1. Nuclear Chemistry (selected topics)
Introduction and Important Terms
Very different than any other kind of “chemistry”!
Spontaneous Nuclear Decay Reactions
Which nuclides decay, and how do they decay? (Zone / Valley of stability)
Conservation “Laws” of all Nuclear Reactions (How to complete a nuclear decay reaction equation)
Kinetics of Nuclear Decay Reactions
Review of 1st order kinetics
E=mc2, and relation to binding energy and mass defect; & “Binding energy per nucleon”

2. I. Introduction and Important Terms
Chemical Reactions? (up till now)
New substances are made through the formation of new nanoscopic “units” by making and/or breaking chemical bonds (Dalton)
All the “action” is outside of the nuclei
Nuclei remain unchanged!
Chemical Bonding involves moving electrons, not nuclei
Nuclear chemistry: Complete opposite!
It’s all about changing the nucleus!
Independent of any “standard” chemical reactions

3. From PS10 Sheet: Review of Terms
Nucleon: a particle that’s part of the nucleus (i.e., either a proton (p) or neutron (n))
Atomic Number (Z): # p’s in nucleus
Defines “who you are” (which element)
Mass number (A): sum of p’s & n’s
**Not a “mass”; a (whole) number
Similar to nuclear mass (to nearest amu)
Isotopes (of an element)
Have same number of protons, but different number of neutrons. E.g., C-14 (8 n’s) vs C-12 (6 n’s)
Complete atomic symbol of an isotope: A X Z

4. New Terms
Nuclide: a nucleus with a specified number of neutrons (almost synonymous with “isotope”)
Refers more to the “thing” rather than the “type of matter”
Radioactive Nuclide: a nuclide that undergoes a spontaneous nuclear decay process
With a corresponding release of some energetic particle (or photon)
Radiation: general (historic) term for the kind of energetic particles (or photons) that are emitted from a sample containing radioactive nuclides. Many kinds:
Alpha, beta, gamma, positron
Stable Nuclide*: a nuclide that does not undergo any spontaneous nuclear decay process. *more on “stable” later

5. Other Nuclear Reactions (not all nuclear reactions are decay!)
Spontaneous Nuclear Decay (discussed first)
Radioactive nuclides (only)
one (“reactant”) nuclide turns into another nuclide
not initiated (just happens)
Other nuclear reactions (later)
Generally involve initiation & more than one nuclide as “reactants”.
Fission and Fusion
Transmutation (bombardment) reactions

6. Two kinds of “stability” in this unit!
One refers to whether a nuclide will undergo spontaneous nuclear decay.
Does the nuclide decay (unstable, radioactive) or not (stable)?
The “valley of stability”
Kinetic Stability
Ex. 206Pb is a stable nuclide. 238U is radioactive
One refers to how stable one nuclide is compared to another, in terms of “overall configuration of nucleons”
Applies to all nuclides, radioactive or not
Assessed by Binding energy per nucleon
Thermo-dynamic Stability
(later)
Ex. 56Fe is more stable than 206Pb or 2H

7. II. Nuclear Decay Reactions
Objectives
Compare and contrast the various kinds of nuclear decay types and their associated particles
Symbolically represent nuclides and particles in a nuclear reaction equation
Determine the “daughter” nuclide of a particular decay process if given the parent nuclide
Using two conservation rules (mass # and charge)
Predict the likely decay process of a nuclide by using the “Valley of Stability” and related ideas

8. Kinds of Nuclear Decay (and kinds and symbols of particles)
A. Alpha (a) decay [loss of an a particle] or
234 Th 90
What is the nuclide formed? (or complete the eqn)
 Apply conservation of mass # and charge*:
238 = ?  ? = (= mass number)
234
92 = ?  ? = (= “charge” [# of protons]) 90
*Note: Unlike what we do with ions, charge of nuclei or nuclear particles is represented by the lower left subscript. Why?

9. Kinds of Nuclear Decay (and kinds and symbols of particles)
B. Beta(b) decay [emission of a b particle]
A high-energy electron (b or e)
131 Xe 54 -1
What is the nuclide formed? (or complete the eqn)
 Apply conservation of mass # and charge*:
131 = ?  ? = (= mass number)
131
53 = ?  ? = (= “charge” [# of protons]) 54
*Note: Charge of nuclei or nuclear particles is represented by the lower left subscript.

10. Take a step back…what’s really happening in b decay?
 A neutron is turning into a _______!
proton 1 p 1 -1
131 54 Xe -1
NOTE: The electron in b decay is produced by the process (it is not a pre-existing electron)

11. Kinds of Nuclear Decay (What else can happen?)
C. Gamma g radiation [emission of a g particle]
A high-energy photon
Photon = “particle” of light (no mass)
“Repacking” of a nucleus
An “excited” nucleus “relaxes” to lower energy, with an emission of a photon
Not unlike an electron in an atom
Usually happens after another nuclear reaction

12. Kinds of Nuclear Decay (What else can happen?)
C. Gamma g radiation [emission of a g particle]
A high-energy photon
Basically, nothing appears to happen!

13. Kinds of Nuclear Decay (What else can happen?)
D. Positron emission [emission of a positron]
A “positive electron”, 30 Si 14
What is the nuclide formed? (or complete the eqn)
 Apply conservation of mass # and charge*:
30 = ?  ? = (= mass number) 30
15 = ?  ? = (= “charge” [# of protons]) 14

14. Take a step back…what’s really happening in positron emission?
 A proton is turning into a neutron! 1 n +1 30 14 Si
NOTE: A proton will not decay this way spontaneously unless it is in certain nuclei. Free protons are “stable”.

15. A comment on “antimatter”
Antimatter is real!
It is true that “when matter meets antimatter, they mutually annihilate one another to form pure energy”
A positron is a type of antimatter; an electron is a type of (regular) matter.

16. Kinds of Nuclear Decay (Guess what
Kinds of Nuclear Decay (Guess what? There is a second way to turn a p into a n!)
E. Electron Capture
Different than the others
“Added particle” is a reactant (not “produced”)
A preexisting electron (inner shell) gets “snagged” by the nucleus (?!) 7 Li 3

17. Overview: Table 19.1 in Tro (partial)
Ppt 06 Nuclear Chemistry

18. Overview: Table 19.1 in Tro (2nd part)
Ppt 06 Nuclear Chemistry

19. Nuclear Stability Patterns— The Valley of Stability
How can we predict which kinds of nuclear decays occur in which nuclides?
Is there a pattern?
Yes! But let’s start by looking at which nuclides are stable.
NOTE: I will not be explaining why these ones are stable. This is, primarily, empirical.
Ppt 06 Nuclear Chemistry

20. Nuclear Stability Patterns— The Valley of Stability
Make a plot of number of neutrons (N) vs number of protons (Z) for stable nuclides
This “defines” the so-called “valley of stability” (also “zone” or “belt” of stability)
See board first. Then figures.
Ppt 06 Nuclear Chemistry

21. Ppt 06 Nuclear Chemistry

22. There are no stable nuclides with atomic numbers larger than 83.
The stable nuclides lie in a very narrow band of neutron-to-proton ratios.
The ratio of neutrons to protons in stable nuclides gradually increases as the number of protons in the nucleus increases.
Light nuclides, such as 12C, contain about the same number of neutrons and protons.
Heavy nuclides, such as 238U, contain up to 1.6 times as many neutrons as protons.
There are no stable nuclides with atomic numbers larger than 83.
This narrow band of stable nuclei is surrounded by a sea of instability.
Nuclei that lie below the band don't have enough neutrons and are therefore neutron-poor.
Nuclei that lie above the band have too many neutrons and are therefore neutron-rich.
Ppt 06 Nuclear Chemistry

23. NOTE:
The farther away a nuclide is from the valley of stability, the shorter its half life.
“Farther = less
(kinetically) stable”
Ppt 06 Nuclear Chemistry

24. Table 19.2 Number of Stable Nuclides with Even and Odd Numbers of Nucleons
Even numbers (of nucleons) appear to correlate with stability. Theory of nucleon energy levels is beyond the scope of this course (and my knowledge!)
Ppt 06 Nuclear Chemistry

25. More from the web… http://en.wikipedia.org/wiki/Isotope

26. Figure (Zumdahl) A Plot of (Potential) Energy versus the Separation Distance (particles = protons)
Ppt 06 Nuclear Chemistry 26

27. Using The Valley of Stability to Predict “Which decay?”
See board
Ppt 06 Nuclear Chemistry

28. Summary of Strategy for Predicting Decay Type
First determine if “above, below, or beyond” the valley of stability:
If Z > 83, it is “Beyond”
Not always “correct”, but correct prediction
If Z ≤ 83, Figure out if the nuclide has:
“too many neutrons” (“Above”) OR
“too few neutrons” (“Below”)
(NOTE: long way or shortcut way*; even if you use shortcut, be able to relate it to the n/p ratio!)
Then make conclusion by noting which process makes daughter closer to the “valley” (next slide)
*Discussed later

29. Summary of Strategy for Predicting Decay Type (continued)
It turns out that…
A radioactive nuclide tends to decay in such a way that its daughter nuclide is closer to the valley of stability
b decay: turns n to p
 used by nuclides above valley (“neutron rich”)
PE or EC: turns p to n
 used by nuclides below valley (“neutron poor”)
a decay: lose both n and p
 used by nuclides beyond valley (too many of both)

30. How to determine if a nuclide is “above”, “below”, or “beyond”?
(if you don’t have a valley of stability table)
Long way:
Calculate n/p (=N/Z) ratio
Compare actual n/p ratio to ~stable n/p ratio:
Know that for Z = 1-20, n/p = 1 is ~stable
Know that for Z = ~80, n/p = 1.5 is ~stable
Know that for Z ~40, n/p ~1.25 is stable
Short way: (next slide)

31. “Above, Below, or Beyond?” (continued)
Short way (makes some assumptions, but…):
 Compare A to “aam”
A is the mass number of the isotope; “aam” = average atomic mass of element
If A > aam, predict “too many neutrons”
If A < aam, predict “too few neutrons”
Why does this work?
It is likely to be the case that the most abundant isotopes on Earth are “stable”.
Thus, the average atomic mass, if rounded, is likely to be close to the mass number of nuclides near the valley of stability!

32. Examples
See handout sheet and board examples

33. Nuclear Decay Kinetics
See board first

34. Table 18.3 The Half-Lives of Nuclides in the 23892U Decay Series
Ppt 06 Nuclear Chemistry

35. Table 18.4 Syntheses of Some of the Transuranium Elements
Ppt 06 Nuclear Chemistry

36. Figure 18.3 The Decay of a 10.0-g Sample of Strontium-90 Over Time
Ppt 06 Nuclear Chemistry

37. Figure 18.4 The Half-Lives of Radioactive Nuclides
Ppt 06 Nuclear Chemistry

38. Figure 18.7 Geiger-Muller Counter
Rates of nuclear reactions (“activities”) can be directly measured using a Geiger counter.

39. Table 19.6 Some Radioactive Nuclides, with Half-Lives and Medical Applications as Radiotracers
Ppt 06 Nuclear Chemistry

40. Bone Scan (using gamma ray emissions of Tc-99m)
Chapter 19, Unnumbered Figure, Page 894
Ppt 06 Nuclear Chemistry

41. Energy-related Issues
See Board
Consider a nucleus of an atom of U-238
How much mass do you think it should contain?
How about a whole atom of U-238?
mass of a proton = amu
mass of a neutron = amu
mass of an electron = amu
Ppt 06 Nuclear Chemistry

42. Important Clarification
Note: Although binding energy technically refers to the E required to separate a nucleus into free nucleons, and thus “mass defect” represents the difference between the “mass of free nucleons” and the “mass of the nucleus”, the way we calculate mass defect from mass data usually involves a slightly different quantity because experimentally it is the mass of an atom that is known, not the mass of “just” the nucleus. [next page]

43. To calculate Mass Defect From “mass data”…(rationalizing Tro’s approach)
Let mass defect be abbreviated Dmmd
Dmmd = mass of free nucleons – mass of nucleus
= m(p’s + n’s) – m(nucleus)
m(p’s + e’s + n’s) – m(nucleus + e’s)
= m(H atoms + n’s) – m(atom)
This “works” because the energy lowering associated with binding the electrons to the nucleus (electrostatic force at large distance) is almost negligible relative to the energy lowering associated with binding the nucleons to one another (strong force at small distance)
bonded
Tro

44. EXAMPLE 19.7 Mass Defect and Nuclear Binding Energy
Calculate the mass defect and nuclear binding energy per nucleon (in MeV) for C-16, a radioactive isotope of carbon with a mass of amu. *
*Means atomic mass here, not nuclear mass!
SOLUTION
= m(H atoms + n’s) – m(atom) [prior slide]
Calculate the mass defect as the difference between the mass of one C-16 atom and the sum of the masses of 6 hydrogen atoms and 10 neutrons.
Calculate the nuclear binding energy by converting the mass defect (in amu) into MeV.
(Use 1 amu = MeV.)*
*Tro’s solution disappoints me! I want you to be able to use E = mc2! Otherwise there’s little “learning value” IMO. So:
mc2 (in J)
m (in kg)
converts to MeV
© 2011 Pearson Education, Inc.

45. EXAMPLE 19.7 Mass Defect and Nuclear Binding Energy
Calculate the mass defect and nuclear binding energy per nucleon (in MeV) for C-16, a radioactive isotope of carbon with a mass of amu.
SOLUTION
Calculate the mass defect as the difference between the mass of one C-16 atom and the sum of the masses of 6 hydrogen atoms and 10 neutrons.
Calculate the nuclear binding energy by converting the mass defect (in amu) into MeV.
(Use 1 amu = MeV.)*
Determine the nuclear binding energy per nucleon by dividing by the number of nucleons in the nucleus.
© 2011 Pearson Education, Inc.

46. To calculate Mass Defect From “mass data”…(Mines method in some answer keys)
Let mass defect be abbreviated Dmmd
Dmmd = mass of free nucleons – mass of nucleus
= m(p’s + n’s) – m(nucleus)
 m(p’s + n’s) – [m(atom) – m(e’s)]
I used to find this way easier to “follow” (students tend to find it odd that you use the mass of an H atom instead of the mass of a proton), but I’ve recently switched in lecture to Tro’s way (despite what I wrote in some past answer keys).

47. Binding Energy per nucleon indicates the thermodynamic stability of a nucleus
Although we typically think that being “low in (potential) energy” is associated with more stability, that isn’t quite so for nuclei.
The different number of nucleons in different nuclei make Eb an “unfair” comparison.
Dividing Eb by the number of nucleons (Eb per nucleon) allows for a fair comparison!
It’s like comparing the price of two boxes of cereal, one with 11 oz and one with 16 oz. If you find the “price per ounce” you can tell which is the better buy!

48. 6 He-5 nuclei
3 Be-10 nuclei
2 N-15 nuclei
1 Mg-30 nucleus
If separated nucleons had zero potential energy, the nuclides (bound nucleons) would have negative potential energy (lower than zero).
Ppt 06 Nuclear Chemistry

49. NOTE: I’m assuming zero for potential energy of separated nucleons.
Ppt 06 Nuclear Chemistry

50. Does it continue this way if we consider combining larger amounts of nucleons? Say, six times more (i.e., 240)?

51. Ppt 06 Nuclear Chemistry

52. Figure 18.9 The Binding Energy per Nucleon as a Function of Mass Number
Ppt 06 Nuclear Chemistry

53. Figure 18.10 Both Fission and Fusion CAN Produce More Stable Nuclides and are thus Exothermic
Spontaneous IF nuclide is very large;
(fusion of large nuclides would be endothermic!!)
Spontaneous IF nuclide is small. (fission of small nuclides would be endothermic!!)
Ppt 06 Nuclear Chemistry

54. Figure Fission
Ppt 06 Nuclear Chemistry

55. Figure 18.12 Fission Process in which each Event Produces Two Neutrons
Ppt 06 Nuclear Chemistry

56. Figure 18.13 Result of Too Small a Mass of Fissionable Material
Ppt 06 Nuclear Chemistry