Radioactivity

1. Review of Radioactivity
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2. Mass attenuation coefficient, Atomic attenuation coefficient and Electronic
attenuation coefficient
• Mass attenuation coefficient, µm = µ/ρ
• Atomic attenuation coefficient, µa = µ/(N/V), it is the linear attenuation coefficient
per unit number density.
• Then, µa = µM/ ρNA
• Electronic attenuation coefficient, µe = µa/Z, it is the atomic attenuation
coefficient per unit atomic number.
Practice 3: What are the total mass, atomic, and electronic attenuation coefficients
of the copper slab 10−2
m thick, when 2000 mono-energetic photons is reduced to
1000 ? Copper has a density of 8.9 × 103
kg/m3
, a gram-atomic mass of 63.6, and an
atomic number of 29. Ans: 0.0078 m2
/kg, 8.2 × 10−28
m2
/atom, 2.8 × 10−29
m2
/electron

3. SI, LET and Range
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•

4. Assuming that the average specific ionization is 4 × 106
ion pairs per meter (IP/m), calculate the
average LET of α-particles in air. Calculate the range in air for 4-MeV α-particles.
Ans: 1.35 × 105
keV/m, 3 cm in air
Major Interaction of x or gamma rays with materials
• Coherent scattering
• Photoelectric absorption
• Compton scattering
• Pair Production
• Photodisintegration
I0

5. Coherent Scattering
Photons are deflected or scattered with negligible loss of energy by the process
of coherent or Rayleigh scattering
The classical description assumes that a photon interacts with electrons of an
atom as a group rather than with a single electron within the atom.
Usually the photon is scattered in approximately the same direction as the
incident photon.
Although photons with energies up to 150 to 200 keV may scatter coherently in
media with high atomic number, this interaction is important in tissue only for
low-energy photons.
Negligibly small amount of energy is deposited in the attenuating medium.
Coherent scatter sometimes reduces the resolution of scans obtained with low-
energy, γ -emitting nuclides (e.g., 125
I) used in nuclear medicine.

6. Photoelectric Absorption
Photoelectric absorption of a photon with energy hν.
The photon disappears and is replaced by an electron ejected from the atom
with kinetic energy Ek = hν − Eb , where Eb is the binding energy of the electron.
Photoelectrons resulting from the interaction of low-energy photons are
released approximately at a right angle to the motion of the incident photons.
The probability of photoelectric interaction decreases rapidly as the photon
energy increases.
The mass attenuation coefficient τm for photoelectric absorption varies roughly
as 1/(hν)3
, where hν is the photon energy.
 The photoelectric mass attenuation coefficient varies with Z3
.

7. Compton Scattering
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8. Attenuation coefficient decreases gradually with increasing photon energy.
The Compton mass attenuation coefficient varies directly with the electron density
(electrons per kilogram) of the absorbing medium because Compton interactions occur
primarily with loosely bound electrons.
 A medium with more unbound electrons will attenuate more photons by Compton
scattering than will a medium with fewer electrons. The Compton mass attenuation
coefficient is nearly independent of the atomic number of the attenuating medium.
Radiographs exhibit very poor contrast when exposed to high-energy photons. When
most of the photons in a beam of x or γ rays interact by Compton scattering, little
selective attenuation occurs in materials with different atomic number.
A 210-keV photon is scattered at an angle of 80 degrees during a Compton interaction.
What are the energies of the scattered photon and the Compton electron?
Ans: = 0.0020 nm, 50 keV

9. Show that, irrespective of the energy of the incident photon, the maximum energy is 255
keV for a photon scattered at 180 degrees and 511 keV for a photon scattered at 90
degrees
Pair production
• Formation or materialization of two electrons, one negative and the other positive
(positron), from a pulse of electromagnetic energy traveling through matter,
usually in the vicinity of an atomic nucleus.
• Pair production is a direct conversion of radiant energy to matter. It is one of the principal
ways in which high-energy gamma rays are absorbed in matter.
• The energy equivalent to the mass of an electron is 0.51 MeV, the creation of two
electrons requires 1.02 MeV. Consequently, photons with energy less than 1.02 MeV do
not interact by pair production.
• This energy requirement makes pair production irrelevant to conventional radiographic
imaging.
• During pair production, energy in excess of 1.02 MeV is released as kinetic energy of
the two electrons.
hν = 1.02 + (Ek )e− + (Ek )e+

10. A 5-MeV photon near a nucleus interacts by pair production. Residual energy is
shared equally between the negative and positive electron. What are the kinetic
energies of these particles?
Ans: 1.99 MeV

11. • Photo disintegration can be defined as the process of ejection of at least
one nuclear particle after absorption of photon by a nucleus.
• Occasionally multiple nucleon may be ejected.
• This phenomenon occurs in the energy range of 15 MeV to 20 MeV.
• It occurs in radiotherapy
Photodisintegration