Nuclear Medicine PhysicsCourse No. 311RAD

Dr. Mohammed Alnafea

alnafea@ksu.edu.sa

www.ksursd.net

Course Objective:

Physics and instrumentation impact all of the sub-specialty area of nuclear medicine because of their fundamental importance.

This course is designed to provide an introductory course to the two subsequent nuclear medicine courses namely (RAD 432 and RAD 466).

Aim of the Course:

This course aims to give the student the following:

1. A review of the general physical principle of nuclear medicine, its procedures and instrumentations to be of permanent value to them to be able to perform the basic nuclear medicine procedures.

Aim of the Course:

2. A broad overview of the basic elements contained in the course as well as gives students an orientation to the operation of a nuclear medicine department.

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Course Content• The course will cover several topics

including atomic and nuclear structure, production of radioisotopes, radioactive decay, the radioactive decay law, unit of radiation measurements, attenuation of gamma-rays, scintillation detectors, nuclear medicine imaging systems and radiation protection in nuclear medicine.

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Course Contents– Topics:

»Atomic & Nuclear Structure »Radioactive Decay »The Radioactive Decay Law»Production of Radioisotopes »Units of Radiation Measurement » Interaction of Radiation with Matter»Radiation Protection in Nuclear Medicine

. »Attenuation of Gamma-Rays »Scintillation Detectors »Nuclear Medicine Imaging Systems

Course References:1. Medical imaging physics, William R. Hendee, E. Russell Ritenour, 4th edition, 2002.

2. Physics in Nuclear Medicine, James A. Sorenson (Editor), Michael E. Phelps (Editor) Grune & Stratton; ISBN: 0808918044; 2nd edition (January 1987).

3. An Introduction to the Physics of Nuclear Medicine by Paul N. Goodwin Charles C Thomas Pub Ltd; ISBN: 0398035695; (June 1977).

4. Essentials of Nuclear Medicine Physicsby Rachel A., Md Powsner, Edward R. Powsner Blackwell Science Inc; ISBN: 0632043148; 1st edition (September 15, 1998).

5. Essentials of Nuclear Medicine Imaging by Fred A., Jr., M.D. Mettler, Milton J., Md. Guiberteau, Barbara Mettler W B Saunders Co; ISBN: 0721651216; 4th edition (January 15, 1998)

Evaluation & Assessment Methods

Students are assessed as follows:

1. 1st mid term exam 10 marks

2. 2nd mid term exam 10 marks

3. Assignment or report 10 marks

4. Oral Presentation 10 marks

5. Hospital & Practical report + Oral exam

20 marks

6. Final exam 40 marks

7. Total 100 marks8

Academic year: 1429-1430H

Week 1

Week 2

Week 3

Week 4

Week 5 1st mid term exam

Week 6

Week 7

Week 8

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Academic year: 1429-1430H

Week 9

Week 10 Assignment or report

Week 11 2nd mid term exam

Week 12 Oral Presentations

Week 13 Hospital report + Oral exam

Week 14

Week 15

Week 16

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Oral Presentation– A list of topics of the oral presentations for the

course RAD-3111. The Physical and chemical properties of NaI

detector.2. Detectors & new detector materials.3. Radionuclide for PET and their production.4. Baby cyclotron for PET.5. 2 & 3 annihilation and their uses in PET.6. The principle of planar gamma camera7. The principle of SPECT imaging.8. SPECT in Brain Function Imaging.9. Molecular imaging with PET & SPECT.10.Small animal imaging.11.FDG and blood flow.

Atomic & Nuclear Structure

The Atom is the smallest indivisible particle of matter, i.e. something that cannot be divide.

All atoms are composed of just three particles: protons, neutrons & electrons.

The centre of an atom is called the nucleus.

Atomic & Nuclear StructureThe nucleus contains protons (P) & neutrons (N).

P & N have virtually the same mass i.e. same as the hydrogen atom. So P & N are given a relative mass of one like the hydrogen atom.

Protons are Positively charged, but neutron are neutral.

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Atomic & Nuclear Structure » More than 99.9% of the atom is empty space

occupied by moving electrons (E).

» E have a mass about 2000 times less than P & N.

» Electrons are negatively charged.

» Negative charge on one electron just balances the positive charge on one proton.

» The electrons move around the nucleus very rabidly and remains in layers or shells at different distances from the nucleus.

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Atomic Structure Particle Position

with the atom

Mass relative to a hydrogen

atom

Charge Mass (gm)

Proton nucleus 1 +1 1.672810-24

Neutron nucleus 1 0 1.67410-24

Electron

Shells 0.0005 -1 9.0910-27

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Atomic Structure» Protons, neutrons & electrons are the building blocks for

atoms.

» Different atoms have different number of protons, neutrons and electrons.

» Hydrogen atoms are the simplest atoms as each atom contains one proton & one electron.

» Some of the heaviest atoms have 100 or more protons, neutrons & electrons. For instance, each atom of lead has 82 protons, 82 electrons and 125 neutrons.

» NB: Why same No. of protons and electrons? This allows the +ve charges in the protons to balance the –ve charges on the electrons so each atom is neutral overall.

» The electrons move around the nucleus very rabidly and remains in layers or shells at different distances from the nucleus.

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Atomic number & mass number

The No. of protons in an atom tells you which elements it is and thus, is called atomic number (Z).

Thus, hydrogen has atomic number of one.

Notice that the mass of an atom depends on the No. of protons & neutrons in its nucleus.

Atomic number (Z) = No. of protons (P) Mass number (A) = No. of protons (P) + No. of neutrons (N).

The mass No. (A) & atomic No. can be shown with the symbol for an element.

e.g. carbon atoms with 6 protons & 6 neutrons can be represented as

C126C

126

C12)(.6)(.

ANomassZNoatomic

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Relative atomic mass & isotopes

Several elements have relative atomic masses which are whole numbers. For example Al have:

13 P- relative mass =13

13 E- relative mass =0.0

14 N- relative mass =14

---------------------------

total relative mass =27

Relative mass of an atom sometimes referred as one mole of the element.

C126C

126

Element Symbol relative mass

Carbon C 12.0

Hydrogen H 1.0

Oxygen O 16.0

Copper Cu 63.5

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Isotopes

Some elements have relative atomic masses that are not whole numbers e.g. Iron (Fe) =55.8

One element could have atoms with different

masses. Atoms of the same element with different masses are called isotopes. For e.g. naturally occurring chlorine Cl has two isotopes

C126C

126

cl cl 3717

3517

Each of the above isotope has 17 protons & 17 electrons. Both have atomic No. of 17. but one has 18 neutrons & the other has 20 neutrons.

Isotopes are atoms with the same atomic

No., but different mass numbers.

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Isotopes of Hydrogen

• The most common isotope of hydrogen has no neutrons at all;

• there's also a hydrogen isotope called deuterium, with one neutron, and another, tritium, with two neutrons.

Hydrogen-1Hydrogen

1H

Hydrogen-2(deuterium)

2H

Hydrogen-3(tritium)

3H

Z=1A=1

Z=1A=2

Z=1A=3

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Other forms of atoms

• Isobars are nuclides having the same mass number, i.e. sum of protons & neutrons; Carbon-12 & Boron-12.

• Isotones two nuclides are isotones if they have the same number of neutrons N. For example, Boron-12 and Carbon-13 both have 7 Neutrons.

• Nuclear isomers are different excited states of the same type of nucleus e.g. 99mTc (has different amount of nuclear energy.

Electron Structures & the Periodic Table

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1st lecture Questions

1. Show how the mass No. & atomic No. can be represented for sodium and aluminium?.

Na has 11 P & 12 N but Al has 13 P & 14 N.

2. Calculate the relative atomic mass of naturally occurring chlorine contain three chlorine-35 atoms for every chlorine-37.

RAM= (335)+37/4=35.5

3. There are three isotopes of the element hydrogen what are they and how do we distinguish between them?

Hydrogen has two naturally occurring isotopes, normal

hydrogen, which contains no neutrons, and heavy hydrogen, which has one neutron in each atom. The third isotope, tritium, has two neutrons.

Na23

11 Al27

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Electron Structures & Periodic Table

During chemical reactions, changes occur in the No. of electrons belonging to atoms.

Some atoms gain E, some lose E & other share E. NB: once these changes in E structure have taken place, the atoms or ions are usually more stable i.e. less reactive.

Some atoms never react e.g. helium & neon. Why? Have very stable electron structures.

Atom or ions will have very stable electrons structure if they have 2 E (like helium), 10 E (like neon) 18 E (like argon) & so on. These stable E structures are closely related to the way in which E are arranged in layers or shell.

The No. of E in an atom in each shell is determined by this equation:

No. of electrons= 2 n2

Where n is the shell number i.e. 1 for K, 2 for L, 3 for M…..

Electron Structures & Periodic Table The No. of E in an atom in each shell is determined by this

equation:

No. of electrons= 2 n2

Where n is the shell number i.e. 1 for K, 2 for L, 3 for M…..

For example Na has 11 protons: at (K shell) n=1 the No. of E = 2(1)2 =2 at (L shell) n=2 the No. of E = 2(2)2 =8 at (M shell) only one E

The above equation tells us that the capacity of the 1st shell is 2 electrons and the capacity of the 2nd shell is 8 electrons. The 3rd shell has a total capacity of 2 x 32 = 18 electrons

NB: E shells actually have sublevels. The first sublevel (the s sublevel) holds 2 electrons. The second, p, sublevel holds 6. The third, d, sublevel holds 10.  After levels 3s and 3p are filled, E shell #3 acts as if it has reached capacity with only 8 total E. 

In other words, in an atom with 20 E (which is the element calcium, Ca) the first 2 electrons are located in the 1st shell, the next 8 in shell #2, the following 8 in shell #3 and the remaining 2 electrons are located in shell #4.

Al2713

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Electron Structures & Periodic Table

The atoms can be arranged according to their electron structure and chemical properties.  This is where we encounter the Periodic Table of Elements.

The periodic "law" of chemistry recognises that many properties of the chemical elements are periodic functions of their atomic number (the number of protons within the element's atomic nucleus).

The periodic table is an arrangement of the chemical elements ordered by atomic number in columns (groups) and rows (periods) presented so as to emphasize their periodic properties.

Atoms are ordered by their atomic number in the Periodic Table.  The Table is set up so as to indicate the number of electron shells in each atom and the number of valence electrons (electrons in the outermost shell) in the atom. 

As you read the Table from left to right in any one row, the number of valence electrons increases.  For example, hydrogen has 1 electron (in the first shell).  Helium (He), the 2nd element in the first row, has 2 electrons (thus filling its valence shell). 

Electron Configuration Table

The electron configuration is the arrangement of electrons in an atom, molecule, or other physical structure. It basically describes how many electrons are in each energy level of an atom and how the electrons are arranged within each energy level.

For example, this is the electron configuration table for gold (Au):

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Binding Energy• In general, binding energy represents the mechanical work

which must be done in acting against the forces which hold an object together, while disassembling the object into component parts separated by sufficient distance.

• Nuclear binding energy is derived from the strong nuclear force and is the energy required to disassemble a nucleus into free unbound neutrons and protons, strictly so that the relative distances of the particles from each other are infinite (far enough).

• Nuclei are made up of protons and neutron, but the mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it.

• The difference is a measure of the nuclear binding energy which holds the nucleus together.

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Binding Energy• If a composite object is stable, for instance, the nucleus of

a helium atom does not spontaneously split into the two protons and two neutrons that are its constituents:

• Energy of the composite object + energy expended to split it up = sum of the energies of the separate parts after the split.

• We can also move the expended energy to the right side of the equation, which leaves us with

• Energy of the composite object = sum of the energies of its parts - energy needed to split the object apart.

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Binding Energy• Nuclear binding energy can be calculated from the Einstein

relationship:

Nuclear binding energy = Δmc2

• According to Einstein, to every energy there corresponds a mass, and to every mass there can be assigned a corresponding energy.

• Einstein showed that mass and energy are really two different forms of the same thing; the "vanishing" mass of the protons and neutrons is simply converted to energy.

• For most nuclei, the binding energy per nucleon is about 8 MeV. • The relativistic mass of a bound system is somewhat smaller

than the sum of the masses of its constituent parts, namely:

• Mass of bound system = sum of masses of its parts - (binding energy)/c2.

• Light nuclei can gain binding energy per nucleon by fusing; heavy nuclei by fissioning.

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Binding EnergyBinding Energy

• The unit for binding energies per The unit for binding energies per nucleon is the Mega-electron-Volt nucleon is the Mega-electron-Volt (MeV). (MeV).

• One MeV is defined as the energy One MeV is defined as the energy gained by an electron accelerated gained by an electron accelerated by an electrical voltage of one by an electrical voltage of one million Volt (it is also the energy million Volt (it is also the energy corresponding to twice the mass of corresponding to twice the mass of an electron at rest). an electron at rest).

• The comparison of the alpha The comparison of the alpha particle binding energy with the particle binding energy with the binding energy of the electron in a binding energy of the electron in a hydrogen atom is shown in Fig. hydrogen atom is shown in Fig.

• The nuclear binding energies are on The nuclear binding energies are on the order of a million times greater the order of a million times greater than the electron binding energies than the electron binding energies of atoms. of atoms.

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Electron Binding Energy

• Electron binding energy is a measure of the energy required to free electrons from their atomic orbits.

• The unit is electron volt (ev).

• Electron volt- the energy required by an electron to be accelerated through 1 volt potential difference

• Electrons can only have discrete energy levels i.e. K, L, M, …. shells.

• Electrons in the K-shell are tightly bound electrons

• K shell has maximum energy (due to its stability).

• To remove an electron from its shell E electron binding energy.

• NB: Binding energy increases rapidly with atomic No. (Z).

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Ionization

• Ionization is the physical process of converting an atom or molecule into an ion by adding or removing charged particles such as electrons or other ions.

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Ionization

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Excitation

• Excitation is an elevation in energy level above an arbitrary baseline energy state.

• Excitation by absorption of light and de-excitation by emission of light

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Questions1. Given that 1u has a mass of 1.65511×1027kg, calculate the

energy (MeV) of 1u using Einstein's equation?.

2.2. From the graph From the graph calculate the binding calculate the binding energy per nucleon for energy per nucleon for the following the following elements:elements:

a.a. Iron (Nucleon number Iron (Nucleon number - 56)- 56)

b.b. Magnesium (Nucleon Magnesium (Nucleon number - 24) number - 24)

c.c. Titanium (Nucleon Titanium (Nucleon number - 48)?.number - 48)?.

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Answer1. Given that 1u has a mass of 1.65511×10-27kg, we can calculate

the energy of 1u.

E = mc2

= (1.65511×10-27) × (3.0×108)2 J= 1.489599 × 10-10J

However, 1eV = 1.6×10-19J, so

E= 1.48959 × 10-10 / 1.6×10-19 eV= 9.31 × 108 eV= 931 MeV

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Questions

1. Show how the mass No. & atomic No. can be represented for sodium and aluminium?.

2. Calculate the relative atomic mass of naturally occurring chlorine contain three chlorine-35 atoms for every chlorine-37.

3. There are three isotopes of the element hydrogen what are they and how do we distinguish between them?