Relation Between Packing Fraction & Binding Energy per Nucleon

Relation between Packing X fraction (f) and Binding energy per nycleon (B/A) Xi f= MA-A f= MA A - I A B= [2MH + (A-Z)mn- - MA]C2 B - A Z A MH + (A-Z) A mn- - MA A ] c2 MA = 1+f A = Z MH + Mn - - Zm A Mn - (1+f)].c B A = Z A ( MH- mn) + mn - (1+f)]c2 B.E and B.E. per nucleon tells the stability of the nucleus. page-8 9 8 Graph 7- Fe56 2.6.19 (mpx B/A) 2 f 20 Go

B.E per nucleon is almost Constant (-8Mev) 1 except some lighter nuclei. B Const. BLA A 56 B maximum for Fe = 8.7 Mev A nucleon. For even- - even nuclei 4 He, 8 Be, 12 9,0 116 20 Ne etc. for which A = 4n In-integer), Peaks are observed. Thus these nyclei are most stable than their neighbours. 13 stable isotopes having no. of protons equal to no. of neutrons 4 HH, 2He, 3 Li6, 5B,6C1, 7 w 8 016 10 Ne2 20 1/2 Mg 24 28 32 36 Ca+ 40 14 Si, 165, 18 18Ar, 20 3 only ,H' and 2He are stable having no. of protons > no. of neutrons.