ENTC 4390 MEDICAL IMAGING RADIOACTIVE DECAY

Nuclear Particles & Radiation Only a few of the many different nuclear emanations are used in medicine. In order of importance, the entities are: x-rays Electromagnetic waves of very short wavelength that behave in many ways like particles. Gamma (g) rays Electromagnetic waves similar to x-rays, but of even shorter wavelength. Neutrons Actual particles that are produced during the decay of certain radioacitve materials.

Radioactivity Don’t be confused by this picture! A single radioactive source does not emit all three types a, b and g.

3 Types of Radioactivity Radioactive sources B field into screen detector a particles: helium nuclei Easily Stopped b particles: electrons Stopped by metal g : photons (more energetic than x-rays) penetrate!

The nucleus of an atom consists of neutrons and protons, referred to collectively as nucleons. In a popular model of the nucleus (the “shell model”), the neutrons and protons reside in specific levels with different binding energies.

Materials Science Fundamentals The structure of an atom:

Materials Science Fundamentals 2. Elements/Atomic Number (Z) & Atomic Masses Key: Chemical Behavior Determined by Z and Ionization

Materials Science Fundamentals Atomic Number: # of Protons Mass Number: # of Protons and Neutrons Atomic Weight: Total Mass of Atom

If a vacancy exists at a lower energy level, a neutron or proton in a higher level may fall to fill the vacancy This transition releases energy and yields a more stable nucleus. The amount of energy released is related to the difference in binding energy between the higher and lower levels. The binding energy is much greater for neutrons and protons inside the nucleus than for electrons outside the nucleus. Hence, energy released during nuclear transitions is much greater than that released during electron transitions.

If a nucleus gains stability by transition of a neutron between neutron energy levels, or a proton between proton energy levels, the process is termed an isometric transition. In an isomeric transition, the nucleus releases energy without a change in its number of protons (Z) or neutrons (N). The initial and final energy states of the nucleus are said to be isomers. A common form of isomeric transition is gamma decay (g) in which the energy is released as a packet of energy (a quantum or photon) termed a gamma (g) ray An isomeric transition that competes with gamma decay is internal conversion, in which an electron from an extranuclear shell carries the energy out of the atom.

It is also possible for a neutron to fall to a lower energy level reserved for protons, in which case the neutron becomes a proton. It is also possible for a proton to fall to a lower energy level reserved for neurons, in which case the proton becomes a neuron. In these situations, referred to collectively as beta (b) decay, the Z and N of the nucleus change, and the nucleus transmutes from one element to another. In beta (b) decay, the nucleus loses energy and gains stability.

In any radioactive process the mass number of the decaying (parent) nucleus equals the sum of the mass numbers of the product (progeny) nucleus and the ejected particle. That is, mass number A is conserved in radioactive decay

In alpha (a) decay, an alpha particle (two protons and two neutrons tightly bound as a nucleus of helium ) is ejected from the unstable nucleus. The alpha particle is a relatively massive, poorly penetrating type of radiation that can be stopped by a sheet of paper.

An example of alpha decay is: Radium Radon alpha particle

ENTC 4390 MEDICAL IMAGING DECAY SCHEMES

A decay scheme depicts the decay processes specific for a nuclide (nuclide is a generic term for any nuclear form). Energy on the y axis, plotted against the Atomic number of the nuclide on the x axis.

Given a generic nuclide, Given a generic nuclide, there are four possible routes of radioactive decay. a decay to the progeny nuclide by emission of a nucleus. (a) b+ (positron) decay to progeny nuclide by emission of positive electron from the nucleus. (b) b- (negatron) decay to progeny nuclide by emission of negative electron from the nucleus. g decay reshuffles the nucleons releasing a packet of energy with no change in Z (or N or A).

Energy Z Z+1 Z-2 Z-1 Z+2     Atomic Number

ENTC 4390 BETA DECAY

Nuclei tend to be most stable if they contain even numbers of protons and neutrons and least stable if they contain an odd number of both. Nuclei are extraordinarily stable if they contain 2, 8 ,14, 20, 28, 50, 82, or 126 protons. These are termed nuclear magic numbers and Reflect full occupancy of nuclear shells.

The number of neutrons is about equal to the number of protons in low-Z stable nuclei. As Z increases, the number of neutrons increases more rapidly than the number of protons in stable nuclei.

Can get 4 nucleons in each energy level- lowest energy will favor N=Z, But protons repel one another (Coulomb Force) and when Z is large it becomes harder to put more protons into a nucleus without adding even more neutrons to provide more of the Strong Force. For this reason, in heavier nuclei N>Z.

ENTC 4390 ISOMERIC TRANSITIONS

Isomeric transitions are always preceded by either electron capture or emission of an a or b (+ or -) particle. Sometimes one or more of the excited states of a progeny nuclide may exist for a finite lifetime. An excited state is termed a metastable state if its half-life exceeds 10-6 seconds.

An isometric transition can also occur by interaction of the nucleus with an electron in one of the electron shells. This process is called internal conversion. The electron is ejected with kinetic energy Ek equal to the energy Eg released by the nucleus, reduced by the binding energy Eb of the electron The ejected electron is accompanied by x rays and Auger electrons as the extranuclear structure of the atom resumes a stable configuration.

The rate of decay of a radioactive sample depends on the number N of radioactive atoms in the sample. This concept can be stated as where DN/Dt is the rate of decay, and the constant l is called the decay constant.

The decay constant has units of time . It has a characteristic value for each nuclide. It also reflects the nuclides degree of instability; a larger decay constant connotes a more unstable nuclide i.e., one that decays more rapidly. The rate of decay is a measure of a sample’s activity.

The activity of a sample depends on the number of radioactive atoms in the sample and the decay constant of the atoms. A sample may have a high activity because it contains a few highly unstable (large decay constant) atoms, or because it contains many atoms that are only moderately unstable (small decay constant).

The SI unit of activity is the becquerel (Bq.) defined as 1 Bq = 1 disintegration per second (dps) An older, less-preferred unit of activity is the curie (Ci), defined as 1 Ci = 3.7 x 1010 dps

Example a. has a decay constant of 9.49 x 10-3 hr -1. Find the activity in becquerels of a sample containing 1010 atoms.

Example How many atoms of with a decay constant of 2.08 hr -1 would be required to obtain the same activity in the previous problem. More atoms of than of are required to obtain the same activity because of the difference in decay constants.

Note that the equation can be written as

Rearranging and solving for N, where No is the number of atoms at time to . natural log format

The physical half-life, T1/2, of a radioactive nuclide is the time required for decay of half of the atoms in a sample of the nuclide.

Example The half-life is 1.7 hours for 113mIn (Indium). A sample of 113mIn has a mass of 2mg.

ENTC 4390 MEDICAL IMAGING DECAY SCHEMES

X-Rays Strong or high energy x-rays can penetrate deeply into the body. Weak or soft x-rays are used if only limited penetration is needed The energy of x-rays, as well as other nuclear particles is measured in electron-volts (ev) thousands of electron-volts (kev) millions of electron-volts (Mev)

The diagnostic use of x-ray depends on the fact that various types of absorbs x-rays to a greater or lesser degree. Absorption by bone is quite high, Absorption by fatty tissue is low. This allows the use of the x-ray beam for delineating the details of body structure.

Gamma Rays X-rays are generally produced electrically. g_rays are the result of a radioactive transition in a substance that has been activated in a nuclear reactor. Once again, energy is measured in electron-volts (ev) thousands of electron-volts (kev) millions of electron-volts (Mev)

The higher energy g-rays penetrate all human tissue quite easily. g-rays are used in conjunction with scanning systems to detect anomalies due to disease or neoplastic growth.

Neutrons Neutron applications in medicine are limited. Again, energy is measured in electron-volts (ev) thousands of electron-volts (kev) millions of electron-volts (Mev)

Preflight - Gamma Ray Emission Gamma rays are emitted due to electrons making transitions to nuclear energy levels. true false No, gamma rays are high energy photons emitted when nucleons make transitions between their allowed quantum states.

Preflight - Nuclear Beta Decay Beta rays are produced when the atom spontaneously repels all its electrons from its orbits. true false Beta particles are electrons. However, the atom does not emit its atomic electrons. Beta electrons are emitted by a nucleus along with a neutral weakly interacting particle called the neutrino when one of the neutrons in the nucleus decays. Free neutrons are unstable - they decay. Sometimes in atoms with large numbers of neutrons, one of its neutrons may be loosely bound - spontaneous decay!

Preflight - Positrons Beta particles are: Always negatively charged. Always positively charged. Some beta decays could produce positively charged particles with properties similar to those of electrons. Some radioactive elements emit a positively charged particle which is in all other respects similar to an electron! Anti-matter!! Positrons!!!

Preflight - Alpha Particles Alpha particles are: Electrons Protons. Nuclei of Helium atoms Nuclei of Argon atoms Some nuclei have lots of protons and many more protons. Lowest energy bound-states require about equal numbers of protons and neutrons. Those nuclei emit most tightly bound nuclear matter, i.e., Helium nuclei with two protons and two nuclei.