NUCLEAR REACTORS DIPLOMA, CAIRO UNIVERSITY

Beta Absorption Experiment 1

Ahmed Mohsen Handoussa

5/25/2013

Beta Particle A beta particle (fast moving electron or positron) is a light negatively or positively

charged particle which is emitted at a relatively high speed by an unstable (radioactive)

nucleus in order to reach a more stable state. Although it is identical to an atomic

electron, it was not part of the nuclear structure before emission. A beta particle maybe

released from a natural or man-made source of radioactivity such as carbon-14, carbon-

11, strontium-90 and cesium-137 and it is released as one of the products of the three

radioactive beta decay processes.

The velocity of the beta particle can range from zero to nearly the speed of light. A beta

particle is more penetrating relative to an alpha particle and can travel long distances in

air, but it can easily be stopped by a piece of clothing or a few millimeters of a substance

such as aluminum.

Figure 1 A beta particle can be stopped by a few millimeters of a substance such as aluminum

Distinction between a Beta Particle and an Electron A beta particle is essentially a non pre-existing electron which is released in nuclear

decay where it always involves a range of energies up to some maximum. Electrons may

be referred to as Mono-energetic electrons from an energy standpoint since they have a

clearly defined range of energy.

Beta Particle Emission Processes (Beta decay processes) Thousands of nuclei can be produced and studied in the laboratory but only less than

300 are stable nuclei, the rest are unstable (radioactive). The degree of instability of a

nucleus grows with the increase in distance between a nuclide and a stable nuclide of

the same mass number. Some heavy nuclei decay through alpha decay process where

the nuclei have to emit an alpha particle to reduce their mass and move toward stability.

Alpha decay process is limited to certain regions where the Q-value provides sufficient

energy to tunnel through the coulomb barrier. The majority of unstable nuclei lie in

regions where alpha decay in unfavorable and the nuclei go through one or another

form of beta decay to reach stability.

Beta radioactive decay processes are caused by weak interactions, and they take place

when electrons or positrons are released from atomic nuclei. The beta decay process

must satisfy the conservation of energy, momentum and charge through its constituents.

Beta decay is a weak decay in which a neutron is converted into a proton or a proton is

converted into a neutron inside a nucleus to become more stable while maintaining a

constant mass number. When the atom contains an excess of neutrons, a neutron decays

by emitting negatively charged particles (negatrons) and incase the atom has an excess

of protons it decays by emitting positively charged particles (positrons) or by capturing

an orbital electron.

The nucleus that suffers beta particle emission will not have a change in its mass

number but its atomic number will increase by a single unit.

Beta decay may be one of three processes,

1. Beta decay/Negative beta particle emission ( Decay)

2. Positron beta decay/Positive beta particle emission ( Decay)

3. Orbital electron capture

Figure 2 Beta decay due to the weak interaction

Figure 3 Alpha decay

Figure 4 Neutron & Proton decay

Figure 5 Internal conversion

Negative Beta Particle Emission ( decay) When a neutron decays it is converted into a proton (p), negative beta particle (

) and

an anti-neutrino ( ),

At the moment of beta decay a negative beta particle and an anti-neutrino are created.

Decay of Cobalt-60 ( )

( )

Figure 6 Decay scheme of cobalt-60

Decay of Cesium-137

Cesium-137 can decay via two routes to barium-137,

1. Two step process 97%

A beta particle with a limiting energy of 0.514 MeV yields metastable barium-

137 with a shorter life which eventually emits a gamma ray with 0.662 MeV

2. Single step process (7%)

7% of the cesium-137 decays may directly yield a stable barium-137 by emitting

a ray with limiting energy 1.176 MeV

Figure 7 decay scheme of a cesium-137 source

Positive Beta Particle Emission When a proton decays it is converted into a neutron (p), positive beta particle (

) and

an neutrino ( ),

Orbital Electron Capture Decay The third beta decay process is orbital electron capture, where an orbital electron is

captured by the nucleus and becomes combined with a proton to become a neutron.

In case the decay energy is less than 1.02 MeV, the beta decay of a proton rich nucleus to

its daughter must take place by orbital electron capture. Above 1.02 MeV orbital

electron capture and positive beta decay compete. Orbital electron capture leaves a

vacancy in the atomic electron shells which produces secondary processes necessary to

fill that vacancy by emitting X-rays and auger electrons. It is more common in high Z

nuclei for orbital electron capture to occur.

Beta Particle Energy An electron does not exist inside a nucleus, but in beta decay an electron is created from

the available decay energy inside the nucleus. Beta particles are released with kinetic

energies ranging from a few keVs to a few MeVs. The Q-value energy of negative beta

decay,

( )

Kinetic Energy of the Beta Particle Released The total kinetic energy released in beta decay is the difference in rest energy between

the initial nucleus and the end-products and it is on the order of 1 MeV.

Since the beta particle and neutrino are relatively light compared to the final nucleus,

energy and momentum conservation dictate that the new nucleus get very little energy

although it carries much linear momentum.

However, the beta particle and neutrino share their energy in various ways, thus there

is not a single beta kinetic energy but a range from zero to a unique maximum.

So as a conclusion, beta particles can have various energies depending on the share

taken by the anti-neutrino and the share taken by the recoil nucleus.

Energy Loss and Range of Beta Particles Because of the ionizing action, the incident beta particle will continuously lose its

kinetic energy as it traverses through matter and will subsequently come to rest after

traversing the range.

For a particle with a known mass and charge there will be a unique range associated

with each incident energy.

Figure 8 Ionizing action of beta particles

A formula can be theoretically deduced for the rate of energy loss and hence the range

of the traversing beta particle for a given stopping material with known electron

density and ionization potential.

Figure 9 Beta Absorption Curve

In general the range of beta particles is greater than alpha particles and a few

millimeters of aluminum or tissue paper can stop few MeV beta particles.

Since beta particles are relatively light, they do not follow a straight path through the

material as they lose energy in matter by ionization.

Figure 10 Range of a beta particle inside a material

Beta Particle Interactions The amount of beta particles in a beam decreases as it passes through a material, and

this decrease in particles is due to the interactions made by the beta particles with

matter.

Beta particles can interact with matter through two main types of interactions,

1. Collisional interactions

a. Elastic collision

b. Inelastic collision

2. Radiative Interactions

Collisional Interactions In collisional interactions, beta particles interact with atoms and nuclei of the

substances they pass through, collisional interactions are divided into two types,

1. Elastic collisions

2. Inelastic collisions

Elastic Collisions

In this type of collision, the beta particles collide with atoms of substances without

losing their kinetic energy. Therefore they do not excite or ionize the collided atom and

do not lose energy by radiation in this type of collision.

The probability of this collision increases as the square of the atomic number (Z) of the

matter it passes through, and therefore the cross-section of elastic collision is

proportional to the atomic number squared (Z2).

Inelastic Collisions

In inelastic collisional interactions the beta particle bombards another particle or atom

loses some of its kinetic form of energy to it, and in case it loses energy the particle it

bombards gains energy in the form of atomic excitation or ionization.

In case the energy of the incident beta particles is sufficient to make the electron excited

to a higher level in the atom but still less than the ionization potential of the atom, then

the collision leaves the bombarded atom in an excited state. While if the energy of the

incident beta particles is larger than the incident beta particles, the atoms maybe

ionized.

Electrons that are released from atoms due to ionization after collision and have

sufficient energy to ionize other atoms are called delta electrons.

Radiative Interactions Another type of interaction with matter associated with the beta particle is the Radiative

interaction where a high energy incident electron passes through the coulomb field of a

nucleus thereby forced to deflect in a deceleration process and loses part of its energy as

electromagnetic radiation of continuous spectra in the X-ray range. This deceleration

process is referred to as bremsstrahlung (braking radiation). The rate of energy loss by

bremsstrahlung is proportional to the square of the atomic number of the atom. Emitted

radiation is referred to as braking radiation or bremsstrahlung radiation.

Beta Particles Absorption

Absorption Curve

The absorption curve is simply a relation between the thickness of the absorber

material and the logarithm of the count rate. By studying the variation of beta particles

count (n, count/mn) with the thickness (d, g/cm2) of the absorbing material they pass

through then we obtain the “beta-particles absorption curve”.

Aluminium sheets are used in the absorption experiment because they pass beta

particles and gamma rays. Gamma radiation emission due to excitation of atomic nuclei

caused by inelastic collision of beta particles with atomic nuclei causes the absorption

curve to contain errors.

There are two methods to deduce the range of beta particles in the absorber material

and hence the energies of them,

1. Visual method

2. Analytical method

Figure 11 Beta absorption curve

Visual Method

In this method the beta absorption curve is extrapolated to the x-axis. In order to plot

a pure beta absorption curve a tail must be extended under the curve and then the line

obtained (tail) is subtracted from the absorption curve.

( )

( )

Analytical Method

The number of beta particles ( ) was found to depend upon the residual range (R-d)

as follows,

( )

In the analytical method we use the relation above to plot

against the absorber

thickness to obtain a straight line. After obtaining the range (R, g/cm2) from the straight

line plot, the energy of the beta particles (E, MeV) can be determined by the empirical

range-energy formula,

Figure 12 Straight line plot in analytical method

Good Geometry

For reliable results, we need to consider good geometry. Good geometry in the beta

absorption experiment means that the absorber material has to be close to the Geiger

counter as possible.

Beta particles that reach the absorber material may encounter one of two situations,

1. Interacts with the absorber material

2. Passes through the absorber material after losing some energy

As the distance between the Geiger counter and the absorber increases, the solid angle

increases and the probability for some particles to pass undetected increases. The closer

the absorber material is to the counter, the solid angle decreases and the particles

cannot escape the counter undetected.

Error Bars

For,

Therefore,

√

√

√

For,

√

(

) (

)

(

)

Experimental Procedure

Aim

The aim of this experiment is to,

1. Study the absorption of beta particles as they travel through matter

2. Determine the range of beta particle in aluminium

3. Determine the maximum energy of the beta particles

Procedure

1. Adjust the counter at the operating voltage (700 V)

2. Adjust the counter time (1 mn)

3. Measure the average background rate (nb, count/mn)

4. Measure the absorber thickness (x, cm)

5. Insert the absorber sheet

6. Place the cesium-137/strontium-90 source

7. Take the reading of the first thickness (x1)

8. Increase the thickness and tabulate your results

9. Repeat 1-8 for the 2nd source

10. Plot the relation between ln(n) on the y-axis & the thickness on the x-axis to

obtain the absorption curve

11. Obtain the pure absorption curve for the beta particles

12. Find the maximum range and maximum energy of the emitted beta particles for

both sources

Data

For the cesium-137 source,

1. Absorber material: Aluminium

2. Aluminium density: 2.70 g/cm-3

3. Aluminum thickness: 0.012 cm

4. Voltage: 800 V

5. Time: 1 mn

6. Background count rate (nb): 54 count/mn

Table 1 Data for cesium-137

Serial Absorber thickness

(x, cm)

Count rate with

background ( ,

count/mn)

Count rate without

background ( ,

count/mn)

Statistical error

√

1 0 975 921 6.83 0.38

2 0.012 682 628 6.44 0.39

3 0.024 539 485 6.18 0.40

4 0.036 420 366 5.90 0.41

5 0.048 406 352 5.86 0.41

6 0.06 305 251 5.53 0.43

Table 2 Beta absorption curve for Cs-137

Absorber thickness

(x, cm)

Statistical error

√

0 769.59 6.65 0.036 5.27 1.32

0.012 476.59 6.17 0.046 4.67 1.17

0.024 333.59 5.81 0.055 4.27 1.07

0.036 214.59 5.37 0.068 3.83 0.96

0.048 200.59 5.30 0.071 3.76 0.94

0.06 99.59 4.60 0.100 3.16 0.79

0.072 79.59 4.38 0.112 2.99 0.75

0.92 25.59 3.24 0.198 2.25 0.56

1.14 31.59 3.45 0.178 2.37 0.59

1.39 17.59 2.87 0.238 2.05 0.51

5.00

5.20

5.40

5.60

5.80

6.00

6.20

6.40

6.60

6.80

7.00

0 0.012 0.024 0.036 0.048 0.06 0.072 0.92 1.14 1.39 1.78 2.26 3.48

ln(n

) (c

ou

nts

/mn

)

Absorber thickness (x, cm)

BETA-ABSORPTION CURVE FOR Cs-137

1.78 1.59 0.46 0.793 1.12 0.28

2.26 13.59 2.61 0.271 1.92 0.48

3.48 11.59 2.45 0.294 1.85 0.46

Therefore the range of beta particles is given by,

( ) ( )

( )

For the strontium-90 source,

1. Absorber material: Aluminium

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 0.012 0.024 0.036 0.048 0.06 0.072 0.92 1.14 1.39 1.78 2.26 3.48

ln(n

) (co

un

ts/m

n)

Absorption thickness (cm)

0.48

1.48

2.48

3.48

4.48

5.48

6.48

7.48

0 0.012 0.024 0.036 0.048 0.06 0.072 0.92 1.14 1.39 1.78 2.26 3.48

n^

1/4)

Absorption thickness (cm)

2. Aluminium density: 2.70 g/cm-3

3. Voltage: 820 V

4. Time: 1 mn

5. Background: 107 count/mn

Table 3 Data for strontium-90

Serial Absorber thickness

(x, cm)

Count rate ( ,

count/mn)

Count rate without

background ( ,

count/mn)

1 0.21 13936 13829

2 0.24 14539 14432

3 0.26 14182 14075

4 0.27 13885 13778

5 0.31 10583 10476

6 0.32 10968 10861

7 0.33 10695 10588

8 0.34 11085 10978

9 0.36 10813 10706

10 0.78 7998 7891

Table 4 Data for strontium-90

Serial Absorber thickness

(x, cm)

Count rate without

background ( ,

count/mn)

Visual method Ln( )

Statistical error

√

Analytical

Statistical error

1 0.21 13829 9.53 0.32 10.84 2.71

2 0.24 14432 9.58 0.32 10.96 2.74

3 0.26 14075 9.55 0.32 10.89 2.72

4 0.27 13778 9.53 0.32 10.83 2.71

5 0.31 10476 9.26 0.33 10.12 2.53

6 0.32 10861 9.29 0.33 10.21 2.55

7 0.33 10588 9.27 0.33 10.14 2.54

8 0.34 10978 9.30 0.33 10.24 2.56

9 0.36 10706 9.28 0.33 10.17 2.54

10 0.78 7891 8.97 0.33 9.43 2.36

Table 5 Beta absorption curve for St-90

Table 6 Visual method

Table 7 Pure beta absorption curve

For strontium-90,

The range of beta particles in aluminium is 0.31 cm, therefore the energy of the beta

particles can be obtained, (

)