Physics Applied to Radiology RADI R250 Fall 2003

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Physics Applied to RadiologyRADI R250 -- Fall
2003

• Chapter 4 The Atom

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(No Transcript)
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Atomic Models
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Matters Fundamental Particles

• electron proton neutron
• MASS SI (absolute value) 9.1 x 10-31 kg
  1.7x10-27 kg 1.7x10-27 kg
• relative (to e-) 1 1836 1838
• relative (to p) 1/2000 1 1
• atomic mass number 0 1 1
• atomic mass unit .000549 1.00728
  1.00867
• CHARGE SI (absolute value) -1.6x10-19 C
  1.6x10-19 C 0
• relative -1 1 0
• LOCATION orbit nucleus nucleus
• SYMBOL e- p no

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Term Atomic Number (Z)

• identifies an element
• every element has a different atomic number
• of protons in the nucleus
• electrically neutral atom p e
• abbreviation Z

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Electron Orbits
Shell Numbers n
Shell Letter Designations

• Bohr's model too simplified but useful concept
• energy levels or shells that contain e-
• each shell has specific binding energy (Eb)
• e- must gain energy to move outward
• e- loses energy to move inward

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Binding Energy (Eb)

• strength of the nuclear pull on the e-
• inner shells higher Eb
• outer shells lower Eb
• each element has unique set of Eb
• ground state all e- as close to nucleus as
  possible

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Eb (cont.)
Ground State
Excited State
1 or more e- above ground
12C 2k 4l
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Eb Atomic Number
High Z atom
Low Z atom

• greater of p in high Z
• higher Eb for all shells

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Quantum Numbers

• more precise location to individual e- of an atom
• 1st principle main energy level (shell) n
• 2nd orbital subshells shape of orbit l
• 3rd spatial orientation to nucleus ml
• 4th spin magnetic orientation ms
• Pauli exclusion principle -- no 2 e- may have the
  same 4 quantum numbers
• Maximum of e- in an inner shell 2n²
• Maximum of e- in an outer shell 8 (except k
  2)

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Shell e- Capacity
k shell
n 1 2n2 2 outer shell 2
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Shell e- Capacity (cont.)
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Electronic Transitions

• movement of e- between shells
• e- at lowest (ground) E state
• e- needs E to move to a higher shell
• E to D Eb
• E released when e- returns to ground state
• characteristic xray

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Orbital Transitions

• Determine the energy gain that the electron
  receives in the example to the right.
• Ee D Eb En - Eo
• -50 eV - (-900 eV)
• 850 eV
• Determine the characteristic x-ray energy emitted
  in the example to the right.
• Ex D Eb Eo - En
• -40 eV - (-1000 eV)
• 960 eV

Eb
Ee
n -35 eV
m -50 eV
l -300 eV
k -900 eV
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Neutral vs. Ionized Atoms

• Neutral atom
• p e-
• electrically uncharged

• Ionization
• any process that or - e- from an atom p ¹
  e-
• ion -- electrically charged atom
• ion pair -- charged atom charged particle

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Periodic Law

• chemical physical properties of elements repeat
  at regular intervals
• enables classification of elements
• inert gasses
• metals
• based on
• elements Z
• of outer shell orbital e-

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Periodic Table (Bushong figure 4-4, page 40)

• chart of all known elements
• illustrates the Periodic Law

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The Periodic Table Atomic

• elements listed by increasing Z

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Groups (columns)

• represents of electrons in the outer shell of
  element
• element in the same group will react similarly

Outer shell e- I 1 e- II 2 e- III 3 e-
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Periods (rows)

• represents the principle quantum number (n) of
  the outermost electron shell of the element

ç n 3 è
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Periodic Table -- example of use

• For the shaded box on the table, determine the Z,
  total of e-, of orbital shells, of e- in
  each shell?
• Z 17
• e- 17
• shells 3
• e- in sh. k 2 l 8 m7

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Structure of the Nucleus

• central core of the atom
• contains p n0 ( other particles)
• identifies the atom as a specific element
• held together by fundamental force ("strong")

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Nucleon(s)

• generic term for the particles found in the
  nucleus
• reference to protons neutrons in the nucleus
  without being specific

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NUCLEUS

• complex arrangement of nucleons empty space
• of p in nucleus defines an element (Z)
• p n are in all elements except hydrogen
• many other subatomic particles (50)

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Protons

• of p in nucleus defines the element
• called the atomic number (Z)
• 1 p hydrogen
• 2 p helium
• 3 p lithium
• neutral atom e- p

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Neutrons

• element (specific p) may exist with differing
  numbers of neutrons
• example p n0
• hydrogen 1 0
• hydrogen 1 1
• hydrogen 1 2
• neutron number (N) n0 in the nucleus

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Nuclear Nomenclature

• atomic mass number (A) total number of nucleons
• A Z N
• symbolic notation

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Nuclide

• generic term
• helps identify nuclear configuration
• p n
• gt100 elements but gt1500 nuclides
• classification of nuclides by similarities
• isotope p Z same element
• isobar nucleons A
• isotone n N
• isomer p n Z N excess energy

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Isotope Example
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Isotopes

• varies for each Z
• 3 for hydrogen, 26 for tin
• some are man-made
• isotopic configurations of nuclides
• stable (at ground state)
• unstable (excited state) radionuclide
• non-existent

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Isobar Example
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Isotone Example
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Isomer Example
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Nuclide Set Selection Example

• From the following set of nuclides, select sets
  of isotopes, isotones and isobars
• A
• Z
• N 32 33 33 33 32
• isotope Z 60Ni, 61Ni 59Fe, 58Fe
• isotone N 59Fe, 60Co, 61Ni 58Fe, 60Ni
• isobar A 60Ni, 60Co

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60
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61
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Ni
Co
Fe
Ni
Fe
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27
26
28
26
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Radioactivity

• definition see notes
• property of unstable nuclei
• spontaneous break up of nucleus
• forms other nuclide and emits radiation
• many factors that determine radioactivity
• N/P ratio
• too many or too few neutrons
• nuclear energy state
• above its ground energy state (excited)

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N/P Ratio Thompson figure 3-9, page 68
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Radionuclide

• nuclear configuration that is unstable and
  exhibits radioactivity
• activity
• quantity that measures amount of radioactive
  material
• indicates rate that radiation is emitted
• units
• common Curie (Ci) 3.7 x 1010 d/s
• SI Bequerel (Bq) 1 d/s
• d/s disintegrations/s

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Radioactive Decay (disintegration)

• process used by atom
• original radionuclide is unstable
• it ejects energy /or particles
• and changes into a different nucleus
• new nuclide may be stable or unstable
• If stable, nuclide exists and persists
• If unstable, it will decay continuing the process
  until stability is reached
• Decay series (or chain) formed

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Radioactivity Flow Chart
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Radioactivity

• definition see notes
• property of unstable nuclei
• spontaneous break up of nucleus
• forms other nuclide and emits radiation
• many factors that determine radioactivity
• N/P ratio
• too many or too few neutrons
• nuclear energy state
• above its ground energy state (excited)

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NP Ratio

• Plot of p (Z) vs. n (N) for all stable nuclides
• any nuclide combination that exists off of the
  line of stability is unstable
• unstable nuclides will emit radioactive energy
  /or particles to move closer to line of
  stability

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Physical Half-Life (T½)

• time required to reduce the activity of a
  radionuclide to ½ of its original value
• rate of decay of the radionuclide
• each radionuclide has a specific T½
• no 2 radionuclides have the same T½.

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T½ Example
T½ 3.8 d
start
after 1T½ 3.8 d
after 2T½ 7.6 d
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Using T½ to determine activity

• Need T½ for radionuclide
• Find the T½ that have passed since know A
• T½ time / T½
• Example
• How many half-lives occur in 32 days for a
  radionuclide with a T½ of 13.2 days?
• T½ ?? Time 32 days T½ 13.2 days
• T½ time / T½
• 32 days / 13.2 d/T 1/2
• 2.42424242 T1/2
• 2.4 T1/2

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Using T½ to determine activity

• Find of original that will remain (3 ways)
• 1. Formula .5T½ use yx calculator key
• 2. Read from graph (see page 51) (estimate)
• 3. Make chart estimate if between whole T½
• T½ decimal
• 0 100 1.00
• 1 50 .50
• 2 25 .25
• 3 12.5 .125

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Using T½ (cont.)

• Find remaining activity
• Multiply starting activity by
• A Ao A0original activity
• Combining Equations
• .5T½ A Ao
• A .5T½A0

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T½ Example

• 82 µCi of radon gas is contained in a closed
  beaker. How much will remain after 9.5 days? (T½
  of Rn 3.8days)
• A?? 82 µCi A0 9.5delapsed t 3.8d T½
• T½ time / T½ 9.5d / 3.8d 2.5
• .5T½ .52.5 0.1767766952966
• A A0
• 0.1767766952966 82 µCi
• 14.49568901432 µCi
• 14 µCi

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Alpha Decay a
Process
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Alpha Decay a

• Description 2p 2n0 (helium nucleus)
• Origin high Z nucleus (Zgt82)
• Effect on nucleus Z 2
• N 2
• A 4
• Charge 2
• Mass Number 4
• Ionization high
• Penetration low
• After KE lost captures 2 e- becomes He gas

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Beta- Decay b-
Process
Decay Equation
Decay Schematic
5730 yr
b- ( .156 MeV)
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Beta- Decay b-

• Description negatron (electron)
• Origin neutron rich nucleus
• Effect on nucleus Z 1
• N 1
• A (isobar) n0 D p
• Charge -1
• Mass Number 0
• Ionization low
• Penetration moderate
• After KE lost becomes free e-

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Beta Decay b
Process
Decay Equation
Decay Schematic
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Beta Decay b

• Description positron (positive electron)
• Origin neutron deficient nucleus
• Effect on nucleus Z 1
• N 1
• A (isobar) p D n0
• Charge 1
• Mass Number 0
• Ionization low
• Penetration moderate
• After KE lost attracts e- annihilates

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Annihilation Radiation
b e- Þ M
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Gamma Ray Emission g
Decay Equation
Process
Decay Schematic
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Gamma Ray Emission g

• Description electromagnetic radiation
• Origin nucleus with excess energy
• Effect on nucleus energy (isomeric transition)
• No D in Z, A or N
• Charge none
• Mass Number none
• Ionization very low
• Penetration high
• After E lost ceases to exist

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Other Radiation Processes

• Neutron emission
• Proton emission
• electron capture e
• fission
• fusion
• others

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Combination Emissions

• many radionuclides decay in multiple modes
• example

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NP Graph

• a -- High Z only

b- -- n D p (isobar) b -- p D n (isobar)
D N -- isotope
D p -- isotone