas are used as absorbers.
3. To calculate the mass attenuation
coefficient from the measured
values.
Laboratory Experiments Physics 225
LEP
5.2.41
-01
Law of distance and absorption of gamma or beta rays
Related topics
Radioactive radiation, beta-decay, conservation of parity, antineutrino, gamma quanta, half-value thickness, absorption
coefficient, term diagram, pair formation, Compton effect,
photoelectric effect, conservation of angular momentum, forbidden transition, weak interaction, dead time.
Principle
The inverse square law of distance is demonstrated with the
gamma radiation from a 60CO preparation, the half-value
thickness and absorption coefficient of various materials
determined with the narrow beam system and the corresponding mass attenuation coefficient calculated.
Equipment
Radioactive sources, set
Absorption plates for b-radiation
Unit-construction plate for radioactivity
Counter holder, magnet held
Source holder, magnet held
Plate holder for demonstration board
with magnet
Vernier caliper
Screened cable, BNC, l = 750 mm
Counter tube, type A, BNC
09047.50
09024.00
09200.00
09202.00
09201.00
1
1
1
1
1
09204.00
03010.00
07542.10
09025.11
1
1
1
1
Geiger-Müller Counter
Absorption material, lead
Absorption material, Plexiglas
Absorption material, iron
Absorption material, concrete
Absorption material, aluminium
13606.99
09029.01
09029.04
09029.02
09029.05
09029.03
1
1
1
1
1
1
Tasks
1. To measure the impulse counting rate as a function of the
distance between the source and the counter tube.
2. To determine the half-value thickness d1/2 and the absorption coefficient m of a number of materials by measuring the
impulse counting rate as a function of the thickness of the
irradiated material. Lead, iron, aluminium, concrete and
Plexiglas are used as absorbers.
3. To calculate the mass attenuation coefficient from the
measured values.
Set-up
According to Fig. 1.
The distance between the front edge of the source rod and the
counting tube window is approximately 4 cm; consequently,
the absorption plates can be easily inserted into the radiation
path.
Fig. 1: Experimental set-up for measuring the half-value thickness of different materials.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
25241-01
1
LEP
5.2.41
-01
Law of distance and absorption of gamma or beta rays
Theory and evalution
The cobalt isotope 60
27 Co has a half-life of 5.26 years; it undergoes beta-decay to yield the stable nickel isotope 60
28 Ni– see
Fig. 2.
Fig. 3: Law of distance relating to rays which are propagated
in a straight line from a point source.
From the regression lines from the measured values in Fig. 4,
applying the exponential expression
.
N ( r) = a · rb,
we obtain the value
b = – 2.07 ± 0.01
for the exponent.
This thus proves the applicability of the inverse square law.
Fig. 2: Term diagram of
60
27
Co.
As with most beta emitters, disintegration leads at first to
daughter nuclei in an excited state, which change to the
ground state with the emission of gamma quanta. Whereas
the energy levels of the beta electrons can assume any value
up to the maximum because of the antineutrinos involved, the
gamma quanta which participate in the same transition process have uniform energy, with the result that the gamma
spectrum consists of two discrete, sharp lines (Fig. 2).
.
The impulse counting rate N ( r) per area A around a pointsource decreases in inverse proportion to the square of the
distance provided the gamma quanta can spread out in
straight lines and are not deflected from their track by interactions.
r2 2 r1
A2 4 · A1 a
r2 2
b · A1
r1
The reason for this is that, as shown by Fig. 3, the area of a
sphere round the source through with a beam of rays passes,
increases as the square of the distance r. In vacuum (in air),
therefore
N 1r2
N 1o2
1 2
·
r
A
A
4p
.
If we plot the counting rate N( r) versus the distance r on a loglog scale, we obtain a straight line of slope – 2.
2
25241-01
Fig. 4: Counting rate plotted against distance (log-log plot).
The attenuation of the gamma rays when they pass through an
absorber of thickness d is expressed by the exponential law
.
.
N (d) = N (o) · e–Nd,
.
where N (d) is the. impulse counting rate after absorption in the
absorber, and N (o) is the impulse counting rate when no
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEP
5.2.41
-01
Law of distance and absorption of gamma or beta rays
absorption takes place: N is the absorption coefficient of the
absorber material and depends on the energy of the gamma
quantum.
The absorption of the gamma rays is brought about by three
independent effects – the Compton effect, the photelectric
effect and pairformation.
The relative contributions of these three effects to total
absorption depends primarily on the energy of the quanta and
on the atomic number of the absorber (Fig. 5).
.
Fig. 6: Impulse counting rate N as a function of the thickness
d of the absorber.
The half-value thickness d1/2 of a material is defined as the
thickness at which the impulse counting rate is reduced by
half, and can be calculated from the absorption coefficient in
accordance with
d1/2 =
ln 2
.
m
Fig. 5: Absorption of gamma rays by leads as a function of the
energy (NCo = fraction due to Compton effect, NPh =
fraction due to photoelectric effect, NPa = fraction due
to pair formation). The total absorption coefficient
(attenuation coefficient) is N = NCo + NPH + NPa
From the regression lines from the measured values in Fig. 6
we obtain the following values for N = b and for d1/2 and N/S,
with the relevant standard errors, using the exponential
expression
.
N = aebd.
We can see from the N/E curves in Fig. 6 that lead is particularly suitable as an absorber of gamma rays of low or high
energy.
Lead: (S = 11.34 gcm-3)
N
= 0.62 cm-1,
d1/2 = 1.12 cm,
m
= 0.055 cm2g-1;
The attenuation of gamma rays therefore takes place predominantly in the electron shell of the absorber atoms. The
absorption coefficient N should therefore be proportional to
the number of electrons in the shell per unit volume, or
approximately proportional to the density S of the material.
The mass attenuation coefficient N/S is therefore roughly the
same for the different materials.
r
sN = 0.009 cm-1
sd1/2 = 0.02 cm
sN/S = 0.001 cm2g-1
Aluminium: (S = 2.69 gcm-3)
N
= 0.15 cm-1,
sN = 0.01 cm-1
d1/2 = 4.6 cm,
sd1/2 = 0.3 cm
m
= 0.056 cm2g-1;
sN/S = 0.004 cm2g-1
r
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
25241-01
3
LEP
5.2.41
-01
Law of distance and absorption of gamma or beta rays
Iron: (S = 7.86 gcm-3)
N
= 0.394 cm-1,
d1/2 = 1.76 cm,
m
r
= 0.050 cm2g-1;
Plexiglas: (S = 1.119 gcm-3)
sN = 0.006 cm-1
sd1/2 = 0.03 cm
sN/S = 0.001 cm2g-1
Concrete: (S = 2.35 gcm-3)
N
= 0.124 cm-1,
sN = 0.009 cm-1
d1/2 = 5.6 cm,
sd1/2 = 0.4 cm
m
r
4
= 0.053 cm2g-1;
25241-01
sN/S = 0.004 cm2g-1
N
= 0.078 cm-1,
d1/2 = 8.9 cm,
m
r
= 0.066 cm2g-1;
sN = 0.004 cm-1
sd1/2 = 0.5 cm
sN/S = 0.003 cm2g-1
Comment
The procedure and evaluation are shown here in an exemplary
experiment for g-quanta; however, they can also be performed
in an analogous manner for electrons. In the latter case, the
Sr-90 source rod from the radioactive sources set (09047.50)
and the absorption plate set for b-radiation (09024.00) must
be used.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
LEP
5.2.41
-11
Law of distance and absorption of gamma or beta rays with Cobra3
Related topics
Radioactive radiation, beta-decay, conservation of parity, antineutrino, gamma quanta, half-value thickness, absorption
coefficient, term diagram, pair formation, Compton effect,
photoelectric effect, conservation of angular momentum, forbidden transition, weak interaction, dead time.
Principle
The inverse square law of distance is demonstrated with the
gamma radiation from a 60Co preparation, the half-value thickness and absorption coefficient of various materials determined with the narrow beam system and the corresponding
mass attenuation coefficient calculated.
Equipment
Cobra3 BASIC-UNIT
Cobra3 Power supply
RS232 data cable
Cobra3 Radioactivity Software
Counter tube module
Unit-construction plate for radioactivity
Counter tube, magnet held
Source holder, magnet held
Plate holder for demonstration board
with magnet
Counter tube, type A
Screened cable, BNC, l = 300 mm
12150.00
12151.99
14602.00
14506.61
12106.00
09200.00
09201.00
09202.00
1
1
1
1
1
1
1
1
09204.00
09025.11
07542.10
1
1
1
Vernier caliper
Radioactive sources, set
Absorption plates for b-radiation
Absorption material, lead
Absorption material, iron
Absorption material, aluminium
Absorption material, Plexiglas®
Absorption material, concrete
PC, Windows® 95 or higher
03010.00
09047.50
09024.00
09029.01
09029.02
09029.03
09029.04
09029.05
1
1
1
1
1
1
1
1
Tasks
1. To measure the impulse counting rate as a function of the
distance between the source and the counter tube.
2. To determine the half-value thickness d1/2 and the absorption coefficient N of a number of materials by measuring the
impulse counting rate as a function of the thickness of the
irradiated material. Lead, iron, aluminium, concrete and
Plexiglas are used as absorbers.
3. To calculate the mass attenuation coefficient from the
measured values.
Set-up
According to Fig. 1.
The distance between the front edge of the source rod and the
counting tube window is approximately 4 cm; consequently,
the absorption plates can be easily inserted into the radiation
path.
Fig. 1: Experimental set-up.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
25241-11
1
LEP
5.2.41
-11
Law of distance and absorption of gamma or beta rays with Cobra3
Procedure
— Activate the ”Radioactivity” program module, and start the
measurement stand-by phase (cf. Fig. 2).
— Measure the background radiation without the radiation
source. To do this, it is advisable to use a gate time of
more than 500 s. The measured background rate remains
in the Cobra3’s memory until it is overwritten by a new
background measurement.
Fig. 2. Measuring parameters.
— Diagram settings:
y axis:
0 to 15
x axis:
0 to 30 mm
— Activate measurement by clicking on <Continue>.
— During the measurement the distance between the counting tube and the source (Co-60) must not be changed.
Initially, enter ”0” in the input field for the absorber layer (cf.
Fig. 3) and click on <Measure>.
Remarks
Immediately after <Continue> has been clicked on in the
Parameter field (Fig. 2), the measurement process begins,
i.e. one must wait until a gate time period has elapsed
before a measuring result appears in the display.
— After each measurement increase the layer thickness of
the lead absorber by 5 mm, enter the new thickness value
of the absorber layer in the appropriate field and click on
<Measure>. Continue in the same manner until the maximum thickness of 30 mm has been reached. After the last
measurement has been made, click on the <Close> button.
— Perform absorption measurements in the same manner
with the following absorber materials:
Iron, aluminium, Plexiglas®, concrete.
Results
— Figure 3 shows the counting rate as a function of the
absorber layer thickness. The data (measured) points confirm the approximately exponential decrease in the counting rate as a function the layer thickness.
— The g-quanta emitted by the source (Co-60) are absorbed
in the lead layer to differing degrees depending on the
layer thickness d. Accordingly, the quantum flux I is attenuated by the absorption layer compared to quantum flux I0
in the air. The attenuation of the quantum flux occurs in
accordance with the absorption law; the quantum flux I
decreases approximately exponentially with increasing
layer thickness d.
I I0 · e md
Fig. 3. Typical display structure during the measurement;
counting rate (Co-60) as a function of the absorber
layer thickness (Pb plates).
2
25241-11
Fig. 4. Half-value thickness and the attenuation for lead
absorber plates.
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
Law of distance and absorption of gamma or beta rays with Cobra3
where m is the attenuation coefficient characteristic for the
material (and the energy of the g-radiation).
For a very specific layer thickness dH the initial quantum
flux is reduced to half of its original value.
1
I I0 · e mdH
2 0
From this it follows that the half-value thickness dH is
determined by the attenuation coefficient m.
dH ln 2
m
or
m
ln 2
dH
.
LEP
5.2.41
-11
— In the second part of the experiment layers of material
exhibiting differing thickness d and different densities r are
positioned in the radiation field between the g-source Co60 and the counter tube. In a manner analogous to the
evaluation described above, determine the half-value
thicknesses for iron, aluminium, Plexiglas® and concrete,
and calculate their attenuation coefficient:
Material
Density
g/cm3
Half-value (layer)
thickness
dH in cm
Attenuation
coefficient
m in cm-1
Lead
11.11
1.41(1)
0.50
Iron
7.68
2.3(4)
0.30
Aluminium
2.70
7(3)
0.09
Concrete
1.87
6(3)
0.12
Plexiglas®
1.19
35(82)
0.02
The attenuation coefficient m characterises the absorption
behaviour of the material with respect to g-quanta.
— Determination of the half-value thickness and the attenuation coefficient m.
Both parameters are displayed if the exponential measurement curve in the active image can be seen and then the
evaluation functions <Analysis>, <Half-value time /-layer
thickness> are selected.
Naturally, these parameters can also be manually determined by initially calculating the natural logarithm of the
measured values with <Channel modification> and by subsequently fitting a straight line through the thus manipulated measured values. The following is then true for the halfvalue layer thickness dH:
ln 2
dH ,
m
The attenuation coefficient m increases approximately proportionally to the density r of the absorption material.
m mm · r
The proportionality factor, the mass attenuation coefficient mm
for lead is obtained from the attenuation coefficient m according to the following equation:
mm m
cm2
0.045
.
r
g
The mass attenuation coefficient mm is approximately the
same for all materials (if the energy of the g-quanta is fixed).
Consequently, the attenuation law is also pragmatically written
in the following form:
where m is the slope of the straight line.
In this exemplary measurement the half-value thickness of
lead is dH = 1.416 ± 0.009 cm and the attenuation coefficient is m = 0.5 ± 0.1 cm-1.
Fig. 5. Attenuation coefficient m of different materials as a
function of the material density r (from left to right:
Plexiglas®, concrete, aluminium, iron, lead).
I I0 · e mmm''
with
m'' r · d .
The mass coverage m” states which mass an absorption layer
has per unit surface. The mass coverage m” is a decisive
parameter for the attenuation of a g-flux.
Remarks
— The counting rates measured depend on the source used
and on the age of the specimen.
— The attenuation coefficients m are also a function of the
energy of the emitted g-quanta, which is relatively high for
Co-60 (hard g-radiation). At lower energies (soft g-radiation) the attenuation coefficients exhibit different values.
— When using radioactive substances, conform absolutely to
the stipulations of the respective applicable radiation protection regulations. Radioactive substances can be hazardous to your health! Always reduce the time spent handling radioactive substances to a minimum. Do not eat or
drink in the presence of radioactive substances and
always wash you hands after contact with radioactive substances!
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen
25241-11
3
LEP
5.2.41
-11
4
Law of distance and absorption of gamma or beta rays with Cobra3
25241-11
PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen