Facultyetsuedublantonlecture3radiationppt3714
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Facultyetsuedublantonlecture3radiationppt3714 Facultyetsuedublantonlecture3radiationppt3714 Presentation Transcript

  • ENTC 4390MEDICAL 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 (γ) 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 α, β and γ.
  • 3 Types of Radioactivity B field into screen Radioactive detector sources α particles: helium nuclei Easily Stopped β particles: electrons Stopped by metal γ : 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 Fundamentals1. The structure of an atom:
  • Materials Science Fundamentals2. Elements/Atomic Number (Z) & Atomic MassesKey: 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 (γ) in which the energy is released as a packet of energy (a quantum or photon) termed a gamma (γ) 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 (β) decay, the Z and N of the nucleus change, and the nucleus transmutes from one element to another. • In beta (β) 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 (α) decay, an alpha particle (two protons and two neutrons tightly bound 4 as a nucleus of helium 2 He ) 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: 226 88 Ra→ 222Rn+ 2 He 86 4 Radium Radon alpha particle
  • ENTC 4390MEDICAL 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.
  • A Given a generic nuclide, X there are four Z possible routes of radioactive decay. 1. A−4 α decay to the progeny nuclide Z −2 P by emission of 4 a 2 He nucleus. 2. (a) β+ (positron) decay to progeny nuclide Z −AQ by 1 emission of positive electron from the nucleus. 3. A (b) β− (negatron) decay to progeny nuclide by Z +1 R emission of negative electron from the nucleus. 4. γ decay reshuffles the nucleons releasing a packet of energy with no change in Z (or N or A).
  • A Z X A− 4  Z −2 P  A  Z +1 REnergy A Z −1Q  A Z +1 S Z-2 Z-1 Z Z+1 Z+2 Atomic Number
  • ENTC 4390BETA DECAY
  •  Nucleitend 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 eachenergy level- •lowest energy will favor N=Z,•But protons repel one another(Coulomb Force) and when Z islarge it becomes harder to putmore protons into a nucleuswithout adding even moreneutrons to provide more of theStrong Force. •For this reason, in heavier nuclei N>Z.
  • ENTC 4390ISOMERIC TRANSITIONS
  •  Isomeric transitions are always preceded by either electron capture or emission of an α or β (+ 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 E equal to k the energy Eγ 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 ∆N = −λN ∆t • where ∆N/∆t is the rate of decay, and the constant λ 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.
  •  Theactivity 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) Anolder, less-preferred unit of activity is the curie (Ci), defined as • 1 Ci = 3.7 x 10 10 dps
  • Examplea. 201Tl has a decay constant of 9.49 x 10-3 hr -1. Find 81the activity in becquerels of a sample containing 1010atoms. ∆N 9.49 × 10 −3 atomsActivity ( A) = − = λN = × 1010 atoms = 9.49 × 107 ∆t hr hr 7 atoms 1 hr 4 atoms A = 9.49 × 10 × = 2.64 × 10 hr 3600 sec sec A = 2.64 × 10 4 Bq
  • Exampleb. How many atoms of 11C with a decay constant of 6 2.08 hr -1 would be required to obtain the same activity in the previous problem. atoms atoms sec 2.64 × 10 4 2.64 × 10 4 × 3600 A sec = sec hr N= = λ 2.08 / hr 2.08 / hr N = 4.57 × 107 atoms• More atoms of 11C than of 201Tl are required to obtain 6 81 the same activity because of the difference in decay constants.
  •  Note that the equation ∆N = −λN ∆t • can be written as dN = −λN dt
  •  Rearranging and solving for N, dN = −λdt N ∫ ∫natural log format dN = ln N = − λdt = −λt N e ln N = e − λt N = N o e − λt • where No is the number of atoms at time to .
  •  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. N = N o e − λt N 1 − λT 1 / 2 T 1 / 2⇒ = =e No 2 1 ln   2  =T = 0.693 1/ 2 −λ λ
  • Example The half-life is 1.7 hours for 113mIn (Indium). a. A sample of In has a mass of 2µg. 113m
  • ENTC 4390MEDICAL 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. Thisallows the use of the x-ray beam for delineating the details of body structure.
  • Gamma Rays X-rays are generally produced electrically. γ_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)
  • higher energy γ-rays penetrate all The human tissue quite easily.  γ-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 EmissionGamma 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.
  • Beta rays are produced when the atom spontaneously Preflight - Nuclear Beta Decay repels all its electrons from its orbits. • true • falseBeta particles are electrons. However, the atom doesnot emit its atomic electrons.Beta electrons are emitted by a nucleus along with aneutral weakly interacting particle called the neutrinowhen one of the neutrons in the nucleus decays. Free neutrons are unstable - they decay. Sometimes in atoms with large numbers p + - υ n → e of neutrons, one of its neutrons may be loosely bound - spontaneous decay!
  • Preflight - PositronsBeta 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 positivelycharged particle which is in all other respectssimilar to an electron! Anti-matter!! Positrons!!!
  • Preflight - Alpha Particles Alpha particles are: • Electrons • Protons. • Nuclei of Helium atoms • nuclei of Argon of protons and many moreSome Nuclei have lots atomsprotons. Lowest energy bound-states require aboutequal numbers of protons and neutrons. Thosenuclei emit most tightly bound nuclear matter, i.e.,Helium nuclei with two protons and two nuclei.