Lecture Note
University
Princeton UniversityCourse
PHY 103 | General Physics IPages
5
Academic year
2023
abdulsalam23745
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Semi-emperical B.E or Mass Formula X Atomic mass. B(A,Z) = FZMH + (A-Z) Mn - M(A,z)]c2 H-atom M(A,z) = Z MH + (A-Z) Mn - B(A,Z) C2
Binding energy B (A,Z) can be expressed as 29 a Sym of a number of terms as given below (in terms of A and 2) 1. Volume Energy (Ev) B.E = Const. B.E.A A Volume A V=4TTR3 R=RoAY3 EvaxA : Ev Volume Ev = av A av 1/6 15.7MeV 2. Surface energy (Es) :- X Esd surface Area (4TTR2 = 471 R2A13) a Es as A 2/3 as = 17.8 MeV -ve sign is used since this factor is decreasing B.E of nucleus. 3. Coulomb Energy (Ec):- Coylomb repulsion between protons decreases stability or B.E of nucleus Q=+ZC Ec= -3 1 (ze)2 3 I Q2 R U= 5 4TTE R s 4TTE R Ec = 3 4 TTEw e2 ) RoAY3 z2 spherical 5
Ec = - ac z2 3e2 A 1/3 ac = LOTTER Coulomb energy Coepfi. ac = 0.71 MeV e2 = 1.44 Mev- fm 4TTEo e2= 1.144 Mev-fm in esu (electrostatic unit) 1/6-1 4ITE Older literature Zc2 z(z-1) = 2 pr Ec= - ac z(z-1) Could also be A 1/3 Considered Correct 4 Asymmetry Energy:- Easym or Ea or Esym. (N-2)2 lighter nuclei- Easym = -aasym A Z=N (symmetry) eg. 2He+ N no. of neutrons. 34 2=3 235 N= 4 N=A-Z g2U NYZ Eayym = aasym (A-22)' Region of NT stability A Clagyn = 23.6MeV.
5. Pairing Energy (Ep) :- 30 P and n tend to form in pairs. Even. Z, Even-N nuclei both are in pairs more stable. Even Z- odd+N or odd Z -evon N only one is in pair less stable than above. Odd Z- odd N Both are unpaired i least stable. eg. 4 2He 2P 2n ) 2x6 PP mr mm PP mm even-even nuclei 34°7 3P PP P one P is unpaired. 4n m m pairing Energy Ep= S S = + 9.A 3/4 if Z= Even , N= Even A= even if Z = even, , N= odd 0 A=odd. or Z= odd, N= even -3/4 - ap A if Z= odd, N= odd A=even ap = 33.5MeV
Modern experimental data indicate that a Value of A 1/2 with Ap = +12MeV is nearer to experiments + ap A 1/2, Even -Z- Even N S= odd. Z- - even or Even z-odd N O - - ap A 1/2 odd Z - odd N Adding all the energy terms B(A,Z) = avA- as A 2/3 ac z2 alasym. (A-22) + S A 1/3 A M(A,Z) = ZMH+ (A-z) Mn - C2 I [B(A,Z)] Binding Energy per nucleon (plot) B(A,Z) av A 1/3 as - ac z2 A4/3 - aasym. (A-22) A A2 B(A,2) Ev A A S is not involved A B/A,2 in B V/s 'A plot A A Es/A A Notes peaks at lower A Cannot be explained Ec/A This Plot by liquid drop Model shows better results for A>40
Semi Empirical Binding Energy or Mass Formula
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