Chapter 21: Nuclear Chemistry

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Chapter 21 Nuclear Chemistry

• Chemistry The Molecular Nature of Matter, 6E
• Jespersen/Brady/Hyslop

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How are atoms formed?

• Big BangIntense heat 109 K
• Cooled quickly to 106 KT of stars
• e, p, n formed and joined into nucleiatoms
• Mostly H and He (as in our sun)
• Rest of elements formed by nuclear reactions
• Fusiontwo nuclei come together to form another
  heavier nucleus
• Fissionone heavier nucleus splits into lighter
  nuclei
• Various other types of reactions

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Nuclear Shorthand

• Nucleons
• Subatomic particles found in the nucleus
• Protons (p)
• Neutrons (n)
• Nuclide
• Specific nucleus with given atomic number (Z )
• Atomic Number (Z )
• Number of protons in nucleus
• Determines chemical properties of nuclide
• Z p
• Mass Number (A)mass of nuclide
• A n p

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Shorthand for Writing Nuclides

• Where X atomic symbol
• e.g.
• In the neutral atom e p Z
• Isotopes
• Nuclides with same Z (same number of p), but
  different A (different n)

Hydrogen Deuterium Tritium
1 p 1 p 1 n 1 p 2 n
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Radioactivity

• Radioactive isotopes
• Isotopes with unstable atomic nuclei
• Emit high energy streams of particles or
  electromagnetic radiation
• Radionuclides
• Another name for radioactive isotopes
• Undergo nuclear reactions
• Uses
• Dating of rocks and ancient artifacts
• Diagnosis and treatment of disease
• Source of energy

6
Mass Not Always Constant

• Mass of particle not constant under all
  circumstances
• It depends on velocity of particle relative to
  observer
• As approaches speed of light, mass increases
• When v goes to zero
• Particle has no velocity relative to observer
• v/c ? 0
• Denominator ? 1
• and m mo

m mass of particle v velocity of particle m?
rest mass c speed of light
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Why dont we observe mass change?

• In lab and ordinary life, velocity of particle is
  small
• Only see mass vary with speed as velocity
  approaches speed of light, c
• As v ? c, (v/c) ? 0 and m ? 8
• In lab, m mo within experimental error
• Difference in mass too small to measure directly
• Scientists began to see relationship between mass
  and total energy
• Analogous to potential and kinetic energies

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Law of Conservation of Mass and Energy

• Mass and energy can neither be created nor
  destroyed, but can be converted from one to the
  other.
• Sum of all energy in universe and all mass
  (expressed in energy equivalents) in universe is
  constant
• Einstein Equation
• ?E (?mo)c 2
• Where c 2.9979 108 m/s

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Mass Defect

• Rest mass of nuclide is always less than sum of
  masses of all individual nucleons (neutrons and
  protons) in that same nuclide
• Mass is lost upon binding of neutrons and protons
  into nucleus
• When nucleons come together, loss of mass
  translates into release of enormous amount of
  energy by Einstein's relation
• Energy released Nuclear Binding Energy
• Nuclear Binding Energy
• Amount of energy must put in to break apart
  nucleus

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What is Mass Loss?
For given isotope of given Z and A
or
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Ex. 1 Binding Energy Calculation

• What is the binding energy of 7Li3 nucleus?
• Step 1. Determine mass loss or mass defect
• A. Determine mass of nucleus
• mass of 7Li3 m (7Li isotope) 3me
• 7.016003 u 3(0.0005485 u)
• 7.0143573 u
• B. Determine mass of nucleons
• mass of nucleons 3 mp 4 mn
• 3(1.007276470 u) 4(1.008664904 u)
• 7.056489026 u

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Ex. 1 Binding Energy Calculation (cont.)

• C. ?m mnucleus mnucleons
• 7.0143573 u 7.056489026 u
• 0.0421317 u
• mass lost by nucleons when they form nucleus
• Step 2. Determine energy liberated by this change
  in mass
• ?E (?mo)c2
• ?E 6.287817 1012 J/atom

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Ex. 1 Binding Energy Calculation (cont.)

• ?E 6.287817 10?12 J/atom 6.0221367 x
  1023 atoms/mole
• ?E 3.78655 1012 J/mole
• 3.78655 109 kJ/mole
• Compare this to
• 104 105 J/mol (102 103 kJ/mol) for chemical
  reactions
• Nuclear 1 10 million times larger than
  chemical reactions!!

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MeV (Energy Unit)

• Nuclear scientists find it convenient to use a
  different Energy unit MeV (per atom)
• Electron volt (eV)
• Energy required to move e? across energy
  potential of 1 V
• 1 eV 1.602 1019 J
• M(mega) 1 106
• So 1 MeV 1 106 eV
• 1 MeV 1.602 1013 J

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Ex. 1 Binding Energy Calculation in MeV

• For Ex. 1. Converting E to MeV gives
• Often wish to express binding energy per nucleon
  so we can compare to other nuclei
• For Li3 with 3 1p and 4 n this would be

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Ex. 2 Calculate E Released

• The overall reaction in the sun responsible for
  the energy it radiates is
• How much energy is released by this reaction in
  kJ/mole of He?
• m (1H) 1.00782 u
• m (4He) 4.00260 u
• m (0?) 0.00054858 u

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Ex. 2 Calculate E Released (cont.)

• ?m mproducts mreactants
• ?m m (4He) 2m (e ) 4m (1H)
• ?m 4.00260 u 2(0.00054858 u) 4(1.00782 u)
• ?m 0.02758 u
• We will convert u to kg, kg m2/s2 to J, and
  atoms to moles in the following calculation

?E 2.479 1012 J/mol 8.268 109 kJ/mol
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Your Turn!

• Determine the binding energy, in kJ/mol and
• MeV/atom, for an isotope that has a mass defect
  of
• 0.025861 u.
• A. 2.3243 109 kJ/mol 24.092 MeV/atom
• B. 3.8595 1012 kJ/mol 24.092 MeV/atom
• C. 7.7529 kJ/mol 8.03620 108
  MeV/atom
• D. 2.3243 109 kJ/mol 4.1508 102 MeV/atom

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Your Turn! - Solution
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Binding Energies per Nucleon

• Divide binding energy EB by mass number, EB/A
• Get binding energy per nucleon

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Implications of Curve

• Most EB /A in range of 6 9 MeV (per nucleon)
• Large binding energy EB /A means stable nucleus
• Maximum at A 56
• 56Fe largest known EB /A
• Most thermodynamically stable
• Nuclear mass number (A) and overall charge are
  conserved in nuclear reactions
• Lighter elements undergo fusion to form more
  stable nuclei

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Implications of Curve

• Fusion
• Researchers are currently working to get fusion
  to occur in lab
• Heavier elements undergo fission to form more
  stable elements
• Fission
• Reactions currently used in bombs and power
  plants (238U and 239Pu)
• As stars burn out, they form elements in center
  of periodic table around 56Fe

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Radioactivity

• Spontaneous emission of high energy particles
  from unstable nuclei
• Spontaneous emission of fundamental particle or
  light
• Nuclei falls apart without any external stimuli
• Discovered by Becquerel (1896)
• Extensively studied by Marie Curie and her
  husband Pierre (1898 ? early 1920's)
• Initially worked with Becquerel

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Fun Facts

• Marie and Pierre Curie discovered polonium and
  radium
• Nobel Prize in Physics 1903
• For discovery of Radioactivity
• Becquerel, Marie and Pierre Curieall three
  shared
• Nobel Prize in Chemistry 1911
• For discovery of Radium and its properties
• Marie Curie only
• Marie Curie - first person to receive two Nobel
  Prizes and in different fields

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Discovery of Radioactivity

• Initially able to observe three types of decay
• Labeled them ?, ?, ? rays (after first three
  letters of Greek alphabet)
• If they pass through an electric field, very
  different behavior

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Discovery of Radioactivity

• ? rays attracted to negative pole so its
  positively charged
• ? rays attracted to positive pole so its
  negatively charged
• ? rays not attracted to either so its not charged

?
?
?
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Nuclear Equations

• Used to symbolize decay of nucleus
• e.g. 238U ?? 234Th
• parent daughter
• Produce new nuclei so need separate rules to
  balance
• Balancing Nuclear Equations
• Sum of mass numbers (A, top) must be same on each
  side of arrow
• Sum of atomic numbers (Z, bottom) must be same on
  each side of arrow

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90
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Types of Spontaneous Emission

• Alpha (?) Emission
• He nucleus
• 2 n 2 p
• A 4 and Z 2
• Daughter nuclei has
• A decreases by 4 ?A 4
• Z decreases by 2 ?Z 2
• Very common mode of decay if Z gt 83 (large
  radioactive nuclides)
• Most massive particle
• e.g.

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Balancing Nuclear Equations

• The sum of the mass numbers (A the superscripts)
  on each side of the arrow must be the same
• The sum of the atomic numbers (Z the subscripts
  nuclear charge) on each side of the arrow must be
  the same
• e.g.
• A 234 230 4
• Z 92 90 2

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2. Beta (? or e) Emission

• Emission of electrons
• Mass number A 0 and charge Z 1
• But How? No electrons in nucleus!
• If nucleus neutron rich nuclide is too heavy

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2. Beta (? or e) Emission

• Charge conserved, but not mass ?m ? E
• Ejected e has very high KE emits
• Antineutrino variable energy particle
• Accounts for extra E generated
• e.g.

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3. Gamma (?) Emission

• Emission of high energy photons
• Often accompanies ? or ? emission
• Occurs when daughter nucleus of some process is
  left in excited state
• Use to denote excited state
• Nuclei have energy levels analogous to those of
  e in atoms
• Spacing of nuclear E levels much larger
• ? light emitted as ?-rays
• e.g.

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4. Positron (? or e) Emission

• Emission of e
• Positive electron
• Where does ? come from?
• If nucleus is neutron poor)
• Nuclide too light
• Balanced for charge, but NOT for mass

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4. Positron (? or e) Emission

• Product side has much greater mass!
• Reaction costs energy
• Emission of neutrino ?
• Variable energy particle
• Equivalent of antineutrino but in realm of
  antimatter
• e emission only occurs if daughter nucleus is
  MUCH more stable than parent

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4. Positron (?or e) Emission

• What happens to e?
• Collides with electron to give matter
  anti-matter annihilation and two high energy
  ?-ray photons ?m ? E
• Annihilation radiation photons
• Each with E? 511 keV
• What is antimatter?
• Particle that has counterpart amongordinary
  matter, but of opposite charge
• High energy light, massless
• Detect by characteristic peak in ?-ray spectrum

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5. Electron Capture (EC)

• e in 1s orbital
• Lowest Energy e
• Small probability that e is near nucleus
• e actually passes through nucleus occasionally
• If it does
• Net effect same as e emission

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Types of Spontaneous Emission

• 6. Neutron Emission ( )
• Fairly rare
• Occurs in neutron rich nuclides
• Does not lead to isotope of different element
• 7. Proton Emission ( )
• Very rare

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Types of Spontaneous Emission

• 8. Spontaneous Fission
• No stable nuclei with Z gt 83
• Several of largest nuclei simply fall apart into
  smaller fragments
• Not just one outcome, usually several
  differentsee distribution

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SummaryCommon Processes

• 1. Alpha (?) Emission
• Very common if Z gt 83
• 2. Beta (??) Emission e
• Common for neutron-rich nuclidesbelow belt of
  stability
• 3. Positron (?) Emission e
• Common for neutron-poor nuclidesabove belt of
  stability
• 4. Electron Capture (EC)
• Occurs in neutron-poor nuclides, especially if Z
  gt 40
• 5. Gamma (?) Emission
• Occurs in metastable nuclei (in nuclear excited
  state)

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Learning Check

• Complete the following table which refers to
  possible nuclear reactions of a nuclide

Emission ?Z ?p ?n ?e ?A New Element?
?
?
?
EC
?
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Learning Check

• Balance each of the following equations

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Your Turn!

• What is the missing species, , in the
  following nuclear reaction?
• A.
• B.
• C.
• D.

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What Holds Nucleus Together?

• Consider nucleus
• Neutrons and protons in close proximity
• Strong proton-proton repulsions
• Neutrons spread protons apart
• Neutron to proton ratio increases as Z increases
• Strong Forces
• Force of attraction between nucleons
• Holds nuclei together
• Overcomes electrostatic repulsions between
  protons
• Binds protons and neutrons into nucleus

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Table of Nuclides

• Chart where Rows different atomic number
• Columns different number of neutrons
• Symbol entered if element is known
• Stable nuclei
• Natural abundance entered below symbol
• Shaded area
• Trend of stable nuclei Belt of Stability
• Z number of neutrons (for elements 1 to 20)
• Unstable nuclei
• Give type(s) of radioactive decay (spontaneous)
• Outer edges, most of atoms

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Table of Nuclides
Number of neutrons
Atomic number (Z number of protons)
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Table of Nuclides

• Shaded area stable nuclei
• Trend of stable nuclei diagonal line Belt of
  Stability
• Z number of neutrons (for elements 1 to 20)
• Note only a small corner of table is shown. (The
  complete is in Handbook of Chemistry and Physics)

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Belt of Stability

• Each isotope is a dot
• Up to Z 20
• Ratio n /Z 1
• As Z increases, n gt Z and
• By Z 82, n/Z 1.5
• n number of neutrons
• Z number of protons

? Stable nuclide, natural ? Unstable nuclide,
natural ? Unstable nuclide, synthetic
1.5n1p
1.4n1p
Band of Stability
n
e emitters
1.3n1p
1n1p
1.2n1p
1.1n1p
e emitters
1n1p
Z p
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How To Predict if Nuclei are Stable

• 1) Atomic Mass weighted average of masses of
  naturally occurring isotopes, i.e. most stable
  ones
• 2) Compare atomic mass of element to A (atomic
  mass number) of given isotope and see if it is
  more or less
• Atomic Mass gt A too light to be stable
• Atomic Mass lt A too heavy to be stable

Ex. Atomic Mass Conclusion
180Os
135I
190.2
Too light, neutron poor
Too heavy, neutron rich
126.9

• Final note
• All nuclei with Z gt 83 are radioactive

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More Patterns of Stability

• If we look at stable and unstable nuclei, other
  patterns emerge
• 283 stable nuclides (out of several thousand
  known nuclides)
• If we look at which have even and odd numbers of
  protons (Z) and neutrons (n) patterns emerge

Z n stable nuclides
even even 165
even odd 56
odd even 53
odd odd 5
2H, 6Li, 10B, 14N, 138La
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More Patterns of Stability

• Clearly NOT random even must imply greater
  stability
• Not too surprising
• Same is true of electrons in molecules
• Most molecules have an even number of electrons,
  as electrons pair up in orbitals
• Odd electron molecules, radicals, are very
  unstable, i.e. very reactive!!

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Magic Numbers

• Look at binding energies, see certain numbers of
  protons and neutrons result in special stability
• Called Magic Numbers
• 1n and 1p in separate shells
• Magic numbers (for both 1n and 1p) are 2, 8, 20,
  28, 50, 82, 126
• For e pattern of stability is 2, 10, 18, 36,
  54, 86(Noble gases)

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Magic Numbers

• Special stability of noble gases due to closed
  shells of occupied orbitals
• Structure of nucleus can also be understood in
  terms of shell structure
• With filled shells of neutrons and protons
  having added stability
• At some point adding more neutrons to higher
  energy neutron shells decreases stability of
  nuclei with too high a neutron to proton ratio

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Your Turn!

• Isotopes above the band of stability are more
• likely to
• A. emit alpha particles
• B. emit gamma rays
• C. capture electrons
• D. emit beta particles

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Radioactive Nuclei Found in Nature

• Non-naturally occurring elements (man-made
  unstable) are denoted by having atomic mass in
  parentheses
• All nuclei with Z gt 83 are radioactive
• Yet some elements with Z between 83 and 92 occur
  naturally
• Atomic weight is NOT in parentheses
• How can this be?
• There are three heavy nuclei, which have very
  long half-lives
• Long enough to have survived for billions of
  years
• Each parent of natural decay chain

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Decay Chains

• 238U half-life (?½) 4.5 billion years
• ? emitter
• Daughter 234Th is also radioactive
• ? emitter
• Half-life much shorter
• Long sequence of emissions, ? and ?
• Recall that ? emission changes A by 4, while ?
  emission ?A 0
• Result every member of chain has A (4n 2)
  where n some simple integer

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238Uranium Decay Chain
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Decay Chains

• Final stable member of sequence is 206Pb
• Some intermediate nuclides have reasonably short
  half-lives
• Still found in nature because they are constantly
  being replenished by decay of nuclei further up
  chain
• Uranium-containing minerals (pitchblende is most
  famous) contain many radioactive elements

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Your Turn!

• When the reaction, ,
  occurs,
• the particle emitted is
• A. an alpha particle
• B. a beta particle
• C. an electron
• D. a gamma ray

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Transmutation

• Change of one isotope for another
• Caused by
• Radioactive decay
• Bombardment of nuclei with high energy particles
• ? particles from natural emitters
• Neutrons from atomic reactors
• Protons made by stripping electrons for hydrogen
• Protons and ? particles can be accelerated in
  electrical field to give higher E
• Mass and energy of bombarding particle enter
  target nucleus to form compound nucleus

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Non-Spontaneous Nuclear Processes

• Fusion
• Occurs in starsright now
• How elements formed
• Induced Fission
• Bombard heavy nuclei with neutron

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Compound Nucleus

• Designated with
• High energy due to velocity of incoming particle
• Energy quickly redistributed among nucleons, but
  usually unstable
• To get rid of excess energy, nucleus ejects
  something
• Neutron ? Proton
• Electron ? Gamma radiation
• Decay leaves new nucleus different from original

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Example Transmutation
Compound nucleus
New nucleus
Target nucleus
Bombard-ing particle
High energy particle
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Transmutation

• Can synthesize given nucleus in many ways
• Once formed, compound nucleus has no memory of
  how it was made
• Only knows how much energy it has

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Transmutation

• Decay pathway depends on how much energy

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Transmutation

• Used to synthesize new isotopes
• gt 900 total
• Most not on band of stability
• All elements above 93 (neptunium) are man- made
• Includes actinides above 93 104 112 114
• Heavier elements made by colliding two larger
  nuclei
• Also known as fusion

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Your Turn!

• What would be the element produced from the
• fusion of with ? The species
  would
• be in a high energy state and in time would
• undergo decay to other species.
• A. No
• B. Lr
• C. U
• D. Hs

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Measuring Radioactive Decay

• Atomic radiation ionizing radiation
• Creates ions by knocking off electrons
• Geiger Counter
• Consists of a tube with a mica window, low
  pressure argon fill gas and two high voltage
  electrodes
• Detects ? and ? radiation with enough E to
  penetrate mica window
• Inside tube, gas at low pressure is ionized when
  radiation enters
• Ions allow current to flow between electrodes
• Amount of current relates to amount of radiation

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Measuring Radioactive Decay

• Scintillation Counter
• Surface covered with chemical
• Emits tiny flash of light when hit by radiation
• Emission magnified electronically and counted
• Film Dosimeters
• Piece of photographic film
• Darkens when exposed to radiation
• How dark depends on how much radiation exposure
  over time
• Too much exposure, person using must be
  reassigned to other work

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Activity

• Number of disintegrations per second
• Used to characterize radioactive material
• A kN
• k first order decay constant in terms of number
  of nuclei rate than concentration
• N number of radioactive nuclides
• Law of radioactive decay
• Radioactive decay is first order kinetics process

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Units of Activity

• SI unit
• Bequerel (Bq)
• 1 disintegration per second (dps)
• 1 liter of air has 0.04 Bq due to 14C in CO2
• Older unit
• Curie (Ci)
• 3.7 1010 dps 3.7 1010 Bq
• Activity in 1.0 g 226Ra 1 Ci

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Half-Life

• Time it takes for number of nuclides, Nt ,
  present at time, t, to fall to half of its value.
• Half-lives are used to characterize nuclides
• If you know half-life
• Can use to compute k
• Can also calculate A of known mass of radioisotope

73
Ex. 3 Activity of Sr-90

• What is the activity of 1.0 g of strontium-90?
  The half-life 28.1 years
• Step 1. Convert t½ to seconds
• Step 2. Convert t½ to k

74
Ex. 3 Activity of Sr-90 (cont.)

• Step 3. Convert mass of 90Sr to number of atoms
  (N)
• Step 4. Calculate Activity kN

A 5.23 ? 1012 atoms Sr/s ? 1 disintegration/atom
A 5.23 ? 1012 dps or 5.23 ? 1012 Bq
75
Ex. 4 Mass of 3H in Sample

• 3H, tritium, is a ?? emitter with a half-lifet½
  12.26 yrs. MW 3.016 g/mol. How many grams
  of 3H are in a 0.5 mCi sample?
• Step 1. Convert half-life to seconds as Ci is in
  disintegrations per second (dps)
• Step 2. Convert t½ to k

76
Ex. 4 Mass of 3H in Sample (cont.)

• Step 3. Convert Ci to dps
• Step 4. Calculate g 3H to get this activity
• Step 5. Convert atoms to g

5.2 108 g
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Exposure Units

• Not all materials equally absorb radiation, thus
  activity doesnt describe effect of exposure
• 1 gray (Gy) 1 J absorbed energy/kg material
• SI unit of absorbed radiation
• 1 rad absorption of 10-2 J/ kilogram of tissue
• Older unit
• 1 Gy 100 rad
• These units dont take into account type of
  radiation

78
Exposure Units

• Sieverts (Sv)
• SI unit of dose equivalent, H
• Depends on amount and type of radiation as well
  as type of tissue absorbing it
• HDQN
• H dose in Sv
• D dose in Gy
• Q radiation properties
• N other factors
• Rem older unit
• 1 Rem 102 Sv
• Still used in medicine

79
Exposure to Radiation

• Typically X ray 0.007 rem or 7 mrem
• 0.3 rem/week is maximum safe exposure set by US
  government
• 25 rem (0.25 Sv) Causes noticeable changes in
  human blood
• 100 rem (1 Sv)
• Radiation sickness starts to develop
• 200 rem (2 Sv)
• Severe radiation sickness
• 400 rem (4 Sv)
• 50 die in 60 days
• Level of exposure or workers at Chernobyl when
  steam explosion tore apart reactor
• 600 rem (6 Sv) lethal dose to any human

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Your Turn!

• Workers cleaning up the Fukushima reactors were
• exposed to as much as 400 mSv units of radiation
  per
• hour. How many rems of exposure does this
• correspond to?
• A. 4000 rem
• B. 400 rem
• C. 40 rem
• D. 4 rem

81
Why is Radiation Harmful?

• Not heat energy
• Ability of ionizing radiation to form unstable
  ions or neutral species with odd (unpaired)
  electrons
• Free radicals
• Chemically very reactive
• Can set off other reactions
• Do great damage in cell

82
Which Types are Most Harmful?

• High energy gamma (?) radiation and X rays
• Massless
• High velocity
• Penetrate everything but very dense materials,
  such as lead
• Which type is least harmful?
• Alpha (?) particles
• Most massive
• Quickly slow after leaving nucleus
• Dont penetrate skin

83
Background Radiation

• Presence of natural radionuclides means we cant
  escape exposure to some background radiation
• Cosmic rays (from sun) hit earth
• Turn 14N ? 13C
• 13C emits ? particles
• Incorporated into food chain from CO2 via
  photosynthesis
• Radiation from soil and building stone
• From radionuclides native to Earths crust
• Top 40 cm of soil hold 1 g radium (? emmiter) /sq
  kilometer
• 40K emit ? particles
• Total average exposure 360 mrem/year
• 82 natural radiation 18 man made

84
Radiation Intensity

• Intensity of radiation varies with distance from
  the source
• Farther from emitter, lower intensity of exposure
• Relationship is governed by Inverse Square Law,
  where
• I is intensity and
• d is distance from source

85
Ex. 5 Inverse Square Law

• If the activity of a sample is 10 units at 5
  meters from the source, what is it at 10 m?
• What distance is needed to reduce 1 unit at 1 yd
  to the 0.05 units?

86
Your Turn!

• How far away from a radioactive source producing
  40
• rem/hr at a distance of 10 m would you need to be
  to
• reduce your exposure to 0.4 rem/hr?
• A. 32 m
• B. 100 m
• C. 200 m
• D. 1000 m

87
Radioactive DecayKinetics

• Spontaneous decay of any nuclide follows first
  order kinetics
• May be complicated by decay of daughter nuclide
• For now consider single step decay processes
• Rate of reaction for first order process
• A ?? products
• In nuclear reaction, consider rate based on
  number of nuclei N present

88
Radioactive DecayKinetics

• The integrated form is
• ln N ln No kt
• N number of nuclei present at time t
• No number of nuclei present at t 0
• Plot ln N (y axis) versus t (x axis)
• Yields straight lineindicative of first order
  kinetics
• Plot of N vs. time gives an exponential decay.

89
Ex. 6 Activity Calculations

• 131I is used as a metabolic tracer in hospitals.
  It has a half-life, t½ 8.07 days. How long
  before the activity falls to 1 of the initial
  value?

t 53.6 days
90
Your Turn!

• How many hours will it take a radioisotope with
• a half-life of 10.0 hours to drop to 12.5 of its
  
• original activity?
• A. 30.0 hrs
• B. 20.0 hrs
• C. 40.0 hrs
• D. 63.2 hrs
• 12.5 of original activity is 3 half-lives or
  30.0 hrs.

91
Radioisotope Dating

• How old is an object?
• Fields Geology, Archeology, and Anthropology
• Nature provides us with natural clocks or
  stopwatches
• A) Radiocarbon Dating (Willard LibbyNobel Prize
  in 1960)
• Cosmic rays (from space) enter atmosphere
• Some react with N in atmosphere forming
  radioisotope 14C
• ? emitter with t½ 5730 yr

92
14C Dating

• 14C becomes incorporated into atmospheric CO2 in
  very small quantities
• 14C/12C ratio in air is slightly greater than
  Earths crust because of ongoing enrichment
• Living organisms breath, eat, etc
• 14C/12C equilibrate with atmosphere
• Radioactive 14C is uniformly distributed around
  globe
• Tested experimentally
• Checked vs. counting tree rings, etc.
• For precise work, use correction based on
  alternate methods

93
14C Dating

• HOW? Freshly cut wood samples have 15.3 cpm per
  gram of total carbon
• cpm counts per minute
• ? Ao 15.3 cpm/g total C
• Assumption Ao was always 15.3 cpm, i.e. cosmic
  radiation is constant
• When organism dies
• it stops eating, breathing, etc
• 14C starts to decrease

94
14C Dating

• Wooden implement in Egyptian tomb (3000 BC)
• Have about half activity of fresh sample
• 5000 years have elapsed
• Method is applicable for objects
• Few hundred to 20,000 years
• Beyond this
• Activity of sample is very low
• Experimental uncertainties too big
• This method used for dating
• Charcoal in cave paintings
• Linen wraps on Dead Sea scrolls

95
Ex. 7 C-14 Dating

• Geologists examine shells found in cliffs.
  Shells are CaCO3 and are made by living
  organisms. The activity of the shells is found
  to be 6.24 cpm/g total C. How old is the cliff
  formation?

• Can use N/No and A/Ao interchangeably as A kN
• Since ratio, k cancels

A 6.24 cpm/g total C Ao 15.3 cpm/g total C t½
5730 yr
96
Ex. 7 C-14 Dating (cont.)

• Rearranging and solving for t

t 7414 yr
97
B) Other Isotopes Provide Natural Clocks

• Minerals (moon rocks) dated using isotopes with
  much longer half-lives
• t½ 1.27 109 yr
• Compare ratios in rock
• t½ 4.5 109 yr
• Rock with no other source of Pb can be dated
  using ratios

98
Ex. 8 Dating with U

• A sample of lava is found to contain 0.232 g of
  206Pb and 1.605 g 238U. Since lead is volatile
  at the temperature of molten lava, all the 206Pb
  now present came from the decay of 238U,
  calculate the time since the solidification of
  this rock.
• Step 1. Mass of 238U that decayed
• 0.268 g 238U decayed

99
Ex. 8 Dating with U (cont.)

• Step 2. Mass of 238U in lava initially (t 0)
  No 1.605 g 0.268 g 1.873 g

t 1.0 109 yr
100
Your Turn!

• A wooden bowl fragment found at an old camp site
• thought to be approximately 11,000 years old was
• submitted for carbon-14 analysis. The sample was
• found to have 4.67 cpm/g total C. What is the
  actual
• age of the sample?
• A. 4260 yrs
• B. 3347 yrs
• C. 9810 yrs
• D. 2523 yrs
• t (5730 yrs ln(4.67/15.3))/(ln 2) 9810 yrs

101
Fission

• Induce by bombarding unstable nucleus with a slow
  neutron
• Nuclear chain reaction
• Neutrons generated keep going
• With small mass of 235U reaction continues, but
  easily controlled
• Some neutrons are lost to environment

102
Fission

• Critical mass
• Too much 235U in one place
• Too many neutrons absorbed
• Too few lost
• Uncontrollable fission
• Leads to explosion
• Use control rods to absorb excess neutrons and
  keep reaction from going critical

103
Nuclear Reactor

• No chance of nuclear explosion
• Critical mass requires pure 235U
• Reactor rods 2 4 235U rest non-fissionable
  238U
• Core meltdown possible
• If heat of fission not carried away by cooling
  water
• Or
• Explosion possible
• High heat of fission splits H2O into H and O,
  which recombine very exothermically and cause a
  chemical explosion
• What happened at Chernobyl

104
Nuclear Reactors

• Could it happen at U.S. reactors?
• Extremely unlikely
• Chernobyl only single containment system
• U.S. has all double containment systems
• U.S. extra backup systems - both computer and
  mechanical that would prevent

105
Nuclear Reactor

• Use heat from nuclear reaction to heat steam
  turbine
• Use to generate electricity

106
Your Turn!

• Which of the following fission reactions is
• Balanced?
• A.
• B.
• C.
• D.

107
Nuclear Fusion

• Occurs when light nuclei join to form heavier
  nucleus
• On a mass basis, fusion yields more than five
  times as much energy as fission
• Source of the energy released in the explosion of
  a H-bomb
• The energy needed to trigger the fusion is
  provided by the explosion of a fission bomb
• Source of energy in stars

108
Thermonuclear Fusion

• Uses high temperatures to overcome electrostatic
  repulsions between nuclei
• T required are gt100 million C
• Atoms want to fuse stripped of electrons
• High initial energy cost
• Plasma
• Electrically neutral, gaseous mixture of nuclei
  and electrons
• Make plasma very dense (gt200 g/cm3)
• Brings nuclei within 2 fm 2 1015 m
• Pressures several billion atm
• Not there yet, major problem
• Containment of high temperature and pressures
• Magnetic field current approach