1. Chapter 21: Nuclear Chemistry
Chemistry: The Molecular Nature of Matter, 6E
Jespersen/Brady/Hyslop

2. How are atoms formed? Big Bang—Intense heat ~109 K
Cooled quickly to 106 K—T of stars
e–, p, n formed and joined into nuclei—atoms
Mostly H and He (as in our sun)
Rest of elements formed by nuclear reactions
Fusion—two nuclei come together to form another heavier nucleus
Fission—one heavier nucleus splits into lighter nuclei
Various other types of reactions + +

3. Nuclear Shorthand Nuclide Atomic Number (Z )
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

4. 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

5. Radioactivity Radioactive isotopes Radionuclides Uses
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

7. Why don’t 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  ∞
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

8. 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 = × 108 m/s

9. Mass Defect Nuclear Binding Energy
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

10. What is Mass Loss?
For given isotope of given Z and A or

11. 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
= u – 3( u)
= u
B. Determine mass of nucleons
mass of nucleons = 3 mp mn
= 3( u) + 4( u)
= u

12. Ex. 1 Binding Energy Calculation (cont.)
C. m = mnucleus – mnucleons
= u – u
= – u
= mass lost by nucleons when they form nucleus
Step 2. Determine energy liberated by this change in mass
E = (mo)c2
E = – × 10–12 J/atom

13. Ex. 1 Binding Energy Calculation (cont.)
E = – × 1012 J/atom × x 1023 atoms/mole
E = – × 1012 J/mole
= – × 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!!

14. 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 = × 10–19 J
M(mega) = 1 × 106
So 1 MeV = 1 × 106 eV
1 MeV = × 10–13 J

15. 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

16. 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) = u
m (4He) = u
m (0+) = u

17. Ex. 2 Calculate E Released (cont.)
m = mproducts – mreactants
m = m (4He) + 2m (e +) – 4m (1H)
m = u + 2( u) – 4( u)
m = – 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

18. Your Turn!
Determine the binding energy, in kJ/mol and MeV/atom, for an isotope that has a mass defect of – u. A. – × 109 kJ/mol; MeV/atom B. – × 10–12 kJ/mol; MeV/atom C. – kJ/mol; × 10–8 MeV/atom D. – × 109 kJ/mol; × 10–2 MeV/atom

19. Your Turn! - Solution

20. Binding Energies per Nucleon
Divide binding energy EB by mass number, EB/A
Get binding energy per nucleon

21. 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

22. Implications of Curve Fusion Fission
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

23. 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

24. Fun Facts Marie and Pierre Curie discovered polonium and radium
Nobel Prize in Physics 1903
For discovery of Radioactivity
Becquerel, Marie and Pierre Curie—all 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

25. 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

26. 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   

27. Nuclear Equations e.g. 238U  234Th + parent daughter
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 92 90

28. 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 > 83 (large radioactive nuclides)
Most massive particle
e.g.

29. 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 =
Z: =

30. 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

31. 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.

32. 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.

33. 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

34. 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

35. 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 among ordinary matter, but of opposite charge
High energy light, massless
Detect by characteristic peak in -ray spectrum

36. 5. Electron Capture (EC) e– in 1s orbital If it does: 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
1s orbital very small in size, especially at large Z

37. 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

38. Types of Spontaneous Emission
8. Spontaneous Fission
No stable nuclei with Z > 83
Several of largest nuclei simply fall apart into smaller fragments
Not just one outcome, usually several different—see distribution

39. Summary—Common Processes
1. Alpha () Emission
Very common if Z > 83
2. Beta () Emission e–
Common for neutron-rich nuclides—below belt of stability
3. Positron (+) Emission e+
Common for neutron-poor nuclides—above belt of stability
4. Electron Capture (EC)
Occurs in neutron-poor nuclides, especially if Z > 40
5. Gamma () Emission
Occurs in metastable nuclei (in nuclear excited state)

40. Learning Check
Complete the following table which refers to possible nuclear reactions of a nuclide:
Emission
Z = p n e A
New Element?  – + EC  –2 –4
yes +1 –1
yes +1 –1
yes +1 –1
yes no

41. Learning Check
Balance each of the following equations

42. Your Turn!
What is the missing species, , in the following nuclear reaction? A. B. C. D.

43. 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

44. 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

45. Atomic number (Z = number of protons)
Table of Nuclides
Number of neutrons
Atomic number (Z = number of protons)

46. 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)

47. Belt of Stability Each isotope is a dot Up to Z = 20
Ratio n /Z = 1
As Z increases, n > 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
1.5n:1p
1.4n:1p
Band of Stability n
e– emitters
1.3n:1p
1.2n:1p
1n:1p
1.1n:1p
e+ emitters
1n:1p
Z = p

48. 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 > A too light to be stable
Atomic Mass < A too heavy to be stable
Ex.
Atomic Mass
Conclusion
180Os
135I
190.2
Too light, neutron poor
126.9
Too heavy, neutron rich
Final note:
All nuclei with Z > 83 are radioactive

49. 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
165
odd 56 53 5
2H, 6Li, 10B, 14N, 138La

50. 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!!

51. 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)

52. 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

53. 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

54. Radioactive Nuclei Found in Nature
Non-naturally occurring elements (man-made unstable) are denoted by having atomic mass in parentheses
All nuclei with Z > 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

55. 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

56. 238Uranium Decay Chain 238U 234Th 5109 y  25 d ,  234Pa 7 hr 234U
, 
8104 y
226Ra
2103 y
222Rn
4 d
218Po
3 m
214Pb
27 m
214Bi
20 m
214Po
1.610–4 s
210Pb
22 y
210Bi 
5 d
210Po
138 d
206Pb 92 90 91 88 86 84 82 83
A stable isotope

58. 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

59. 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

60. 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

61. Non-Spontaneous Nuclear Processes
Fusion
Occurs in stars—right now
How elements formed
Induced Fission
Bombard heavy nuclei with neutron

62. 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

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

64. 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

65. Transmutation
Decay pathway depends on how much energy

66. Transmutation Used to synthesize new isotopes
> 900 total
Most not on band of stability
All elements above 93 (neptunium) are man- made
Includes actinides above –
Heavier elements made by colliding two larger nuclei
Also known as fusion

67. 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

68. 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

69. 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

70. Activity A = kN Law of radioactive decay
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

71. Units of Activity SI unit Older unit Bequerel (Bq) Curie (Ci)
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

72. 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-life t½ = yrs. MW = 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 × 10–8 g

77. Exposure Units
Not all materials equally absorb radiation, thus activity doesn’t 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 don’t take into account type of radiation

78. Exposure Units Sieverts (Sv) Rem = older unit
SI unit of dose equivalent, H
Depends on amount and type of radiation as well as type of tissue absorbing it
H=DQN
H = dose in Sv
D = dose in Gy
Q = radiation properties
N = other factors
Rem = older unit
1 Rem = 10–2 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

80. 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 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
Don’t penetrate skin

83. Background Radiation
Presence of natural radionuclides means we can’t 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 Earth’s 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 % 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 m

87. Radioactive Decay—Kinetics
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 Decay—Kinetics
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 line—indicative 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 hrs B hrs C hrs D 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 Libby— Nobel 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 Earth’s 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 When organism dies
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 g of 206Pb and 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 =
= g 238U decayed

99. Ex. 8 Dating with U (cont.)
Step 2. Mass of 238U in lava initially (t = 0) No = g g = 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 yrs B yrs C yrs D 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 Core meltdown possible
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 >100 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 (>200 g/cm–3)
Brings nuclei within 2 fm = 2 × 10–15 m
Pressures = several billion atm
Not there yet, major problem
Containment of high temperature and pressures
Magnetic field current approach