EXPERIMENT # 2

“To Determining the Absorption Coefficient of Lead for Gamma Rays using
GM Counter Assembly”
Contents:

➢ Abstract
➢ Introduction
➢ Theoretical background
➢ Experimental details
➢ Setup Diagram
➢ Procedure
➢ Observations
➢ Table
➢ Graph
➢ Calculations
➢ Result
Abstract:
This experiment aims to determine the absorption coefficient of lead for gamma rays.
In this experiment, we set out to determine the absorption coefficient of lead for gamma rays using
a GM counter assembly. The absorption coefficient is a fundamental parameter in the study of
gamma ray interactions with materials, with broad applications in radiation shielding and
radiological safety. By varying the thickness of lead sheets and measuring the resulting gamma ray
counts, we established a clear relationship between lead thickness and absorption. Our results
revealed an absorption coefficient of [insert value], contributing to the understanding of gamma
ray interactions with matter and their practical applications.

Introduction:
Gamma rays are high-energy electromagnetic radiation commonly used in a variety of fields,
including medical diagnostics, industrial testing, and radiation therapy. Understanding the
behavior of gamma rays when they interact with matter is essential, especially in applications
where radiation safety is a concern. The absorption of gamma rays, described by the exponential
attenuation law, is a key parameter in this understanding.
The exponential attenuation law, expressed as I = I₀ e-μx relates the intensity of gamma rays (I) to
the initial intensity (I₀), the absorption coefficient (μ), and the thickness of the material (x). The
absorption coefficient (μ) represents the likelihood of gamma rays being absorbed or scattered by
the material.
Lead is commonly used as a shielding material in various applications due to its high density and
strong gamma ray absorption characteristics. Our hypothesis is that as the thickness of lead
increases, the gamma ray counts detected by a GM (Geiger-Muller) counter assembly will
decrease, demonstrating the relationship between lead thickness and gamma ray absorption.
Here, I am going to use virtual method to perform this experiment by using radiation lab. Where
a GM counter tube, a device capable of detecting and measuring ionizing radiations, is virtually
simulated

Theoretical Background:
Gamma rays, a type of high-energy electromagnetic radiation, are produced in various processes,
including nuclear reactions and certain radioactive decays. When gamma rays interact with matter,
their behavior can be described by the exponential attenuation law. This law states that the intensity
of gamma rays, denoted as I, decreases exponentially with the thickness of the absorbing material
(x). The equation is given by:
I = Io e-µx
Where, I is the intensity of gamma rays after passing through the material.
Io is the initial intensity of gamma rays or original intensity of the beam
 µ is the absorption coefficient, representing the probability of an interaction per
unit thickness.
x is the thickness of the absorbing material.
I
ln( ) = -µx
𝐥o

The half value thickness of the absorbing material is defined as the thickness X1/2 which will
decrease the initial intensity by half. This is,

I = Io /2
ln (2) = -µ X1/2
0.693
X1/2 =
µ
The absorption coefficient µ quantifies how effectively a material attenuates gamma rays. For a
given material, the absorption coefficient depends on the energy of the gamma rays. Materials have
different absorption coefficients for different gamma ray energies. In our experiment, we will be
working with gamma rays produced by a Ba-133 source with a specific energy.
Lead is commonly used as a shielding material due to its high density and strong gamma ray
absorption characteristics. It is particularly effective at attenuating high-energy gamma rays. As
lead thickness increases, the probability of gamma ray interactions within the material rises,
leading to a reduction in the detected gamma ray intensity. Our experiment aims to determine the
absorption coefficient of lead for gamma rays with a specific energy, allowing us to better
understand the material’s shielding properties. Furthermore, the Geiger-Muller (GM) counter
assembly is an essential tool in measuring gamma ray counts. The GM counter is a gas-filled
detector that produces an electrical signal when ionized by incoming radiation. It is highly sensitive
and used for various radiation measurement applications.
By measuring the gamma ray counts after passing through lead sheets of varying thickness, we
will be able to establish a clear relationship between lead thickness and gamma ray absorption.
This relationship will help us calculate the absorption coefficient for lead at the specific gamma
ray energy of our Ba-133 source.

Experiment Details:
Experimental Setup:
The experiment was conducted in a controlled laboratory environment to eliminate external
radiation interference. The setup consisted of the following components:
 • GM Counter Assembly:
A GM counter assembly was used to detect gamma ray counts. It was placed at a fixed distance
from the gamma ray source.
• Gamma Ray Source:
We employed a Ba-133 gamma ray source with a known intensity.
• Lead Sheets:
Lead sheets of varying thickness (0.1cm, 0.2cm and 0.3cm) were used as the absorbing material.
• Data Recording System:
A data recording system was employed to record gamma ray counts per unit time accurately.

Setup Diagram:

Figure 1: Setup diagram (Virtual setup)

Procedure:
▪ I set the virtual experimental setup.
▪ The GM counter assembly was calibrated before the experiment to ensure accurate gamma
ray count measurements.
▪ Firstly, the main supply switched on and I noted the background counting rate without any
radioactive source virtually.
▪ A gamma ray source (Ba-133) was set up, and the GM counter was positioned at a fixed
distance from the source.
▪ Then, I placed Lead sheets between the source and the GM counter, one at a time, starting
with the thinnest sheet (0.5 mm).
▪ I adjusted the power supply at the high operating voltage.
 ▪ For each lead thickness, gamma ray counts were recorded over a fixed time interval (e.g.,
30seconds), ensuring steady counting rates.
▪ The experiment was repeated for all lead thicknesses. For (0.1cm, 0.2cm and 0.3cm).
The data recorded was used to establish the relationship between lead thickness and gamma
ray absorption, ultimately allowing us to calculate the absorption coefficient for lead.

Observations and calculations:

Radiation source:
Ba-133
Absorber: Lead
Counting time: 30 sec
Voltage: 950
Distance: 25cm
Background counts: net counts per sec 1.24
Io = 80.6

Table: (1)

Sr # Thickness Recorded gross count for 30 sec Mean Mean Net count
(cm) gross gross rate
count per count per (I)
30 sec sec
i. 1607
ii. 1642
1. 0.1 1610 53.6 52.3
iii. 1581
i. 1370
ii. 1306
2. 0.2 1349 44.9 43.7
iii. 1372
i. 1138
ii. 1100
3. 0.3 1116 37.2 36
iii. 1109
Table: (2)

Sr.no Thickness (cm) ln(

𝐈
)
𝐥𝐨
1. 0.1 -0.433

2. 0.2 -0.612
3. 0.3 -0.805

Graph:

-0.3
0.1 0.2 0.3
-0.4

-0.5
ln (I/Io)

-0.6

-0.7

-0.8

-0.9
thickness (cm)

Calculations:
We have to find the value of µ,
By using Graph (2)
µ = slope
y2−y1
µ=
x2 −x1
−0.433−(−0.612) 0.17
µ= =
0.2−0.1 0.1
 µ = 1.7 cm-1

Half value thickness is

0.693
X1/2 =
µ
0.693
X1/2 =
1.7
X1/2 = 0.41 cm

Conclusion:
The absorption coefficient of lead for gamma rays is µ = 1.7 cm-1. Absorption coefficient depends
upon the nature of radiations, density of the medium and also energy of gamma rays.