Absorption of Nuclear Radiation & Radiation Effects on Matter: Atomic and Nuclear Physics Dr. David Roelant

Atomic and Molecular Weight

Problem 1 Using the data in the table below, compute the atomic weigh of naturally occurring oxygen. Isotope Abundance (%) Atomic Weight 16O 99.759 15.99492 17O 0.037 16.99913 18O 0.204 17.99916

Solution to Problem 1 Using the data in the table below, compute the atomic weigh of naturally occurring oxygen. Isotope Abundance (%) Atomic Weight 16O 99.759 15.99492 17O 0.037 16.99913 18O 0.204 17.99916

Atomic and Nuclear Radii

Increase in Mass Relative to Observer of a Moving Mass

Particle Wavelengths

Energy levels of hydrogen atom E =13.58 eV E = 12.07 eV E =10.19 eV Energy, eV E =0 eV

Introduction to Nuclear Engineering by J.R. Lamarsh Decay Scheme of 60Co Introduction to Nuclear Engineering by J.R. Lamarsh

Radioactivity Calculations

Decay Chain Radioactivity

Fundamental Laws Governing Nuclear Reactions Conservation of nucleons Conservation of charge Conservation of momentum Conservation of energy

Balancing Nuclear Equations

Balancing Nuclear Equations

Problem 2 One of the reactions that occurs when 3H (tritium) is bombarded by deuterons (2H nuclei) is 3H (d,n)4He where, d refers to the bombarding deuteron. Compute the Q-value of this reaction.

Solution to Problem 2 The Q-value is obtained from the following neutral atomic masses (in amu): The Q-value in amu is Q = 5.030151 – 5.011269 = 0.018882 amu. Since 1 amu = 931.481 MeV, Q = 0.018882 x 931.481 = 17.588 MeV. The Q-value is positive and so this reaction is exothermic. This means, for instance, that when stationary 3H atoms are bombarded by 1 – MeV deuterons, the sum of the kinetic energies of the emergent α–particle (4He) and neutron is 17.588 + 1 = 18.588 MeV

Binding Energy per Nucleon as a Function of Atomic Mass Number Introduction to Nuclear Engineering by J.R. Lamarsh

Atomic Density

Nuclear radiation absorption p. 165 Counting efficiency (self, abs s-d, det, geom.) Ionization, excitation, bremsstrahlung, positron annihilation, Cerenkov (.6MeV) (fig. 7.9)

Problem 3 The density of sodium is 0.97 g/cm3. Calculate its atomic density.

Solution to Problem 3 The density of sodium is 0.97 g/cm3. Calculate its atomic density. The atomic weight of Na is 22.990. It is usual to express atomic densities as a factor x 1024

Interaction of Radiation with Matter (in entire target area)

Problem 4 A beam of 1-MeV neutrons of intensity 5 x 108 neutrons/cm•s strikes a thin 12C target. The area of the target is 0.5 cm2 and it is 0.05 cm thick. The beam has a cross-sectional area of 0.1 cm2. At 1 MeV, the total cross section of 12C is 2.6 b. At what rate do interactions take place with the target? What is the probability that a neutron in the beam will have a collision in the target?

Solution to Problem 4 It should be noted that the 10-24 in the cross section cancels the 1024 in atom density. This is the reason for writing atom densities in the form of a number x 1024 In 1 sec, a total of IA = 5 x 108 • 0.1 = 5 x 107 neutrons strike the target. Of these, 5.2 x 105 interact. The probability that a neutron interacts in the target is therefore: 5.2 x 105 / 5 x 107 = 1.04 x 10-2. Thus, only about 1 neutron in 100 has a collision while traversing the target.

Collision Density

Neutron Attenuation

Compound Nucleus Formation 56Fe + n (elastic scattering) 56Fe + n’ (inelastic scattering) 57Fe + γ (radiative capture) 55Fe + 2n (n, 2n reaction)

Elastic Scattering

Energy Loss in Scattering Collisions Fig. 3.6 Elastic Scattering of a Neutron by a Nucleus Introduction to Nuclear Engineering by J.R. Lamarsh

The Energy Released in Fission Introduction to Nuclear Engineering by J.R. Lamarsh

ɣ-Ray Interactions with Matter In nuclear engineering problems only three processes must be taken into account to understand how Ɣ-rays interact with matter. The Photoelectric Effect Pair Production Compton Effect

Photoelectric Effect Incident ɣ-ray interacts with an entire atom, the ɣ-ray disappears, and one of the atomic electrons is ejected from the atom. The hole in the electronic structure is latter filled by a transition of one of the outer electrons into the vacant position. The electronic transition is accompanied by the emission of x-rays characteristic of the atom or by the ejection of an Auger electron.

Dependence of Z on Photoelectric Cross Section where, n is a function of E shown in Fig. 3.14. Because of the strong dependence of σpe on Z, the photoelectric effect is of greatest importance for the heavier atoms such as lead, especially at lower energies. Introduction to Nuclear Engineering by J.R. Lamarsh

Pair Production Photon disappears and an electron pair – a positron and a negatron – is created. This effect doesn’t occur unless the photon has at least 1.02 MeV of energy. Cross section for pair production (σpp) increases steadily with increasing energy. Pair production can take place only if vicinity of a Coulomb field.

Compton Effect Elastic scattering of a photon by an electron, in which both energy and momentum are conserved. A Compton cross section per electron (eσC) decreases monotonically with increasing energy from a maximum value 0.665 b (essentially 2/3 of a barn) at E = 0, which is known as the Thompson cross section, σT.

Attenuation Coefficients Macroscopic ɣ-ray cross sections are called attenuation coefficients. Mass attenuation coefficient (μ/ρ) Introduction to Nuclear Engineering by J.R. Lamarsh

Introduction to Nuclear Engineering by J.R. Lamarsh

Introduction to Nuclear Engineering by J.R. Lamarsh

Introduction to Nuclear Engineering by J.R. Lamarsh

Problem 5 It is proposed to store liquid radioactive waste in a steel container. If the intensity of ɣ-rays incident on the interior surface of the tank is estimated to be 3 x 1011 ɣ-rays/cm2•sec and the average ɣ-ray energy is 0.8 MeV, at what rate is energy deposited at the surface of the container?

Solution to Problem 5 It is proposed to store liquid radioactive waste in a steel container. If the intensity of ɣ-rays incident on the interior surface of the tank is estimated to be 3 x 1011 ɣ-rays/cm2•sec and the average ɣ-ray energy is 0.8 MeV, at what rate is energy deposited at the surface of the container? Steel is a mixture of mostly iron and elements such as nickel and chromium that have about the same atomic number as iron. So as far as ɣ-ray absorption is concerned, there, steel is essentially all iron. From table 3.8, μo/ρ for iron at 0.8 MeV is 0.0274 cm2/g. The rate of energy deposition is then: