Download Atomic Structure

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
C
E
Blue: Electric Field (E)
Green: Magnetic Field (H)
H
The electromagnetic field
travels out (yellow arrows)
from the origin at the
velocity of light (c)
C
Electromagnetic Radiation," Microsoft® Encarta® Online Encyclopedia 2006
http://encarta.msn.com © 1997-2006 Microsoft Corporation. All Rights Reserved
Electromagnetic Radiation
Electromagnetic Spectrum
Lower frequency—longer wavelength—lower energy
<-More Wave like
Electromagnetic Radiation," Microsoft® Encarta® Online Encyclopedia 2006
http://encarta.msn.com © 1997-2006 Microsoft Corporation. All Rights Reserved
Higher frequency—shorter wavelength—higher energy->
More particle like->
Electromagnetic Radiation
Relationship of Wavelength & Frequency
c =λv
and
v = c/λ
C = Velocity of EMR (3x1010cm/s)
λ = Wavelength
v = Frequency (cycles/sec or hertz)
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.
Electromagnetic Radiation
Relationship of frequency to Energy
E = hv
or
E = hc/λ
h = Planck’s Constant = 4.135 X 10-15 eV-sec
(alternatively, 6.626 X 10-34 J-sec or 6.625 X 10-27 erg-sec)
C = velocity of electromagnetic radiation
= 3 X 108 m/s (in a vacuum) or
= 3 X 1018 Angstroms/sec
λ = in Angstroms or 10-10 m (or 0.1 nm)
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 1.602 × 10−19
joules. Abbreviation: eV, ev, Also, electron volt.
Origin:
1925–30
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.
In the radiological sciences, we usually measure
energy in kilo (i.e. 1000) electron Volts, or keV
electronvolt. (n.d.). Dictionary.com Unabridged (v 1.1). Retrieved August 22, 2009, from
Dictionary.com website: http://dictionary.reference.com/browse/electronvolt
Electromagnetic Radiation
•
Relationship of frequency to Energy
c  
Therefore, we take the
relationship between
wavelength and frequency:

c

E  h
• And substitute it into our
relationship between
frequency and energy:
c
E  h 

 3.0 X 1018 Angstroms / sec 
E  (4.135 X 10 eV sec) 




12.4
E (in keV ) 
 (in Angstroms )
or
15
 (in Angstroms ) 
12.4
E (in keV)
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.
“The Atom," Microsoft® Encarta® Online Encyclopedia 2006
http://encarta.msn.com © 1997-2006 Microsoft Corporation. All Rights Reserved
At the atomic level things get
very strange, for we are dealing
with the fundamentals of
existence.
Atoms & Molecules
• 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.
From “Water Molecule.” Aquadyn Technologies. Retrieved Aug. 27, 2012 from http://www.aquadyntech.com/watermolecule.html
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 2006
http://encarta.msn.com © 1997-2006 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 8
2006)http://csep10.phys.utk.edu/astr162/lect/light/absorption.html
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:
The above equation also shows the direct relationship
between photon energy and wavelength frequency.
6.61 X 10-34 joule sec
--considered to be the energy
associated with a photon itself)
From “Neils Bohr” wikipedia.org, the Free Online Encyclopedia, Sept. 3, 2006. http://en.wikipedia.org/wiki/Bohr_model
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
Paul Christian,
Donald Bernier,
James Langan,
Nuclear Medicine
and Pet:
Technology and
Techniques, 5th
Ed. (St. Louis:
Mosby 2004) p
54.
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.
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.
Paul Early, D. Bruce Sodee, Principles
and Practice of Nuclear
Medicine, 2nd Ed., (St. Louis:
Mosby 1995), pg. 14.
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 = mc2
This converted energy is the binding energy of the nucleus.
Atomic Mass Units (AMU)
• Rest mass of electron = 9.1 X 10-28g
• Using E=mc2 we find that the electron
resting mass is equivalent to 0.511 MeV
– E is in ergs
– m is in grams
– c is in cm/sec (3 X 1010 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 = 12.00000 AMU
6 X 1.00759  6.04554 (6 protons x the mass of a proton in AMUs)
6 X 1.00898  6.05388 (6 neutrons x the mass of a neutron in AMUs)
Total:
12.09942 AMU
•Therefore, 0.09942 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 =
0.09942 AMU 
•(Kahn Academy example: https://www.khanacademy.org/science/chemistry/nuclear-chemistry/radioactivedecay/v/mass-defect-and-binding-energy )

931Mev
  91.682MeV
1.00759
AMU


Side bar—defining an AMU
Back to Atomic Structure
• Atomic Nucleus
– Nucleons
• Protons and neutrons
– Surrounded by electron cloud
•1st 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
From “Atomic Nucleus.” Wikipedia.org. Retrieved 27 Aug 2012 from http://en.wikipedia.org/wiki/Atomic_nucleus
Nuclear Notation
• X = Chemical Symbol
• A = Atomic Mass Number
– Neutrons + Protons
• Z = Atomic Number
A
Z
– Number of protons
• (which defines the element)
For efficiency sake, the Z is usually dropped since
this is dependent upon the element type (X)
X
Nuclear Notation
From “The Periodic Table.” Library.Thinkquest.org retrieved 27 Aug 2012 from http://library.thinkquest.org/3616/chem/Periodic.htm
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
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”)
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.
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
http://www.cosmostv.org/2012/01/researchers-find-cancer-in-ancient.html