chemical engineering 412mjm82/che412/winter2019/lecture... · 2019. 1. 17. · chemical engineering...
TRANSCRIPT
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Chemical Engineering 412
Introductory Nuclear Engineering
Lecture 4Nuclear Energetics
Radiation I
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Spiritual Thought“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
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Roadmap3
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Objectives
• Understand Q and be able to calculate it• Set up, complete and evaluate nuclear
reaction equations• Understand nuclear decay types:
– Name– Properties– Mathematical Descriptions– Equations– Caveats– Q Values
• Decay Charts (KNOW HOW TO USE!)
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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– 1632𝑆𝑆 𝑛𝑛,𝑛𝑛 16
32𝑆𝑆 α%– 1632𝑆𝑆 𝑛𝑛,𝑛𝑛′ 1632𝑆𝑆∗ β% where β=0% if En<XX
– 1632𝑆𝑆 𝑛𝑛, 𝑝𝑝 15
32𝑃𝑃 δ% where δ =0% if En<YY– 1632𝑆𝑆 𝑛𝑛, γ 16
33𝑆𝑆 (1-α-β-δ)%
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Q-value
𝑄𝑄 = 𝐾𝐾𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − 𝐾𝐾𝐸𝐸𝑝𝑝𝑟𝑟𝑝𝑝𝑝𝑝𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟𝑄𝑄𝑐𝑐2
= 𝑟𝑟𝑟𝑟𝑟𝑟𝑐𝑐𝑟𝑟𝑟𝑟𝑛𝑛𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑚𝑚𝑟𝑟𝑟𝑟𝑟𝑟 − 𝑝𝑝𝑟𝑟𝑝𝑝𝑝𝑝𝑝𝑝𝑐𝑐𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑚𝑚𝑟𝑟𝑟𝑟𝑟𝑟
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
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Simple Q-value Calculations
• No:• proton-neutron transformations (𝛽𝛽 emissions),• excited states,• other special cases
• For example, the reaction of lithium with deuterium
36𝐿𝐿𝐿𝐿 1
2𝐻𝐻, 24𝐻𝐻𝑟𝑟 24𝐻𝐻𝑟𝑟
𝑄𝑄 = 𝑀𝑀36𝐿𝐿𝐿𝐿 + 𝑀𝑀
12𝐻𝐻 −𝑀𝑀
24𝐻𝐻𝑟𝑟 − 𝑀𝑀
24𝐻𝐻𝑟𝑟
= 6.015122 + 2.014101 − 2 4.002603 =
= 0.02402 𝑝𝑝 931.5𝑀𝑀𝑟𝑟𝑀𝑀𝑝𝑝
= 22.37 𝑀𝑀𝑟𝑟𝑀𝑀
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Be sure to conserve charge
• Often, reactions notations don’t include electrons– 8
16𝑂𝑂 𝑛𝑛,𝑝𝑝 716𝑁𝑁 or, more explicitly, 8
16𝑂𝑂 𝑛𝑛, 𝑝𝑝 716𝑁𝑁 + −1
0𝑟𝑟
can be represented as816𝑂𝑂 𝑛𝑛, 11𝐻𝐻 7
16𝑁𝑁
• So, to conserve charge, non-ionized particles used.
𝑄𝑄𝑐𝑐2
= 𝑀𝑀 816𝑂𝑂 + 𝑚𝑚𝑟𝑟 −𝑀𝑀 7
16𝑁𝑁 − 𝑀𝑀 11𝐻𝐻
= 15.994915 + 1.0086649156 − 16.006101− 1.007825 = −0.01035/𝑐𝑐2 u = −9.637 MeV
Note: Q-values commonly involve mass differences in the 3rd to 4th decimal point.
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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, +10𝑟𝑟 𝜈𝜈 𝑝𝑝 or 11𝑝𝑝 + 11𝑝𝑝 → 1
2𝑝𝑝 + +10𝑟𝑟 + 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
11𝐻𝐻 1
1𝐻𝐻, 𝜈𝜈+10𝑟𝑟−10𝑟𝑟 12𝐻𝐻
𝑄𝑄𝑐𝑐2
= 2𝑀𝑀 11𝐻𝐻 −𝑀𝑀 1
2𝐻𝐻 − 2𝑚𝑚𝑟𝑟 −𝑚𝑚𝜈𝜈
𝑚𝑚𝜈𝜈 is unknown but known to be very small (negligible) compared to 𝑚𝑚𝑟𝑟
=0.420 MeV
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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*)
510𝐵𝐵(𝑛𝑛,𝛼𝛼)37𝐿𝐿𝐿𝐿∗
𝑄𝑄𝑐𝑐2
= 𝑚𝑚𝑟𝑟 + 𝑀𝑀 510𝐵𝐵 −𝑀𝑀 3
7𝐿𝐿𝐿𝐿∗ − 𝑀𝑀 24𝐻𝐻𝑟𝑟
= 𝑚𝑚𝑟𝑟 + 𝑀𝑀 510𝐵𝐵 −𝑀𝑀 3
7𝐿𝐿𝐿𝐿 − 𝑀𝑀 24𝐻𝐻𝑟𝑟 − 𝐸𝐸∗
𝑚𝑚𝑟𝑟 + 𝑀𝑀 510𝐵𝐵 −𝑀𝑀 3
7𝐿𝐿𝐿𝐿 − 𝑀𝑀 24𝐻𝐻𝑟𝑟 − 𝑄𝑄
37𝐿𝐿𝐿𝐿∗→3
7𝐿𝐿𝐿𝐿= 𝑚𝑚𝑟𝑟 + 𝑀𝑀 5
10𝐵𝐵 −𝑀𝑀 37𝐿𝐿𝐿𝐿 − 𝑀𝑀 2
4𝐻𝐻𝑟𝑟 − 0.48𝑀𝑀𝑟𝑟𝑀𝑀
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Some notes
• Text provides isotopic masses for most isotopes.
• The official masses (in the US) are updated by NIST at http://www.nist.gov/pml/data/comp.cfm.
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Decay Conservations
• Charge• Nucleon Number• Mass/Energy (Total Energy)• Linear Momentum• Angular Momentum
• Classical behavior if liberated energy is much less than rest mass energy
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Decay Mechanisms
• Alpha (𝜶𝜶)• Beta (+/-) (𝜷𝜷+,𝜷𝜷−)• Gamma (𝜸𝜸)• Electron capture (EC)• Proton (P), Deuteron (D) and Triton (T)• Neutron (N)• Internal conversion (IC)• Spontaneous fission (SF)
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Chart of the Nuclides
Z
N
Z=N
StableEC+β+
β-αPN
SFUnknownp drip line
n drip line
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Energy Diagram
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Alpha Decay
• Emission of a 4He nucleus – a (2+) charged particle.• Reduces Z by 2, N by 2, and A by 4. • Common in heavy (> Pb, 82) nuclides, otherwise rare.• Alpha particles have discrete energies (quantized)• Very highly energetic (LARGE)
– rapidly absorbed by other material – WHY?– generally stopped by piece of paper or outer layers of skin.
• Minor source of ionizing external radiation exposure.• Significant exposure if ingested/inhaled.
– Direct damage to lungs and alveoli
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Alpha Particles Tunnel
𝜓𝜓𝐼𝐼(𝑥𝑥) = 𝐴𝐴𝐿𝐿ei𝑘𝑘𝑘𝑘 + 𝐴𝐴𝑟𝑟e−i𝑘𝑘𝑘𝑘
𝜓𝜓II 𝑥𝑥 = 𝐵𝐵e−𝑘𝑘𝑥𝑥 − 𝐵𝐵′e𝑘𝑘𝑥𝑥
𝜓𝜓III(𝑥𝑥) = 𝐴𝐴𝑟𝑟ei𝑘𝑘𝑘𝑘
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Alpha Decay
[ ] α4222
2 +→−−
− DP AZ
AZ
• Two approximations;• Neglect daughter electron Binding Energy (1st Eq.)• Neglect He electron Binding energy (2nd Eq.)
• 4He atom differs from an α particle?• two electrons – the α particle has a net 2+ charge.
( ) ( ) ( )[ ]( ) ( ) ( )[ ]( ) ( ) ( )[ ]HemDMPM
mmDMPM
mDMPMcQ
AZ
AZ
eAZ
AZ
AZ
AZ
42
42
42
42
42
2422
2+−≅
++−≅
+−=
−−
−−
−−−
α
αα
HeDAZ
42
22 +→ −
−
First look at Q for mass (mass difference)
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Alpha Decay
[ ] HeDDP AZ
AZ
AZ
42
22
42
222 +→+→ −
−
−−− α
+
≅
+
=
+
≅
+
=
+=⇒
=
+=+=
α
αα
α
αα
αα
ααα
αααα
αα
αααα
AAAQ
MMMQE
AAAQ
MMMQE
MMvMQ
vMvM
vMvMEEQ
DDD
D
D
D
D
D
DD
DDD
121
21
21
2
22
Energies of alpha and daughter particles are
fixed, and alpha particle energy is uniquely
associated with isotope.
Now look at Q for energy (kinetic energy)
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Alpha Decay Example
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Beta Decay (I)
• β + (positron) decay– occurs in proton-rich nuclei.– proton transforms to a neutron
• positron and neutrino emitted• reduces Z and increases N by 1 without changing A.
– requires parent particle to be at least 2 Me heavier than daughter.
• β - (electron) decay – occurs in neutron-rich nuclei– neutron transforms to a proton
• electron and anti-neutrino emitted• increases Z and decreases N by 1 without changing A.
– requires parent particle to be at least n-p+-e- heavier than daughter.
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Experimental β Decay Spectrum
Source: G. J. Neary, Roy. Phys. Soc. (London), A175, 71 (1940).
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Beta Decay (II)
• Continuous energy spectrum (not discrete) – shares its energy with the neutrino.
• Positron/electrons have a well-defined upper energy limit– with an average energy of about 0.3 Emax.
• High-energy ionizing radiation– penetrates outer skin – Doesn’t penetrate plywood or most construction materials.
• Responsible for both external and internal exposures.
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β - Decay
β - decay
[ ] eA
ZAZ eDP ν++→ −
+
+011
• specific particle energies cannot be determined• continuous range of energies with a defined maximum
value.
( ) ( )[ ]( ) ( )[ ]{ }( ) ( )
( ) ( )
−−−
−
−
−
−
≅
+
=
−−=
−=
++−−≅
++−=
+
+
+
++
βββ
β
νβ
νββ
QQMM
ME
cEDMPM
c
QDMPM
mmmDMPM
mmDMPMc
Q
eD
D
AZ
AZ
AZ
AZ
eA
ZAZ
AZ
AZ
e
e
max,
2
*
12
1
1
12
ground-state daughter
excited-state daughter
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β - Decay Example: Chlorine-38
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β + or Positron Decay
β+ decay
[ ] eA
ZAZ eDP ν++→ +
−
−011
The parent mass must exceed the daughter mass by at least 2 me for this to spontaneously proceed.
( ) ( ) ( )[ ]( ) ( )[ ]{ }( ) ( )
( ) ( )++
+
+
−
≅
−−−=
−−=
+++−≅
++−=
−
−
−
+−
−
ββ
β
νβ
νβ
QEcEmDMPM
c
QmDMPM
mmmDMPM
memDMPMc
Q
eA
ZAZ
eA
ZAZ
eA
ZAZ
AZ
AZ
e
e
max,
2
*
12
1
1
0112
2
2 ground-state daughter
excited-state daughter
+β
eν
+β
p
n
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Positron/β + Decay: Sodium-22
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Electron Capture
• Conversion of proton to neutron & neutrino by capture of inner shell electron.
• Similar to (competes with) β+:– Z decreases and N increases, no change in A
• Differs from β+:– Consumes an electron– Also γ-ray emission and/or Auger electrons
• K-capture (innermost, K electron shell) • No charged particle must be emitted - unique• Gamma rays – excited state decay
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Electron Capture
eA
ZAZ DP ν+→ −
*1
Similar to β+ decay but less energy constrained since it involves a locally bound electron. Daughter must be just
slightly lighter than parent to proceed.
( ) ( )[ ]( ) ( )
( ) ( ) 2
*
12
1
*12
cEDMPM
cQ
DMPM
mDMPMc
Q
AZ
AZ
EC
AZ
AZ
AZ
AZ
ECe
−−=
−≅
+−=
−
−
− ν
ground-state daughter
excited-state daughter
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Electron Capture: Beryllium-7
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Gamma Emission
• Results from energy level rearrangement of nuclides
• Does not change Z, N, or A• Exhibits discrete energy levels (quantized)
– quantized energy states in nucleus.• Low energy compared to α or β+/-
– Not an ion, thus not easily absorbed– penetrates deeply in skin, concrete, etc.– Stopped by thick lead
• Major source of external radiation exposure.
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Gamma emission
No change in Z, N, or A. Energy determined by nuclear states.
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Neutron Decay
• Some drip line isotopes emit a neutron– Daughter has one less nucleon– Daughter generally in an excited state.
• Excited state generally decays via gamma emission.
• Critical to reactor control – “Delayed neutron” generation– Seconds to minutes– Fission neutron lifetime: “prompt neutron” = 0.1 ms– Delayed neutrons slow the reaction - controllability
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Neutron Decay
nPP AZ
AZ
10
*1 +→ −
• Relatively rare • slow (sometimes minutes)• Makes fission reactions controllable.
( ) ( )[ ]
( ) ( ) 2
**1
*12
cEmPMPM
mPMPMcQ
nA
ZAZ
nA
ZAZ
n
−−−=
+−=
−
−
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Proton Decay
• Proton emission happens at the proton drip line.
• Generally rare and relatively unimportant.
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Proton Decay
( ) ( )[ ]( ) ( )[ ]( ) ( )
( ) ( ) ( ) 2
*11
11
2
*11
*11
*112
cEHMDMPM
mmcEDMPM
mmDMPM
mDMPMcQ
AZ
AZ
peAZ
AZ
peAZ
AZ
pAZ
AZ
n
−−−≅
+++−=
++−≅
+−=
−−
−−
−−
−−−
[ ] pDP AZ
AZ
11
*11 +→
−−−