Unit I: Physics Associated with Nuclear Medicine Instrumentation Part A: Atomic Structure and Radiation’s Interaction with Matter Lecture 1 CLRS 321 Nuclear Medicine Physics and Instrumentation 1

Lecture Objectives Describe properties of electromagnetic radiation including its relationship to energy Describe the structure of the atom, its components, and their properties State the relationship of mass and energy in Einstein’s equation Write the correct form of radionuclide notation Define the line of stability Describe the nuclear families and state their characteristics Explain the structure of the chart of nuclides and the trilinear chart and how they relate to the nuclear families

Electromagnetic Radiation Blue: Electric Field (E) Green: Magnetic Field (H) The electromagnetic field travels out (yellow arrows) from the origin at the velocity of light (c) Electromagnetic Radiation," Microsoft® Encarta® Online Encyclopedia © Microsoft Corporation. All Rights Reserved E H C C

Electromagnetic Radiation Electromagnetic Spectrum Electromagnetic Radiation," Microsoft® Encarta® Online Encyclopedia © Microsoft Corporation. All Rights Reserved  Lower frequency—longer wavelength—lower energyHigher frequency—shorter wavelength—higher energy-> <-More Wave like More particle like->

Electromagnetic Radiation Relationship of Wavelength & Frequency c =λv and v = c/λ Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-1, p 40. C = Velocity of EMR (3x10 10 cm/s) λ = Wavelength v = Frequency (cycles/sec or hertz)

Electromagnetic Radiation Relationship of frequency to Energy E = hv or E = hc/λ h = Planck’s Constant = X eV-sec (alternatively, X J-sec or X erg-sec) C = velocity of electromagnetic radiation = 3 X 10 8 m/s (in a vacuum) or = 3 X Angstroms/sec λ = in Angstroms or m (or 0.1 nm) What’s an eV???? (E is energy in eV)

e ⋅ lec ⋅ tron-volt –noun Physics. a unit of energy, equal to the energy acquired by an electron accelerating through a potential difference of one volt and equivalent to × 10 −19 joules. Abbreviation: eV, ev, Also, electron volt. Origin: 1925–30 Dictionary.com Unabridged Based on the Random House Dictionary, © Random House, Inc electronvolt. (n.d.). Dictionary.com Unabridged (v 1.1). Retrieved August 22, 2009, from Dictionary.com website: In the radiological sciences, we usually measure energy in kilo (i.e. 1000) electron Volts, or keV

Electromagnetic Radiation Relationship of frequency to Energy Therefore, we take the relationship between wavelength and frequency: And substitute it into our relationship between frequency and energy:

Atoms & Molecules We cannot see atoms because visible light wavelengths are too big. We can use electron beams to bombard atomic atoms and get information to construct pictures like this—an array of silicon atom pairs. What we are seeing are the electron clouds of pairs of silicon atoms. Atoms are mostly space. The nucleus of the atom is deep within the relatively expansive electron cloud and is infinitesimally small. At the atomic level things get very strange, for we are dealing with the fundamentals of existence. “The Atom," Microsoft® Encarta® Online Encyclopedia © Microsoft Corporation. All Rights Reserved

Atoms & Molecules From “Water Molecule.” Aquadyn Technologies. Retrieved Aug. 27, 2012 from Atom –Smallest division of an element that retains all the chemical properties of an element. Molecule –Smallest form of a chemical compound that retains all the chemical properties of that compound.

Atoms & Molecules Bohr Model of the Atom Photo taken from “A Science Odyssey” by Charles Flowers, page 32 (c 1998 by William Morrow & Co. New York)

Spectral Emissions Apply heat to materials, analyze their emitted light through a prism, and you find each type gives off a very distinctive pattern of wavelengths of visible light. Why? "Spectroscopy," Microsoft® Encarta® Online Encyclopedia © Microsoft Corporation. All Rights Reserved.

Balmer Series Bohr looked at the hydrogen’s spectral emissions (the Balmer Series) and offered an explanation for the specific wavelengths of visible light. Bohr’s model attributed the distinct wavelengths apparent in the Balmer Series to “quantum leaps” between varying energy states of electrons. (UT Astrophysics, Aug. 2006—Sept )

Bohr said the distinct wavelengths were formed as a result of excited electrons returning to a less energetic state by losing a quantum (photon) of energy. The energy states of the electrons are very specific and are not composed of a continuum of varying states of energy. (The “h” in the above equation is Planck’s constant which is: 6.61 X joule sec --considered to be the energy associated with a photon itself) The above equation also shows the direct relationship between photon energy and wavelength frequency. From “Neils Bohr” wikipedia.org, the Free Online Encyclopedia, Sept. 3,

Atomic Structure (according to Bohr) Small central nucleus surrounded by electron shells. Nucleus occupied by nucleons –Positively charged proton –Neutron with mass but no charge Electrons are negatively charged –In shells labeled K, L, M, N, O, P, Q Also subshells! –Negatively charged –Electrons = Protons (in stable atom)

Relative Sizes of Atomic Components Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-4, p 42.

Energy States of Electrons This picture from the Sodee text represents the electron energy states as different speed limits around the nucleus of an atom. In order for a car at 70 mph to go down to the 65 mph speed limit, it must lose a “quantum” of 5 mph. For electrons, this quantum is in the form of a specific wavelength of electromagnetic radiation. Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 11.

Optical Radiation We get spectral lines of visible wavelengths when electrons lower their energy state from one “subshell” to a lower one. Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 13.

Characteristic X-rays This figure from your textbook shows what happens when an electron loses energy to move from the L shell to the K shell. Again Electromagnetic radiation is emitted, but it is of a higher energy (shorter wavelength/higher frequency) than visible light and is in the form of an X-ray photon. Such an emission is called a “characteristic X-ray” and its “character” is dependent upon and equal to the specific difference in energy states between the L and K shells of the atom. Paul Christian, Donald Bernier, James Langan, Nuclear Medicine and Pet: Technology and Techniques, 5th Ed. (St. Louis: Mosby 2004) p 54.

Electron Binding Energy A different but related concept is electron binding energy. This is the specific energy that holds an electron in its orbit. The closer the orbital shell is to the nucleus, the greater its binding energy. (Conversely, the electron energy states increase with the distance of the orbital shell to the nucleus.) This diagram from the Sodee Text gives an example of variations in binding energy (in keV) for a series of electron orbital shells. Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 11.

What the binding energy means is that it takes at least the same amount of energy to remove an electron from its orbital shell. If an electron has a binding energy of 70 keV, then it would require 70 keV of energy to kick that electron out of its shell.

Binding Energy of the Nucleus The positively charged protons and the neutral neutrons have specific binding energies that hold them together in the nucleus. A Helium atom is composed of two protons and two neutrons, plus a couple of electrons. Yet, the mass of two protons and two neutrons by themselves is more than the Helium nucleus (without the electrons). This is referred to as the mass defect. What’s behind it? Some of the mass of the protons and neutrons is being converted into energy, according to Einstein’s famous equation: E = mc 2 This converted energy is the binding energy of the nucleus. Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 14.

Atomic Mass Units (AMU) Rest mass of electron = 9.1 X g Using E=mc 2 we find that the electron resting mass is equivalent to MeV –E is in ergs –m is in grams –c is in cm/sec (3 X cm/sec) Mass of a proton = 931 MeV Mass of a neutron = 939 MeV

Mass Defect of the Carbon Nucleus (text example) AMUs were defined using the weight of a Carbon nucleus: 6 protons and 6 neutrons –A carbon atom nucleus = AMU Therefore, amu is unaccounted for based on Carbon’s standard of 12 amu This mass is converted to binding energy and using the energy of a proton on the previous slide the binding energy in MeV = (Kahn Academy example: decay/v/mass-defect-and-binding-energy ) decay/v/mass-defect-and-binding-energy

Side bar—defining an AMU

Back to Atomic Structure Atomic Nucleus –Nucleons Protons and neutrons –Surrounded by electron cloud From “Atomic Nucleus.” Wikipedia.org. Retrieved 27 Aug 2012 from 1 st 20 elements of periodic table— neutrons to protons is 1:1 Larger nuclei require more neutrons than protons to increase binding energy and maintain nuclear stability Nuclei not having an appropriate neutron to proton ratio are unstable

Nuclear Notation X = Chemical Symbol A = Atomic Mass Number –Neutrons + Protons Z = Atomic Number –Number of protons (which defines the element) For efficiency sake, the Z is usually dropped since this is dependent upon the element type (X)

Nuclear Notation From “The Periodic Table.” Library.Thinkquest.org retrieved 27 Aug 2012 from Interactive Periodic Table Link

Nuclides & Radionuclides Nuclide –Any configuration of protons & neutrons composing an atom –There are about 3100 of these configurations or nuclides 270 nuclides are stable comprising 83 elements The remaining are unstable and are termed… radionuclides Note: “nuclide” does not necessarily mean the same thing as “isotope.” Isotope implies a specific relationship between two nuclides.

Line of Nuclear Stability Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-5, p 43.

Nuclear Families Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-5, p 43. Isotope: Same element, different forms. Isotones: Different elements, same number of neutrons Isobars: Different elements, same atomic mass Isomers: Same atom, different energy state (metastable—”m”)

Chart of the Nuclides Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-6, p 44

Trilinear Chart of Nuclides Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-6, p 44

(Mo-99 to Tc-99) Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-6, p 44

Next time: Decay Processes From “Researchers Find Cancer in Ancient Egyptian Mummy.” The Cosmos News. Retrieved 27 Aug 2012 from