nuclear masses and binding energy - oregon state u ?· nuclear masses • nuclear masses and...

Download Nuclear Masses and Binding Energy - Oregon State U ?· Nuclear Masses • Nuclear masses and atomic…

Post on 17-Sep-2018

212 views

Category:

Documents

0 download

Embed Size (px)

TRANSCRIPT

  • Nuclear Masses and Binding Energy Lesson 3

  • Nuclear Masses

    Nuclear masses and atomic masses

    mnuclc2 = Matomicc

    2 ! [Zmelectronc2 + Belectron (Z)]

    Belectron (Z) =15.73Z7 / 3eV

    Because Belectron(Z)is so small, it is neglected in most situations.

  • Mass Changes in Beta Decay

    - decay

    14C!14N + "# + $ eEnergy = [(m(14C) + 6melectron ) # (m(

    14N) + 6melectron ) #m("#)]c 2

    Energy = [M(14C) #M(14N)]c 2

    + decay

    64Cu!64Ni" + # + + $ eEnergy = [(m(64Cu) + 29melectron ) " (m(

    64Ni) + 28melectron ) "melectron "m(#+)]c 2

    Energy = [M(64Cu) "M(64Ni) " 2melectron ]c2

  • Mass Changes in Beta Decay

    EC decay

    207Bi+ + e!"207Pb+ # eEnergy = [(m(207Bi) + 83melectron ) ! (m(

    207Pb) + 82melectron )]c2

    Energy = [M(207Bi) !M(207Pb)]c 2

    Conclusion: All calculations can be done with atomic masses

  • Nomenclature

    Sign convention: Q=(massesreactants-massesproducts)c2

    Q has the opposite sign as H Q=+ exothermic Q=- endothermic

  • 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 () M(A,Z)-A See appendix of book for mass tables

  • 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

  • Binding energy per nucleon

  • Separation energy systematics

  • Abundances

  • Semi-empirical mass equation

    Btot (A,Z) = avA ! asA2 / 3 ! ac

    Z 2

    A1/ 3! aa

    (A ! 2Z)2

    A "

    Terms

    Volume avA Surface -asA2/3 Coulomb -acZ2/A1/3

    ECoulomb =35Z 2e2

    RR =1.2A1/ 3

    ECoulomb = 0.72Z 2

    A1/ 3

  • Asymmetry term

    !aa(A ! 2Z)2

    A= !aa

    (N ! Z)2

    A

    To make AZ from Z=N=A/2, need to move q protons q in energy, thus the work involved is q2=(N-Z)2/4. If we add that =1/A, we are done.

  • Pairing term A Z N # stable e e e 201

    o e o 69

    o o e 61

    e o o 4

    ! = +11A"1/ 2ee! = 0oe,eo! = "11A"1/ 2oo

  • Relative importance of terms

  • Values of coefficients

    av =15.56MeVas =17.23MeVac = 0.7MeVaa = 23.285MeV

  • Modern version of semi-empirical mass equation (Myers

    and Swiatecki)

    Btot (A,Z) = c1A 1! kN ! ZA

    " # $

    % & ' 2(

    ) *

    +

    , - ! c2A

    2 / 3 1! k N ! ZA

    " # $

    % & ' 2(

    ) *

    +

    , - ! c3

    Z 2

    A1/ 3+ c4

    Z 2

    A+ .

    c1 =15.677MeVc2 =18.56MeVc3 = 0.717MeVc4 =1.211MeVk =1.79! =11A"1/ 2

  • Mass parabolas and Valley of beta stability

    M (Z,A) = Z M (1H )c2 + (A Z )M (n)c2 Btot (Z,A)

    Btot (Z,A) = avA asA2/3 ac

    Z 2

    A1/3 aa

    (A 2Z )2

    A

    aa(A 2Z )2

    A= aa

    A2 4AZ + 4Z 2

    A= aa A 4Z +

    4Z 2

    A

    M = A M (n)c2 av +asA1/3

    + aa

    + Z M (1H )c2 M (n)c2 4aa + Z

    2 acA1/3

    + 4aaA

    This is the equation of a parabola, a+bZ+cZ2

  • Where is the minimum of the parabolas?

    !M!Z

    " # $

    % & ' A

    = 0 = b + 2cZA

    ZA =(b2c

    = M(1H) (M(n) ( 4aa

    2 acA1/ 3

    + 4aaA

    " # $

    % & '

    ZAA

    ) 12

    8180 + 0.6A2 / 3

  • Valley of Beta Stability

Recommended

View more >