# experiment #56,, :,, ,: absorption of gamma the photoelectric and gompbn effects. a third process,...     Post on 20-Jan-2021

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• EXPERIMENT #56,, :,, ,:

Theory, Definitions !J

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

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

The photoelectric effect,(discovered by H. Hertz in 1887) is the liberation of electrons from the surface of a conductor when electromagnetic radiation strikes its surface. The energy of the electromagnetic wave is transferred to electrons in the surface layer of a conductor and - if the electrons are able to escape from the surface of a metal - we can measure the resulting potential difference on the conductor. This means the kinetic energy of an electron is sufficient for it to overcome the surface's potential energy barrier, called the:work function tlr of the emitting surface, Planck's theory gives the relationship forthe so-called threshold frequency (cutt-off frequency) - the minimum frequency f;of electromagnetic radiation that can cause the photoelectric effect for a given metal. The threshold frequency for most metals is in the ultraviolet region (corresponding to wavelengths of 200 to 300 nm), so it is beyond the frequencies of 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.s is Pfanck's constant), 112 m f is the kinetic energy with which electrons leave the metal's surface (m is the mass of an electron, v is its velocity) and tP is the work function (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 the scatbred radiation has lower frequency (longerwavelength) than the incident radiation. This change in frequency depends on the angle through which the radiation is scattered. lf the scattered radiation with wavelength rl' emerges at an angle @ with respect to the direction of incident radiation with wavelength l, we can observe that the difference in wavelength between scattered and incident radiation depends on the angle @

h

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

148

I,

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

Absorption of gamma radiation can be described by an exponential law. The law can be easily derived"in the'followihg way: if'parallel beam of N photons with equal eneryie penetrate a'certain material i4 tfiex-direction, then after covering the distance dx the radiation becomes weaker (less energetic) and dN photons are absorbed by the material. The decrease in the.number of photons is proportional to dx and the initial number 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 described above, which talie place in the absorption of gamma radiation. That is why the absorption 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 the Compton effect,lrp" is the absorption coefficient corresponding to lhe loss of the energy caused by the pirbtoelectric effect, and pro is the absorption coefficient corresponding to 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 In N

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 incident radiation energy by one half. lt can be expressed as

ln2 dttz = p

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

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

(56.41

(56.5)

No

N

The Sl units:

149

• 2.

3.

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

AT Plot the graph of In {} = f(x).N Calculate the absorption coefficient of a given rnetal and check its value with the value obtained from the above graph a{nd with the value^from the graph in Fig. 56-1, 56-2 or 56-3,. The source of gamma radiation is 60co with e-neigy of 1 j 7 3 M e V .

I i '

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

tl (mn

1

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

Fig. 56-1. The absorpti

• 6.

electron4osirorrpair.|sthereanyconditionforthefrequency(wave|ength)of the 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 graph l .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 the

one below:

{0 Wr\$evl

151

• 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 radiation TA... 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 the absorption coefficient of a given metal as ..

L

r52

• I = n l ,

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

- ---i;;-

r Lx i i - 4

Accuracy of lhe ileasurement''The t'otal sror of fte absorption coefficient p is the sum of systematic and random erors. tf fie graph of ln ,VdN = f(x) is really a linear function (as the theory predicts), ne can deduce that the random error of the measurement is negligible and that*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

zflieni gama e lektromag neticke zhfeni fotoefekt Comptn irv jev (rozptyl) ufstupni prSce prahovS frekvence absorp6ni koeficient polotlou5fka " tvorba p6rfi

-

153

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