Experiment 3
Linear Absorption Coefficient
Objective:
1- Verification of the absorption law of Gamma radiation.
2- Determination:
a. The linear absorption coefficient (µ).
b. The mass absorption coefficient.
c. The half value thickness of the absorbing material (X 1/2).
3- Verification of the relation between the atomic number (Z) and
linear absorption coefficient (µ) for the absorbing materials.
Theory:
When Gamma radiation passes through matter, it undergoes
absorption primarily by Compton, photoelectric and pair production
interactions. The intensity of the radiation is thus decreased as a function
of thickness of the absorbing material. The mathematical expression for
intensity ( I ) is given by the following expression:
(1)
where, I0 is the original intensity of the beam.
I is the intensity transmission through an absorber to thickness X.
µ is the linear absorption coefficient for the absorbing material.
If we rearrange eq.(1) and take the logarithm of both sides, the expression
becomes,
X
(2)
The half value layer (HVL) of the absorbing material is defined as that
thickness X1/2 which will cut the initial intensity in half. That is, I=I0/2.
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If we substitute this into eq.(2),
(3)
Putting in numerical values and rearranging eq.(3) becomes,
(4)
Radiation strongly depends on the material density, this dependence is
revealed by dividing the linear absorption coefficient by the material
density ρ, this is called the mass absorption coefficient.
Mass absorption coefficient = µ / ρ
(5)
Apparatus:
Source of radiation .
Sheets of different absorbing materials (Aluminum and Lead).
Geiger detector.
HV power supply.
Procedure:
12345678-
Connect the plugs of the electric mains.
Set the timer to 60s and the operating voltage to 380 Volt.
Record the count rate per one minute for the back ground (IB.G).
Put the source in front of the GM tube.
Record the count rate ( I0 ).
Place Al sheet midway between the source and the GM tube.
Record the count rate (I1 and I2) and then find Iavg..
Repeat steps 6 and 7 with increasing the thickness of the absorbing
material.
9- Place Pb sheet and repeat steps 6,7 and 8.
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10- Plot a graph between ln( I0 / I ) and thickness X, if the relation is a
straight line, then the absorption law is verified.
11- Find the slope from the graph, this is equal to the linear absorption
coefficient.
12- Calculate the mass absorption coefficient.
13- Plot a graph between ( I ) and thickness (X), then find the value of
the half thickness graphically.
14- Calculate the half thickness theoretically by using eq.(4).
15- Plot a graph between the linear absorption coefficient (µ) and
atomic number (Z).
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Results:
Source description
Activity (A0)
( µCi )
Element
For Al:
Z = 13
and
For Pb:
Z = 82 and
Half life (t1/2)
( year )
ρ = 2.7 g/cm3.
ρ = 11.4 g/cm3.
IB.G = ……….. min-1.
I' 0 = ………… min-1.
I0 = I' 0 - IB.G = ……… min-1
sheet
Strip
no.
X (cm)
I1
(min-1)
and
I2
(min-1)
I0 /2 = ……… min-1.
Iavg.
(min-1)
I =Iavg.-IB.G
(min-1)
ln( I0 / I)
Al
Pb
Thickness(X) =
,
where ρ is the density of absorbing material.
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µ= slope = ……….. cm-1.
( From Fig.1)
Mass absorption coefficient = ………… cm2/g.
(X1/2 )Thoertically = ln (2)/ µ= ………. cm.
(X1/2 )graphically = ………..cm.
( From Fig.2)
I (min-1)
ln(I0/I)
I0
I0/2
X (cm)
X1/2
Fig.1
X (cm)
Fig.2
µ (cm-1)
Z
Fig.3
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