Chemical Engineering 412

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Solomon Rice
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1 Chemical Engineering 412 Introductory Nuclear Engineering Lecture 5 Nuclear Energetics 1

2 Spiritual Thought 2 I add my voice to these wise and inspired brethren and say to you that one of the most important things you can do as priesthood leaders is to immerse yourselves in the scriptures. Search them diligently. Feast upon the words of Christ. Learn the doctrine. Master the principles that are found therein. There are few other efforts that will bring greater dividends to your calling. There are few other ways to gain greater inspiration as you serve. But that alone, as valuable as it is, is not enough. You must also bend your efforts and your activities to stimulating meaningful scripture study among the members of the Church. President Ezra Taft Benson

3 Big Picture 3 Introduced subatomic particles Explored Quantum Mechanics and impacts Defined Nucleus Made of protons and neutrons Some mass is converted to energy This holds nucleus together (binding energy) Nuclear Energetics Q Value

4 Nuclear Energetics Study of mass/energy changes in nucleus Reactions Stability Mass Defect Binding Energy/Separation Energy Foundational to understanding radioactive decay

Binding Energy Binding energy is the energy required to disassemble a whole into its separate parts Measure of stability 4 He is locally stable

5 Binding Energy Binding energy is the energy required to disassemble a whole into its separate parts Measure of stability 4 He is locally stable Max stability is A ( 56 Fe single most stable) Chart represents binding energy per nucleon (large nuclei have large total binding energy)

6 Chemistry Reaction Terminology Exothermic reactions Generate heat Negative heat of reaction Endothermic reactions Consume heat Positive heat of reaction Nuclear chemistry Not thermal, because Exothermic = Exoergic it s not traditional heat Positive Q-values transfer; atomic scale Endothermic = Endoergic with wave emission and kinetic energy Negative Q-values

7 Mass Defect/Binding Energy E=mc > ΔE = Δmc 2 Even for macroscopic effects, but tiny 10-8 % for formation of CO 2 molecule Δm = mass defect m = nuclear, M = atomic How to define M? M ZZ AA XX = mm ZZ AA XX + ZZmm ee BBBB ZZZZ cc 2 How to define Δm? mm = BBBB cc 2 = ZZmm pp + AA ZZ mm nn mm ZZ AA XX Binding Energy BBBB ZZ AA XX = ZZZZ 1 1 HH + AA ZZ mm nn MM ZZ AA XX cc 2 Separation Energy SSSS AA ZZ XX = BBBB AA ZZ XX BBBB AA 1 ZZXX Nuclear values Put in terms of atomic values

8 Reactions Nuclear reactions 1 (decay), 2, or 3 (rare) particles Sometimes written like Chemical reactions: 2 4 HHHH NN 17 8 OO HH For single reactions this is common For binary nuclear reactions a more compact nomenclature is typical, 14 7NN αα, pp 17 8 OO Lightest nuclides in parentheses Note: this is the first nuclear reaction detected, by Rutherford

9 Nuclear Conservation Chemical reactions conserve enthalpy, elements, and total mass. Nuclear reactions Don t conserve any of these Do conserve Total energy (mass + kinetic/radiative energy) Nucleons (protons + neutrons) Electrical charge. Note sum of protons and neutrons (nucleons) is conserved. Electrons NOT conserved; charge is.

10 Parallel reactions Chemistry multiple possible reactions Large quantities of reactants Branching ratios, equilibrium, etc. Nuclear single nuclei at a time Statistical probabilities for various outcomes Example, neutron interacting with sulfur 16 SS nn, nn 16 SS α% 16 SS nn, nn 16 SS β% where β=0% if E n <XX SS nn, pp SS nn, γ PP δ% where δ =0% if E n <YY 33 SS (1-α-β-δ)%

11 Q-value QQ = KKEE pppppppppppppppp KKEE rrrrrrrrrrrrrrrrrr QQ = rrrrrrrrrrrrrrrr rrrrrrrr mmmmmmmm pppppppppppppp rrrrrrrr mmmmmmmm cc2 note that this is reactants products, the opposite convention as is used in chemistry 3 special challenges: Charge balancing Reactions with changes in the number of protons Excited-state rather than ground-state isotopes The next several slides cover these

12 Simple Q-value Calculations No: proton-neutron transformations (ββ emissions), excited states, other special cases For example, the reaction of lithium with deuterium 6 3LLLL 2 1 HH, 4 2 HHHH 4 2 HHHH QQ = MM 6 3 LLLL + MM2 1HH MM4 2HHHH MM4 2HHHH = = = uu MMMMMM = MMMMMM uu

13 Be sure to conserve charge Often, reactions notations don t include electrons 16 8OO nn, pp 16 7 NN or, more explicitly, 16 8 OO nn, pp 16 7 NN ee can be represented as 16 8OO nn, 1 1 HH 16 7 NN So, to conserve charge, non-ionized particles used. QQ cc 2 = MM 16 8OO + mm nn MM 16 7 NN MM 1 1 HH = = /cc 2 u = MeV Note: Q-values commonly involve mass differences in the 3 rd to 4 th decimal point.

14 When Z changes Changes in the proton number (Z) require special step Include neutrino or anti-neutrino Sometimes a positron (antimatter electron with positive charge). pp pp, 0 +1 ee νν dd or 1 1 pp pp 2 1 dd ee + νν Drives deuterium formation in the sun Q-value is computed by adding two electrons to each side Form two hydrogens on the left Form deuterium and an extra electron on the right 1 1 HH 1 1 HH, νν 0 +1 ee 0 1 ee 2 1 HH QQ cc 2 = 2MM 1 1 HH MM 2 1 HH 2mm ee mm νν =0.420 MeV mm νν is unknown but known to be very small (negligible) compared to mm ee

15 Excited Nuclei Some reactions produce stable (long decay time) excited-state nuclei Excited states are designated by an asterisk For these, the energy difference between the ground and excited states must be known, (E * ) 10 5BB(nn, αα) 7 3 LLii QQ cc 2 = mm nn + MM 10 5 BB MM 7 3 LLLL MM 4 2 HHHH = mm nn + MM 10 5 BB MM 7 3 LLLL MM 4 2 HHHH EE mm nn + MM 10 5 BB MM 7 3 LLLL MM 4 2 HHHH QQ 7 3 LLii 7 3 LLLL = mm nn + MM 10 5 BB MM 7 3 LLLL MM 4 2 HHHH 0.48MMMMMM

16 Nuclear Fusion vs. Nuclear Fission Nuclear Fusion: 1 2 HH HH 2 4 HHHH Energy released? MeV Nuclear Fission UU PPPP SSSS + nn Energy released? ~210 MeV Why fusion?

17 Some notes Text provides isotopic masses for most isotopes. The official masses (in the US) are updated by NIST at

Strand J. Atomic Structure. Unit 2. Radioactivity. Text

Strand J. Atomic Structure. Unit 2. Radioactivity. Text Strand J. Atomic Structure Unit 2. Radioactivity Contents Page Unstable Nuclei 2 Alpha, Beta and Gamma Radiation 5 Balancing Equations for Radioactive Decay 10 Half Life 12 J.2.1. Unstable Nuclei. The