ENTC 4390MEDICAL IMAGING

STRUCTURE OF MATTER

Since the late 1920s it has been understood that electrons in an atom do not behave exactly like tiny moons orbiting a planet-like nucleus.

Their behavior Is described more accurately if, instead of defining them as point particles in orbits with specific velocities and positions, they are defined as entities whose behavior is described by wave functions.

While a wave function itself is not directly observable, calculations may be performed with this function to predict the location of the electron. • In contrast to the calculations of classical

mechanics in which properties such as force, mass, acceleration, and so on, are entered into equations to yield a definite answer for a quantity such as position in space, quantum mechanical calculations yield probabilities.

At a particular location in space, for example, the square of the amplitude of a particle’s wave function yields the probability that the particle will appear at that location. • However, it is important to emphasize that the

probability of finding the electron at other locations, even in the middle of the nucleus, is not zero.

• This particular result explains a certain form of radioactive decay in which a nucleus captures an electron. • This event is not explainable by classical mechanics, but

can be explained with quantum mechanics.

Atomic Theory

An atom consists of a nucleus of protons and neutrons surrounded by a group of orbiting electrons.• Electrons have a negative charge,

protons have a positive charge.• In its normal state, each atom has an

equal number of electrons and protons.

Atomic Theory

Electrons orbit the nucleus in discrete orbits called shells.

These shells are designated by letters K, L, M, N, etc.

Only certain numbers of electrons can exist within any given shell.

Atomic Theory

The outermost shell of an atom is called the valence shell.

The electrons in this shell are called valence electrons.

No element can have more than eight valence electrons.

The number of valence electrons affects its electrical properties.

The binding energy of an electron (Eb) is defined as the energy required to completely separate the electron from the atom. • When energy is measured in the macroscopic world of

everyday experience, units such as joules and kilowatt-hours are used.

• In the microscopic world, the electron-volt is a more convenient unit of energy • One electron volt is the kinetic energy imparted to an

electron accelerated across a potential difference (i.e., voltage) of 1 Volt.

The electron volt can be convened to other units of energy:

1eV = 1.6 x 10~’9J = 1.6 x 1012 erg = 4.4)< 10~26 kW-hr

Nott~: 103eV = 1 keV lO6eV= lMc\’

The electron volt describes potential as well as kintnic energy. The binding energy of

an electron in an atom is a form oF potential energy

An electron in an inner shell of an atom is attracted to the nucleus by a force greater than that exerted by the nucleus on an electron farther away.

An electron may be moved from one shell to another shell that is farther from the nucleus only if energy is supplied by an external source. • Binding energy is negative (i.e., written with a minus sign)

because it represents an amount of energy that must be supplied to remove an electron from an atom. The energy that must be imparted to an atom to move an electron from an inner shell to an outer shell is equal to the arithmetic difference in binding energy between the two shells.

For example, the binding energy is 13.5 eV for an electron in the K shell of hydrogen and is 3.4 eV for an electron in the L shell. • The energy required to move an electron from

the K to the L shell in hydrogen is (3.4 eV) (13.5 eV) = 10.1 eV

Electrons in inner shells of high-Z atoms are near a nucleus with high positive charge. • These electrons are bound to the nucleus with a force

much greater than that exerted upon the solitary electron in hydrogen.

All of the electrons within a particular electron shell do not have exactly the same binding energy • Differences in binding energy among the electrons in a

particular shell are described by the orbital, magnetic, and spin quantum numbers,

The combinations of these quantum numbers allowed by quantum mechanics provide

• three subshells (LI to LIII) for the L shell and

• five subshells (MI to Mv) for the M shell

• the M subshells occur only if a magnetic field is present.

• Energy differences between the subshells are small when compared with differences between shells.

• These differences are important in radiology however, because they explain certain properties of the emission spectra of x-ray tubes.

Various processes can cause an electron to be ejected from an electron shell.

When an electron is removed from a shell, a vacancy or “hole” is left in the shell • (i.e., a quantum “address” is left vacant. • An electron may move from one shell to another to fill

the vacancy • This movement, termed an electron transition, involves

a

Conductors Materials that have large numbers of free

electrons are called conductors.• Metals are generally good conductors

because they have few loosely bound valence electrons.

• Silver, gold, copper, and aluminum are excellent conductors.

Insulators

Materials that do not conduct because their valence shells are full or almost full are called insulators.• Glass, porcelain, plastic, and rubber are

good insulators.• If high enough voltage is applied, an

insulator will break down and conduct.

Semiconductors

Semiconductors have half-filled valence shells and are neither good conductors nor good insulators.• Silicon and germanium are good

semiconductors.• They are used to make transistors, diodes,

and integrated circuits.

Electrical Charge

Objects become charged when they have an excess or deficiency of electrons.• An example is static electricity.• The unit of charge is the coulomb.• 1 coulomb = 6.24 × 1024 electrons.

ENTC 4390

THE NUCLEUS

Nucleons A nucleus consists of two types of

particles, referred to collectively as nucleons.• The positive charge and roughly half the

mass of the nucleus are contributed by protons.

• The second type of nucleon is the neutron.

Protons Each proton possesses a positive charge

of +1.6 x 10-19 coulombs.• equal to in magnitude and opposite in sign to

the charge of an electron.• The number of protons in nucleus is the

atomic number of the atom.• The mass of a proton is 1.6734 x 10-27 kg.

Neutrons Neutrons are uncharged particles with a

mass of 1.6747 x 10-27 kg.• Outside the nucleus, neutrons are unstable

and divide into protons, electrons, and antineurtrinos.

• The number of neutrons in in a nucleus is the neutron number N for the nucleus.

The mass number• A = Z + N

The standard form used to denote the composition of a specific nucleus is

• where X is the chemical symbol.

XAZ

Isotopes Isotopes are atoms that possess the

same number of protons but a varying number of neutrons.• Isotopes of hydrogen are

• 1H—protium• 2H—deuterium• 3H—tritium

ENTC 4390

NUCLEAR FISSION & FUSION

Nuclear Power Nuclear power may be produced in two ways Nuclear fission involves the splitting of an atom

into two fragments, particles, and the release of energy

Nuclear fusion involves the combination of two nuclei into a single, more massive nuclei, plus energy

Stars are powered by nuclear fusion

Nuclear Fusion Nuclear Fusion has been used since the early

1950’s in Hydrogen bombs These are the most powerful type of nuclear

weapon We have not yet devised a method of utilizing

the power of nuclear fusion in the laboratory, nor in any commercial reactor

Therefore, we will not further consider fusion in this course

Nuclear Fission

Fission induced by neutron bombardment and capture

Fission Diagram

When a heavy nucleus undergoes fission, a variety of fragment pairs may be formed, depending on the distribution of neutrons and protons between the fragments

Fission Yield This leads to probability

distribution of both mass and nuclear charge for the fragments

The probability of formation of a particular fragment is called its fission yield and is expressed as the percentage of fissions leading to it

Fission Products A fission product is any of the lighter

atomic nuclei formed by splitting heavier nuclei (nuclear fission), including both the primary nuclei directly produced (fission fragments) and the nuclei subsequently generated by their radioactive decay

Fission Fragment Decay Fission fragments are highly unstable because

of their abnormally large number of neutrons compared with protons

Consequently, they undergo successive radioactive decays by emitting neutrons, by converting neutrons into protons, antineutrinos, and ejected electrons (beta decay), and by radiating energy (gamma decay)

Fission of 235U One of the many known fission reactions of

uranium-235 induced by absorbing a neutron results, for example, in two extremely unstable fission fragments, a barium and a krypton nucleus

These fragments almost instantaneously release three neutrons between themselves, becoming barium-144 and krypton-89

Barium Decay By repeated beta decay, the barium-144

in turn is converted step by step to other fission products• Lanthanum-144• Cerium-144• Praseodymium-144• Eventually relatively stable neodymium-144

Krypton krypton-89 is similarly transformed by

repeated beta decay to:• Rubidium-89 • Strontium-89 • To stable yttrium-89

Fission Product Identification Fission products are identified by their

chemical properties and by their radioactive properties, such as their half-lives and the kinds of particles they emit

The multiple decays mean fission products are highly radioactive and therefore quite dangerous

Why are Fission Products Radioactive? To maintain stability, the neutron-to-

proton (n/p) ratio in nuclei must increase with increasing proton number

The ratio remains at unity up to the element calcium, with 20 protons

It then gradually increases until it reaches a value of about 1.5 for the heaviest elements