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• CHAPTER 1 Nuclear Radiation - Review

Some Nuclear Units

Nuclear energies are very high compared to atomic processes, and need larger units

However, the sizes are quite small and need smaller units:

Nuclear masses are measured in terms of atomic mass units with the carbon-12 nucleus defined as having a mass of exactly 12 amu. It is also common practice to quote the rest mass energy as if it were the mass. The conversion to amu is:

Engineering Aspects of Food Irradiation 1

• Introduction

2

Relativistic Energy

The famous Einstein relationship for energy

includes both the kinetic energy and rest mass energy for a particle. The kinetic energy of a high speed particle can be calculated from

The relativistic energy of a particle can also be expressed in terms of its momentum in the expression

The relativistic energy expression is the tool used to calculate binding energies of nuclei and the energy yields of nuclear fission and fusion.

Kinetic Energy

Kinetic energy is energy of motion. The kinetic energy of an object is the energy it possesses because of its motion. The kinetic energy* of a point mass m is given by

• Introduction

Kinetic energy is an expression of the fact that a moving object can do work on anything it hits; it quantifies the amount of work the object could do as a result of its motion. The total mechanical energy of an object is the sum of its kinetic energy and potential energy.

For an object of finite size, this kinetic energy is called the translational kinetic energy of the mass to distinguish it from any rotational kinetic energy it might pos-sess - the total kinetic energy of a mass can be expressed as the sum of the transla-tional kinetic energy of its center of mass plus the kinetic energy of rotation about its center of mass.

*This assumes that the speed is much less than the speed of light. If the speed is comparable with c then the relativistic kinetic energy expression must be used.

Rest Mass Energy

The Einstein equation includes both the kinetic energy of a particle and the energy it has as a result of its mass. If the particle is at rest, then the energy is expressed as

which is sometimes called its rest mass energy.

Conservation of Energy

The relativistic energy expression is a statement about the energy an object contains as a result of its mass and is not to be construed as an exception to the principle of conservation of energy. Energy can exist in many forms, and mass energy can be considered to be one of those forms.

Engineering Aspects of Food Irradiation 3

• Introduction

4

Pair Production

Every known particle has an antiparticle; if they encounter one another, they will annihilate with the production of two gamma-rays. The quantum energies of the gamma rays is equal to the sum of the mass energies of the two particles (including their kinetic energies). It is also possible for a photon to give up its quantum energy to the formation of a particle-antiparticle pair in its interaction with matter.

The rest mass energy of an electron is 0.511 MeV, so the threshold for electron-positron pair production is 1.02 MeV. For X-ray and gamma-ray energies well above 1 MeV, this pair production becomes one of the most important kinds of interactions with matter. At even higher energies, many types of particle-antiparti-cle pairs are produced.

Relativistic Kinetic Energy

The relativistic energy expression includes both rest mass energy and the kinetic energy of motion. The kinetic energy is then given by

This is essentially defining the kinetic energy of a particle as the excess of the parti-cle energy over its rest mass energy. For low velocities this expression approaches the non-relativistic kinetic energy expression.

Kinetic Energy for v/c

• Introduction

and the square root expression then expanded by use of the binomial theorem

given

substituting gives

Relative scale model of an atom and the solar system

Do you perceive a gold ring to contain a larger fraction of solid matter than the solar system?

Engineering Aspects of Food Irradiation 5

• Introduction

6

On this scale, the nearest star would be a little over 10,000 miles away.

Data for Scale Model of Atom

Nuclear Size and Density

Various types of scattering experiments suggest that nuclei are roughly spherical and appear to have essentially the same density. The data are summarized in the expression called the Fermi model:

• Introduction

where r is the radius of the nucleus of mass number A. The assumption of constant density leads to a nuclear density.

The most definitive information about nuclear sizes comes from electron scattering.

Nuclear Density and the Strong Force

The fact that the nuclear density seems to be independent of the details of neutron number or proton number implies that the force between the particles is essentially the same whether they are protons or neutrons. This correlates with other evidence that the strong force is the same between any pair of nucleons.

Engineering Aspects of Food Irradiation 7

• Introduction

8

Nuclear Forces

Within the incredibly small nuclear size, the two strongest forces in nature are pit-ted against each other. When the balance is broken, the resultant radioactivity yields particles of enormous energy.

The electron in a hydrogen atom is attracted to the proton nucleus with a force so strong that gravity and all other forces are negligible by comparison. But two pro-tons touching each other would feel a repulsive force over 100 million times stron-ger! So how can such protons stay in such close proximity? This may give you some feeling for the enormity of the nuclear strong force which holds the nuclei together.

The Electromagnetic Force

• Introduction

One of the four fundamental forces, the electromagnetic force manifests itself through the forces between charges (Coulomb's Law) and the magnetic force, both of which are summarized in the Lorentz force law. Fundamentally, both magnetic and electric forces are manifestations of an exchange force involving the exchange of photons. The electromagnetic force is a force of infinite range which obeys the inverse square law, and is of the same form as the gravity force.

The electromagnetic force holds atoms and molecules together. In fact, the forces of electric attraction and repulsion of electric charges are so dominant over the other three fundamental forces that they can be considered to be negligible as determiners of atomic and molecular structure. Even magnetic effects are usually apparent only at high resolutions, and as small corrections.

Nuclear Particles

Nuclei are made up of protons and neutrons bound together by the strong force. Both protons and neutrons are referred to as nucleons. The number of protons is called the atomic number and determines the chemical element. Nuclei of a given element (same atomic number) may have different numbers of neutrons and are then said to be different isotopes of the element.

Proton

Along with neutrons, protons make up the nucleus, held together by the strong force. The proton is a baryon and is considered to be composed of two up quarks and one down quark.

Engineering Aspects of Food Irradiation 9

• Introduction

10

It has long been considered to be a stable particle, but recent developments of grand

unification models have suggested that it might decay with a half-life of about 1031 years. Experiments are underway to see if such decays can be detected. Decay of the proton would violate the conservation of baryon number, and in doing so would be the only known process in nature which does so.

When we say that a proton is made up of two up quarks and a down, we mean that its net appearance or net set of quantum numbers match that picture. The nature of quark confinement suggests that the quarks are surrounded by a cloud of gluons, and within the tiny volume of the proton other quark-antiquark pairs can be pro-duced and then annihilated without changing the net external appearance of the pro-ton.

Neutron

Along with protons, neutrons make up the nucleus, held together by the strong force. The neutron is a baryon and is considered to be composed of two down quarks and one up quark.

A free neutron will decay with a half-life of about 10.3 minutes but it is stable if combined into a nucleus. The decay of the neutron involves the weak interaction as indicated in the Feynman diagram to the right. This fact is important in models of the early universe. The neutron is about 0.2% more massive than a proton, which translates to an energy difference of 1.29 MeV.

• Introduction

The decay of the neutron is associated with a quark transformation in which a down quark is converted to an up by the weak interaction.

The Strong Force

A force which can hold a nucleus together against the enormous forces of repulsion of the protons is strong indeed. However, it is not an inverse square force like the electromagnetic force and it has a very short range. Yukawa modeled the strong force as an exchange force in which the exchange particles are pions and other heavier particles. The range of a particle exchange force is limited by the uncer-tainty principle. It is the strongest of the four fundamental forces.

Engineering Aspects of Food Irradiation 11

• Introd

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