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CHEM 312: Lecture 2Nuclear Properties
• Readings:§ Modern Nuclear Chemistry:
Chapter 2 Nuclear Properties§ Nuclear and Radiochemistry:
Nuclear Properties• Systematic examination of measurable data to determine nuclear
properties§ masses § matter distributions
• Size, shape, mass, and relative stability of nuclei follow patterns that can be understood and interpreted with models § average size and stability of a nucleus described by average
nucleon binding in a macroscopic model§ detailed energy levels and decay properties evaluated with a
quantum mechanical or microscopic modelSimple example: Number of stable nuclei based on neutron and proton number
N even odd even oddZ even even odd oddNumber 160 53 49 4
Simple property dictates nucleus behavior. Number of protons and neutron important
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Which are the 4 stable odd-odd nuclei?
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• Evaluation of Mass Excess• Difference between actual mass of nucleus and expected mass
from atomic number§ By definition 12C = 12 amu
à If mass excess negative, then isotope has more binding energy the 12C
• Mass excess==M-A§ M is nuclear mass, A is mass number§ Unit is MeV (energy)
• Electron Capture (EC)§ Electron comes from parent orbital
à Parent can be designated as cation to represent this behavior§ AZ+ + e- A(Z-1) + n + Q§ Q=DAZ – DA(Z-1)§ 207Bi207Pb + n + Q§ Q=D 207Bi – D 207Pb MeV§ Q= -20.0553- -22.4527 MeV=2.3947 MeV
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Q value• Alpha Decay
§ AZ(A-4)(Z-2) + 4He + Q§ 241Am237Np + 4He + Q
à Use mass excess or Q value calculator to determine Q value
§ Q=D241Am-(D 237Np+D4He)§ Q = 52.937-(44.874 + 2.425)§ Q = 5.638 MeV§ Alpha decay energy for
241Am is 5.48 and 5.44 MeV
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Q value determination• For a general reaction
§ Treat Energy (Q) as part of the equationà Solve for Q
Q value calculation examples• Find Q value for the Beta decay of 24Na
§ 24Na24Mg+ +b- + +n Q§ Q= 24Na-24Mg§ M (24Na)-M(24Mg)
à 23.990962782-23.985041699 à 0.005921 amu
* 5.5154 MeV§ From mass excess
à -8.417 - -13.933 à 5.516 MeV
• Q value for the EC of 22Na§ 22Na+ + e- 22Ne + +n Q§ Q= 22Na - 22Ne § M (22Na)-M(22Ne)§ 21.994436425-21.991385113 § 0.003051 amu
à 2.842297 MeV§ From mass excess
à -5.181 - -8.024 à 2.843 MeV
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Terms from Energy• Binding energy
§ Difference between mass of nucleus and constituent nucleonsà Energy released if nucleons formed
nucleus§ Nuclear mass not equal to sum of constituent
nucleonsBtot (A,Z)=[ZM(1H)+(A-Z)M(n)-M(A,Z)]c2
§ average binding energy per nucleon
à Bave(A,Z)= Btot (A,Z)/A
à Some mass converted into energy that binds nucleus
à Measures relative stability• Binding Energy of an even-A nucleus is generally higher than adjacent odd-A
nuclei• Exothermic fusion of H atoms to form He from very large binding energy of 4He• Energy released from fission of the heaviest nuclei is large
§ Nuclei near the middle of the periodic table have higher binding energies per nucleon
• Maximum in the nuclear stability curve in the iron-nickel region (A~56 through 59)§ Responsible for the abnormally high natural abundances of these elements§ Elements up to Fe formed in stellar fusion
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Mass Based Energetics Calculations
• Why does 235U undergo neutron induced fission for thermal energies while 238U doesn’t?
• Generalized energy equation§ AZ + n A+1Z + Q
• For 235U§ Q=(40.914+8.071)-42.441§ Q=6.544 MeV
• For 238U§ Q=(47.304+8.071)-50.569§ Q=4.806 MeV
• For 233U§ Q=(36.913+8.071)-38.141§ Q=6.843 MeV
• Fission requires around 5-6 MeV§ Does 233U from thermal
neutron?
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Binding-Energy Calculation: Development of simple nuclear model
• Volume of nuclei are nearly proportional to number of nucleons present§ Nuclear matter is incompressible§ Basis of equation for nuclear radius
• Total binding energies of nuclei are nearly proportional to numbers of nucleons present§ saturation character
à Nucleon in a nucleus can apparently interact with only a small number of other nucleons
à Those nucleons on the surface will have different interactions •Basis of liquid-drop model of nucleus
§ Considers number of neutrons and protons in nucleus and how they may arrange
§ Developed from mass dataà http://en.wikipedia.org/wiki/Semi-empirical_mass_formula
§ Interactions of nuclear quadrupole moments with the electric fields produced by electrons in atoms and molecules give rise to abnormal hyperfine splittings in spectra
• Methods of measurement: optical spectroscopy, microwave spectroscopy, nuclear resonance absorption, and modified molecular-beam techniques
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Parity
• System wave function sign change if sign of the space coordinates change§ system has odd or even parity
• Parity is conserved• even+odd=odd, even+even=even, odd+odd=odd
§ allowed transitions in atoms occur only between an atomic state of even and one of odd parity
• Parity is connected with the angular-momentum quantum number l
§ states with even l have even parity§ states with odd l have odd parity
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Topic review
• Understand role of nuclear mass in reactions§ Use mass defect to determine energetics§ Binding energies, mass parabola, models
• Determine Q values• How are nuclear shapes described and
determined§ Potentials§ Nucleon distribution
• Quantum mechanical terms§ Used in description of nucleus
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Study Questions
• What do binding energetics predict about abundance and energy release?
• Determine and compare the alpha decay Q values for 2 even and 2 odd Np isotopes. Compare to a similar set of Pu isotopes.
• What are some descriptions of nuclear shape?• Construct a mass parabola for A=117 and A=50• What is the density of nuclear material?• Describe nuclear spin, parity, and magnetic