10b Lesson Interaction of Photons with Matter MP200 Radiation Physics - 2010 Duke Medical Physics Graduate Program
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Photoelectric Eect
The emission of electrons from a metal surface as a result of light absorption is called the Photoelectric eect. It is of signicance in physics, since it shows the particle nature of light. Light is considered as a discrete quanta(photon) of energy E = h,, where h = Planks constant = frequency of light.
The kinetic energy of the ejected electron, T = h Eb Eb = energy needed to remove electron from metal When Eb is minimum, T is maximum, and then Eb is called the work function of metal. ( i.e. energy of the most loosely bound electron ).
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In the process, the energy of the photon is completely absorbed by the atom. The scattering of the ejected electrons is shown in gure. The gure shows distribution of the angle of ejected photoelectrons vs incident photon energy. Electrons are ejected approx. at right angles when low-energy photons interact photo-electrically.
The interaction cross section per atom ( a ) The probability of ejecting a photoelectron, when a photon strikes an atom is the interaction cross section per atom. It depends on Z and h , and the relation is given by, Zn a k (h )m cm2 .atom1
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Here, n 4 at h = 0.1 M eV and gradually rising to 4.6 at 3 M eV . m 3 at h = 0.1 M eV and gradually decreasing to 1 at 5 M eV . Photoelectric event is important in energy h 0.1 M eV and below. Z4 a h 3
cm2 .atom1
Photoelectric Mass attenuation coecient The photoelectric mass attenuation coecient is also dened as the cross section per unit mass and it is given by, NA = Aa where, NA = 6.023 1023 atoms.mole1 = Avogadros number A = atomic weight in gram Also, A = cZ where c = Constant Simplifying we get,
Z h = density of the material
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cm2 .gram1
The gure shows the mass attenuation coecients for Lead and Carbon vs. photon energy.
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Carbon curve approximate with (h )3 dependence. For lead, there is a break at 88 keV and it is called the K -edge. This is because of the binding energy of two K -shell electrons are 88 keV . Below this energy, these two electrons cannot participate in photoelectric eect.
Energy Transfer Cross section,
T (h Eb ) = h h Then,
tr
tr
Fraction of energy transfer to the photoelectron,
is dened by,
tr (h Eb ) = h If the electron was removed from the inner shell, the fraction of energy transfer changes due to the Auger eect. When an electron is removed from the inner shell, the vacancy can be lled by an electron from an upper shell.
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The photon energy equivalent to the dierence between the donor and recipient level is emitted in this process. For K or L shell vacancies this transition sometimes comes with emission of uorescence or characteristic X -rays with energy hK or hL , equal to the dierence in potential energy between the donor and recipient level. The probability that a uorescence ( characteristic) X -ray escapes from the atom of its origin is called the uorescence yield. YK for K shell vacancy and YL for L shell vacancy.
Figure 1: Fluorescence yield YK,L and fractional participation in the photoelectric eect PK,L by K and L electrons.
Since there are several levels above K or L shells, mean values hK and hL are considered. The value of hK is less than (Eb )K , because (Eb )K is the dierence in potential energy between an electron in the K -shell and one completely
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away from the atom ( at innity ).
If no x-ray is emitted, all of binding Eb is disposed to eject more electrons Auger electrons. Total kinetic energy carried by all Auger electrons the, is original binding energy - sum of all binding energies of all nal vacancies. Example: For KLM auger electrons, total kinetic energy, T = (Eb )K 4(Eb )N Let PK and PL be the fractions of photoelectric interactions. K fraction of all photoelectric interactions that occur in the K-shell, for photons h > (Eb )K PK = and
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Then,
PL =
L
fraction of all photoelectric interactions that occur in the L-shell, for photons, where (Eb )L < h < (Eb )K . Since, YK and YL are probabilities, PK YK = fraction of all photoelectric events in which K uorescence X ray emitted and, PK YK hK = mean energy carried away from the atom by K uores cence X ray, per photoelectric interaction in all shell combined. PL YL = fraction of all photoelectric events in which L uorescence X ray emitted. PL YL hL = mean energy carried away from the atom by L uorescence X ray, per photoelectric interaction in all shell combined. The probability of any other uorescence X -ray except those from K -shell being able to carry energy out of an atom is negligible for h > (Eb )K . Then, the rest of the (Eb )K and all other binding energy involved in photoelectric interactions in other shells, may be assumed to be given to Auger electrons. The mean energy transferred to charged particles per photoelectric event h PK YK hK The photoelectric mass energy transfer coecient h PK YK hK (1 PK )PL YL hL tr = h
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for h > (Eb )K . For energy, (Eb )L1 < h < (Eb )K corresponding tr h PL YL hL = h and for high Z , materials, PL YL hL PL YL (Eb )L1
tr
Photonuclear Interactions
The excitation of a nucleus with high energy gamma rays ( MeV) is called the photonuclear process. The excited nucleus then emits a proton or neutron. (, p) events contribute directly to kerma, but the relative amount is very small ( 0.05 of that due to pair production.) (, n) events have practical importance because the neutron thus produced may lead to the problems in radiation protection. Presence of (, n) neutrons must be taken into account in shielding design.
Total Attenuation Coecients
= mass attenuation coecients for Compton eect
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Figure 2: Mass energy transfer coecients for Carbon and Lead.
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= mass attenuation coecients for pair production R = mass attenuation coecients for Rayleigh scattering = mass attenuation coecients for photoelectric eect The total mass attenuation coecient ( ) is the sum of all mass atten uation coecients due to the above photon interactions. R = + + +
tr Total mass energy transfer coecient ( ) is given by,
tr tr tr tr = + + Substituting for values, we get, tr = T + h
h 2m0 c2 + h
h PK YK hK h
for h > (Eb )K in the elemental absorbing medium,and neglecting L uorescence. For (Eb )L1 < h < (Eb )K , tr tr tr = + tr = T + h
h PL YL hL h
Since neither K -uorescence nor pair production is relevant in this case.
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Mass energy absorption coecient
The mass energy absorption coecient is given by, tr en = (1 g ) Where g is the fraction of energy lost for radiative ( bremsstrahlung) productions and for e annihilation.
Coecients for Compounds and Mixtures
For compounds or mixtures of elements the Bragg rule gives, and, tr tr = fA +
A
=
mix
fA +
A
fB +
B
fC +
C
tr
fB +
B
where, fA , fB , are the weight fractions of separate elements A, B, . The same rule also applies approximately, for mass energy absorption coecients. en en tr en en tr
fA +
A
fB +
B
(1 gA )fA +
A
(1 gB )fB +
B
g = radiation yield fraction.
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