Nuclear Physics and Nuclear Energy
The Nuclear Force.Rohlf Ch. 11. p296
Homework: Ch. 11: 4,5,11,12,42Due Nov. 10
Additional homework: Due Nov. 13
Assume a 238U fissions exactly into two equal nuclei.1. What nuclei are the fission products.2. What is the difference in the total binding energy before and after fission?
Assume this is the energy released by fission.3. Assume the 238U and its fission products are uniformly charged spheres. which repel. What will be their kinetic energy when they fly apart? Compare
with your answer in part. 2 above.
Nuclear Energetics: Liquid Drop ModelRohlf P303
The nucleon-nucleon potential looks similar to the atom-atom potential, but on a different scale.Thus, conglomerations of nucleons should have propertied similar to those of atoms. In particularthey should be rather incompressible, with rather uniform densities within the volume.
Nuclear binding energy = energy required to separate the nucleus into free neutrons and protons.
Eb = Zmpc2 + Nmnc2 M (Z,N )c2
Nuclear Binding Energy
Note: It is nearly constant except for the lightest nuclei.
EbV V R3 =C1A EbS R
2 = C2A2/3 EbC R
1 = C3Z2A1/3
Eb = EbV + EbS + EbC =C1A C2A2/3 C3Z
2A1/3
EbA
=C1 C2A1/3 C3Z
2A4/3
The constants can be obtained by fitting to the empirical data.
Add more terms to binding equation.
Pauli energy: All things being equal, nucleons tend to have an equal number of protons and neutrons due to the Pauli exclusion principle.
EbP (N Z )2 / A. EbP = C4 (A 2Z )
2 / A
Odd-even energy: Nucleon energies are lower when their spins can pair off in the same spatial state. Even-even are more stable than even-odd, which in turn are more stable than odd-odd.
EbEE = EbOO = C5 / A1/2 . EbOE = EbEO = 0.
Weizsaecker semi-empirical binding energy formula:
Eb =15.8A 17.8A2/3 0.711Z2A1/3 23.7(A 2Z )2 / A+11.2A1/2 EE
0 EO,OE
11.2A1/2 OO
MeV
Weizsaecker semi-empirical binding energy formula:
Eb =15.8A 17.8A2/3 0.711Z2A1/3 23.7(A 2Z )2 / A+11.2A1/2 EE
0 EO,OE
11.2A1/2 OO
MeV
, and radioactivity
Lifetime: N = N0et / When t = NN0
= e1 0.368
Half life: NN0
=12= et1/2 / ln 1
2
.693 = t1/2 / t1/2 .693
Alpha Decay 4He has the highest binding energy for a few nucleon system. If EB/A for A-4 + 4He > EB/A for nucleus with A nucleons, it will decay
EB(A 4)+EB(4)>EB(A)EB(4He) = 28MeV
Decay
n p + e +
Lifetime: = 0.9 103 s = 15 min
n p
e-
G
A z,n( ) A z +1,n 1( ) + e +
A z,n( ) A z 1,n +1( ) + e+ +
varies from s to years
- radiation
N N +
E 2(8.5)(115) (7.6)(230) 200MeV
Energetics of Fission Rohlf P319 (brief)
Why dont isotopes with A>200 fission?
d
8.5 MeV
7.6 MeV
neutron capture
increased surface energy
decreased Coulomb energy
d
Spontaneous fission Z2 / A > 46
d ddn
Valley of stability
235U
118Pd
Distribution of fission products.
Fission products are far off the stability curve. Thus there are extra neutrons emitted and numerous beta decays until the products are back in the valley of stability. Some isotopes are very long lived beta emitters.
Exercise: From the A -Z stability curve, estimate the maximum element number Z which can exist, and above which any element would spontaneously and instantly fission.
Spontaneous fission Z2 / A > 46
Pairing energy determines which are fissionable materials
n + 235U
236U
n + 238U
239U
E E
Energetics of Nuclear Fusion in the SunRohlf P316
Begin with 2 separate protons: 2mpc2 = 2(938.27) = 1877.54 MeV
End with deuteron + + + :
= mpc2 +mnc2 EBd( ) +mec2 +mc2 = mdc2 +mec2 + 0
= 938.27 + 939.57 - 2.22( ) + 0.51= 1876.14 MeV
Net energy release: 2mpc2 mdc2 +mec2 +mc2( ) =1.39 MeV.
2 proton-proton fusion reactions: 2 p + p d + + + ( ) release 2(1.39) MeV
2 proton-deuteron fusion reactions: p + d 3He + release 2(5.5) MeV
3He- 3He fusion reaction: 3He+ 3He 4He + p + p releases 12.9 MeV
Total energy release: 26.7 MeV
Net result: 4 protons are converted to 4He + 2+ + 2 + 2
4p 4He + 2+ + 26.7 MeV.
Proton-Proton Cycle
Helium burning.
4He + 4He 8Be 4He + 4He
8Be+ 4He 12C
4He + 12C 16O 4He + 16O 20Ne etc.
Carbon cycle requires higher core temperatures than p-p.
p + 12C 13N + 13N 13C + e+ + e
p + 13C 14N +
p + 14N 15O + 15O 15N + e+ + e
p + 15N 12C + 4He
Nuclear fusion in the sun and stars.
radiation pressure
radiation pressure
radiation pressure
radiation pressure surface: 6x103 K
hydrogen fusion: 10x107 K
helium core
