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Nuclear Masses and Binding Energy

Nuclear Masses and Binding Energy. Lesson 3. Nuclear Masses. Nuclear masses and atomic masses. Because B electron (Z)is so small, it is neglected in most situations. Mass Changes in Beta Decay. β- decay. β+ decay. Mass Changes in Beta Decay. EC decay.

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Nuclear Masses and Binding Energy

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  1. Nuclear Masses and Binding Energy Lesson 3

  2. Nuclear Masses • Nuclear masses and atomic masses Because Belectron(Z)is so small, it is neglected in most situations.

  3. Mass Changes in Beta Decay • β- decay • β+ decay

  4. Mass Changes in Beta Decay • EC decay Conclusion: All calculations can be done with atomic masses

  5. Nomenclature • Sign convention: Q=(massesreactants-massesproducts)c2 Q has the opposite sign as ΔH Q=+ exothermic Q=- endothermic

  6. Nomenclature • Total binding energy, Btot(A,Z) Btot(A,Z)=[Z(M(1H))+(A-Z)M(n)-M(A,Z)]c2 • Binding energy per nucleon Bave(A,Z)= Btot(A,Z)/A • Mass excess (Δ) M(A,Z)-A See appendix of book for mass tables

  7. Nomenclature • Packing fraction (M-A)/A • Separation energy, S Sn=[M(A-1,Z)+M(n)-M(A,Z)]c2 Sp=[M(A-1,Z-1)+M(1H)-M(A,Z)]c2

  8. Binding energy per nucleon

  9. Separation energy systematics

  10. Abundances

  11. Semi-empirical mass equation Terms • Volume avA • Surface -asA2/3 • Coulomb -acZ2/A1/3

  12. Asymmetry term To make AZ from Z=N=A/2, need to move q protons qΔ in energy, thus the work involved is q2Δ=(N-Z)2Δ/4. If we add that Δ=1/A, we are done.

  13. Pairing term

  14. Relative importance of terms

  15. Values of coefficients

  16. Modern version of semi-empirical mass equation (Myers and Swiatecki)

  17. Mass parabolas and Valley of beta stability This is the equation of a parabola, a+bZ+cZ2

  18. Where is the minimum of the parabolas?

  19. Valley of Beta Stability

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