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LEYBOLD Physics Leaflets

Atomic and Nuclear Physics Nuclear physics ␥ spectroscopy

P6.5.5.3

Absorption of ␥ radiation

Objects of the experiments Measuring the intensity of ␥ radiation behind an absorber as a function of the thickness of the absorber. Confirming Lambert’s law. Determining the linear attenuation coefficient ␮ as a function of the material and the ␥ energy. Calculating the absorption half- value thicknesses d 1/2.

Principles Absorption – more precisely attenuation – of ␥ radiation means the decrease of intensity when the radiation passes through matter. The transmission

The proportionality factor ␮ is called the linear attenuation coefficient. Integration of Eq. (II) leads to Lambert’s law

R (I) T R0 R0: initial counting rate, R: counting rate behind the absorber

or ln T

T

d1 2

␮ x

(III) (IV)

ln2 ␮

(V)

After passing this thickness in the absorber, the intensity of ␥ radiation has fallen to half its initial value. Several interaction processes of ␥ radiation with matter contribute to the attenuation: in the photoeffect, a ␥ quantum is absorbed. It transfers its total energy to an atom of the absorber. The probability of the photoeffect taking place strongly decreases with increasing ␥ energy. Then the influence of Compton scattering becomes dominant. In Compton scattering, the ␥ quantum transfers part of its energy to an orbital electron. The scattered ␥ quantum therefore has a smaller energy and moves into another direction than the primary ␥ quantum. This leads to decrease of the intensity at the original energy and in the original direction. The third kind of interaction, pair production, plays a role only at ␥ energies above 2 MeV.

(II)

In the experiment, the attenuation of ␥ radiation in aluminium, iron and lead is measured. The aim of the experiment is to confirm Lambert’s law. Moreover, it is demonstrated that the attenuation depends on the absorber material and on the energy of the ␥ radiation.

0210-Wei

␮ dx

␮ x

From the attenuation coefficient the absorption half- value thickness can be calculated:

characterizes the permeability of the absorber for the radiation. The greater the transmission is, the smaller is the attenuating effect. The transmission depends on the thickness x of the absorber. If the thickness x is enhanced by the small amount d x, the transmission T is decreased by the small amount d T. The relative decrease of the transmission is proportional to the absolute increase of the thickness: dT T

e

1

P6.5.5.3

LEYBOLD Physics Leaflets Setup

Apparatus

The experimental setup is illustrated in Fig. 1.

1 set of 5 radioactive preparations . . . . .

559 83

1 scintillation counter . . . . . . . . . . . . 1 high-voltage power supply 1.5 kV . . . . 1 set of absorbers and targets . . . . . . .

559 901 521 68 559 94

Mechanical setup:

1 MCA-CASSY . . . . . . . . . . . . . . . 1 MS-DOS- Connector L . . . . . . . . . . or from . . . . . . . . . . . . . . . . . . . .

529 780 524 001 524 007

– Plug the photomultiplier connectors of the scintillation

1 stand rod, 47 cm . . . . . . . 1 stand base, V-shape, 20 cm . 1 Leybold multiclamp . . . . . . 1 universal clamp, 0.80 mm dia.

300 42 300 02 301 01 666 555

. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

– Clamp the stand rod with the Leybold multiclamp and the universal stand clamp S at the back of the MCA-CASSY. counter into the detector base socket of the MCA-CASSY.

– Put the plastic tube for overlaying the absorber plates over the scintillation counter.

Connecting the MCA-CASSY:

– Connect the MCA-CASSY to the high- voltage power supply with the high- voltage cable and to the MS-DOSConnector L with the flat line. – Switch the MCA-CASSY on to activate the amplifier stage.

additionally required :

1 PC with MS-DOS 3.0 or higher version

Fig. 1

Safety notes When radioactive preparations are handled, country specific regulations must be observed such as the Radiation Protection Regulation (StrSchV) in Germany. The radioactive substances used in this experiment are approved for teaching purposes at schools in accordance with the StrSchV. Since they produce ionizing radiation, the following safety rules must nevertheless be kept to: Prevent access to the preparations by unauthorized persons. Before using the preparations make sure that they are intact. For the purpose of shielding, keep the preparations in their safety vessel. To ensure minimum exposure time and minimum activity, take the preparations out of the safety vessel only as long as is necessary for carrying out the experiment. To ensure maximum distance, hold the preparations only at the upper end of the metal holder and keep them away from your body as far as possible.

2

Experimental setup for measuring the absorption of ␥ radiation.

P6.5.5.3

LEYBOLD Physics Leaflets Carrying out the experiment

– Lay the 10 mm aluminium plate over the scintillation counter, start a new measurement, and determine the integrated counting rate. – Add further aluminium plates, and repeat the measurement. – Repeat the measurement with iron and lead plates.

a) Co 60 Recording the ␥ spectrum:

– Clamp the Co 60 preparation so that there is enough space left for the absorber plates.

b) Cs 137

– Start the program “MCA”. – Choose “Define settings” in the main menu:

– Reduce the measuring time to 30 s. – Replace the Co 60 preparation with the Cs 137 prepara-

Resolution = 8 bit (256 channels) Line diagram (confirm with ) Meas. time = 300 s

tion, and record the spectrum without absorber.

– Define the new limits of integration so that the peak of total absorption is covered, and determine the counting rate.

– Choose “Record measurement” in the main menu:

– Repeat the measurements with absorber plates over the scintillation counter (see Table 2).

Choose spectrum = Spectrum 1

– Start the measurement in the measuring screen with . – Delete old measuring values with , and start a

c) Am 241

– Choose the measuring time 45 s. – Replace the Cs 137 preparation with the Am 241 prepara-

new measurement with . – Slowly increase the voltage UPM, and adjust it so that the spectrum is distributed over all channels. – Delete old measuring values with , and start a new measurement with .

tion.

– Define the new limits of integration so that the peak of total absorption is covered, and determine the counting rate.

– Repeat the measurements with absorber plates over the scintillation counter (see Table 3).

Determining the integrated counting rate

– When the detection time is over, change to “Graphical evaluation” in the main menu, and switch on the graphics cursor with and the channel display with . – Place the cursor to the left of the two peaks of total absorption with (cursor moves to the left) and (cursor moves to the right), and enter the left limit of integration with .

– Move the cursor to the right of the two peaks of total absorption and enter the right limit of integration with . – Display the range of integration with (see Fig. 2). – Display the integrated counting rate with , and take it down.

Fig. 2

3

Co 60 spectrum with the left and right limit of integration around the two peaks of total absorption.

P6.5.5.3

LEYBOLD Physics Leaflets

Measuring example Table 1: Co 60 (E␥ = 1253 keV*): integrated counting rate N in dependence on the absorber material and the thickness d of the absorber, measuring time 300 s.

Table 3: Am 241 (E␥ = 60 keV): integrated counting rate N in dependence on the absorber material and the thickness d of the absorber, measuring time 45 s.

N

absorber material

without

d mm 0

11080

without

Al

10

9708

Al

20

absorber material

Fe

Pb

d mm 0

11488

2

10733

8655

5

8919

30

7590

7

8180

40

6671

10

7096

3

10237

12

6377

7

8543

15

5201

10

7654

17

4838

14

6684

20

4177

17

6170

21

1

5328

5099

2

2496

24

4601

3

1529

28

4191

3

9454

5

8571

8

7093

10

6352

13

5311

15

4802

18

4336

20

3744

Fe

N

Evaluation

* mean value Table 2: Cs 137 (E␥ = 662 keV): integrated counting rate N in dependence on the absorber material and the thickness d of the absorber, measuring time 30 s. absorber material

d mm

N

without

0

12630

Al

10

10724

20

9133

30

8026

40

6780

50

5960

4

10699

8

8893

12

7531

16

6444

20

5441

24

4568

28

3835

Fe

Pb

32

3195

2

10986

5

8657

7

7377

10

5529

12

4411

15

3520

17

2785

20

2070

4

Fig. 3

Co 60 (E␥ = 1253 keV): integrated counting rate as a function of the thickness of the absorber. ( ) aluminium, ( ) iron, (쑿) lead.

Fig. 4

Cs 137 (E␥ = 662 keV): integrated counting rate as a function of the thickness of the absorber. ( ( ) aluminium, ( ) iron, (쑿) lead.

P6.5.5.3

LEYBOLD Physics Leaflets

Fig. 5

Am 241 (E␥ = 60 keV): integrated counting rate as a function of the thickness of the absorber. ( ) aluminium, ( ) iron, (쑿) lead.

Figs. 3 5 are semilogarithmic plots of the integrated counting rate N as a function of the thickness d of the absorber. According to Eq. (IV), the attenuation coefficient ␮ (see Table 4) is obtained from the slopes of the straight lines through the measuring values. Its dependence on the ␥ energy is shown in Fig. 6. The values for the absorption half-value thickness d 1/2 calculated from the attenuation coefficients can be read from Table 5 and Fig. 7.

Fig. 7

The absorption half-value thickness d 1/2 as a function of the ␥ energy E. ( ) aluminium, ( ) iron, (쑿) lead.

Table 5: The absorption half-value thickness d 1/2 for different absorber materials and ␥ energies. Am 241

Cs 137

Co 60

Al

1.4 cm

4.3 cm

5.3 cm

Fe

0.09 cm

1.6 cm

1.9 cm

0.8 cm

1.3 cm

Pb

Table 4: Linear attenuation coefficient ␮ for different absorber materials and ␥ energies. 60 keV

662 keV

1253 keV

Al

0.51 cm–1

0.16 cm–1

0.13 cm–1

Fe

7.4 cm–1

0.43 cm–1

0.36 cm–1

0.86 cm–1

0.55 cm–1

Pb

Fig. 6

Results Absorption of ␥ radiation of energy E␥ in a certain material obeys Lambert’s law. The linear attenuation coefficient ␮ or the absorption half- value thickness d 1/2 respectively depend on the absorber material and the ␥ energy.

The linear attenuation coefficient as a function of the ␥ energy E. ( ) aluminium, ( ) iron, (쑿) lead.

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