EXPERIMENT #56,, :,, ,:

ABSORPTION OF GAMMA RADIATION

Theory, Definitions !J

Gamma radiation is a subset of electromagnetic radiation. So it has the samegeneral characteristics - it always propagates with the speed of light c = 3 x 108 m.s-1in a vacuum - but it can have different frequencies f (or wavelengths ,,1). Anyelectromagnetic radiation that fits into the wavelength interval of 10-11 to 10-13 m iscalled the gamma radiation.

Gamma rays lose their energy as they penetrate a substance, mainly throughthe photoelectric and Gompbn effects. A third process, pair production, is importantat very high energies of gamma rays. In this process, two charged particles (an electronand its antiparticle, a positron) 3re formed.

The photoelectric effect,(discovered by H. Hertz in 1887) is the liberation ofelectrons from the surface of a conductor when electromagnetic radiation strikes itssurface. The energy of the electromagnetic wave is transferred to electrons in thesurface layer of a conductor and - if the electrons are able to escape from the surfaceof a metal - we can measure the resulting potential difference on the conductor. Thismeans the kinetic energy of an electron is sufficient for it to overcome the surface'spotential energy barrier, called the:work function tlr of the emitting surface, Planck'stheory gives the relationship forthe so-called threshold frequency (cutt-off frequency)- the minimum frequency f;of electromagnetic radiation that can cause the photoelectriceffect for a given metal. The threshold frequency for most metals is in the ultravioletregion (corresponding to wavelengths of 200 to 300 nm), so it is beyond the frequenciesof a visible light. ,...

The correct explanation of the photoelectric effect was given by Einstein in 1905

hf 1 "= t

^v ' tW ,

where h f is the energy of a photon of electromagnetic radiation (h = 6.63 x 10-e J.sis Pfanck's constant), 112 m f is the kinetic energy with which electrons leave themetal's surface (m is the mass of an electron, v is its velocity) and tP is the workfunction (which depends on the material of a metal).

The Compton effect (Compton scattering) was first observed in 1924 by A.H.Compton. When electromagnetic radiation strikes the surface of matter, some of thescatbred radiation has lower frequency (longerwavelength) than the incident radiation.This change in frequency depends on the angle through which the radiation isscattered. lf the scattered radiation with wavelength rl' emerges at an angle @ withrespect to the direction of incident radiation with wavelength l, we can observe that thedifference in wavelength between scattered and incident radiation depends on theangle @

h

A,_A= " (1 _cos@).mc

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I,

We image the scattering process as a collision of two particles - the incidentphoton (moving with velocity c) and an electron (initially at rest). During this process, theincident photon gives up some of its energy and momentum to the electron.

Absorption of gamma radiation can be described by an exponential law. The lawcan be easily derived"in the'followihg way: if'parallel beam of N photons with equaleneryie penetrate a'certain material i4 tfiex-direction, then after covering the distancedx the radiation becomes weaker (less energetic) and dN photons are absorbed by thematerial. The decrease in the.number of photons is proportional to dx and the initialnumber of photons N

_dN = ;r N dx , (56.1)

where p is an absorption coefficient.Eq. (56.1) gives

fi/ = No e-P' (56.2)

The absorption coefficientp depends on allthree of the processes describedabove, which talie place in the absorption of gamma radiation. That is why theabsorption coefficient can be expressed as

p = lJ"+ lJp"* lJ, , , (56.3)

where p. is the absorption coefficient corresponding to the loss of energy due to theCompton effect,lrp" is the absorption coefficient corresponding to lhe loss of the energycaused by the pirbtoelectric effect, and pro is the absorption coefficient correspondingto the pair formation.

Eq. (56.2) can also be exPressed as

tn4fs = ux ,N

which means that In I 'r proportional to the thickness of the material; in the InN

versus d graph it is represented by a line through the origin (its slope is p).

The half-tlrickness dnof a material is the thickness that decreases the incidentradiation energy by one half. lt can be expressed as

ln2dttz = p

absorption coefficient [P] = m'1half-thickness [dru] = m

Objectives of the Measurement1. Gheckrthe validity ot,Eq. (56.3) by measurement measuri$.flo'Ni' Be sure thati,. ,1., you arg able to secure conditions such that the relative error o-f each

(56.41

(56.5)

No

N

The Sl units:

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2.

3.

measlrrement of number of photons Niwill be similar and will never exceed 4%

ATPlot the graph of In {} = f(x).

NCalculate the absorption coefficient of a given rnetal and check its value with thevalue obtained from the above graph a{nd with the value^from the graph inFig. 56-1, 56-2 or 56-3,. The source of gamma radiation is 60co with e-neigy of1 j 7 3 M e V .

I i '

When you measure pp6, d^eJermine the relation among all three processes inwhich gamma radiation of ouCo loses its energy.

tl(mn

1

0.3 0.40.5,,0.7 1.0 3 4 5 7 10W (MeV)

Fig. 56-1. The absorpti<in coefficient of ironas a function of the energy of gamma radiation

Gafculate the half-thickness duz .at a given material of an absorber.Determine the least energy that a gamma radiation photon must have to form an

I,

150

6.

electron4osirorrpair.|sthereanyconditionforthefrequency(wave|ength)ofthe gamrna radiation?irtii.t the enors of 1t, dtn'

Fig' 55'2' The absorption co9m951t'of cooper

ii"i i"""tion of tnl Inergy of gamma radiation, '.,

procedure of the Measurement ,. . .,--^^^ ̂r *rra rnarer at the graphl .Whenmeasur ing$,chgsgth icknessof themater ia l insuchawayth

In No/N = ttii'"in be plotted as preciselyas possible'

Z. When meaiuring Ni, chose tid; ilt"ry?lt t' in'such a way t[at the relative errors

of Ni ?re approximately-equal and do not exceed 4 o/o' ::"''''"

3. Measure t#'ffib"i 6t pnoton, lvo = Mry.".ori"rpondingio the longest time

interval Afi. Catculate the ""ir".'k

nlo,'irom N' ;- witli respect to all time

4 ilfiy'"B$tffi:lltf,::r,:?iJiiT#;,,red varues, use a chart simirarto theone below:

{0Wr$evl

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I Xi ti Ati o,{wi) _ N n, l n '' N ' '

00 ,1 0 ,20 ,5 125107050' ; \ (MeV)

i ' : .

Fig. 56-3. The absorption coefficient for lead versus energy of gamma radiationTA... totalabsorption . PE ... photpelectric effect

:i .:, CE... Compton effect ,, PF... Fair.formation

4. lf the variations of fn NdN = f(x) can be expressed as a linear function, calculate theabsorption coefficient of a given metal as ..

L

r52

I = n l ,

Ftn sq, , - 7 = t N i,r

- ---i;;-

rLx ii - 4

Accuracy of lhe ileasurement''The t'otal sror of fte absorption coefficient p is the sum of systematic andrandom erors. tf fie graph of ln ,VdN = f(x) is really a linear function (as the theorypredicts), ne can deduce that the random error of the measurement is negligible andthat*4s systematic enor can dominate. lt can be estimated as

x (tt) = 1rt*" - tJ .: r i - . :

Determine the relative enor of your measurement too.

r . i : ! 1 : : i . ' , ,

' ' ' i

Glcsary

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