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Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 1 Nuclear Binding Energy B tot (A,Z) = [ Zm H + Nm n - m(A,Z) ] c 2 B m.

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Presentation on theme: "Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 1 Nuclear Binding Energy B tot (A,Z) = [ Zm H + Nm n - m(A,Z) ] c 2 B m."— Presentation transcript:

1 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 1 Nuclear Binding Energy B tot (A,Z) = [ Zm H + Nm n - m(A,Z) ] c 2 B m HW 9 B ave (A,Z) = B tot (A,Z) / A HW 9 Krane 3.9 HW 10 Atomic masses from: HW 10 Krane 3.12 http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=ascii&isotype=all Separation Energy Neutron separation energy: (BE of last neutron) S n = [ m(A-1,Z) + m n – m(A,Z) ] c 2 HW 11 = B tot (A,Z) - B tot (A-1,Z) HW 11 Show that HW 12 HW 12 Similarly, find S p and S. HW 13HW 14 HW 13 Krane 3.13HW 14 Krane 3.14 Magic numbers

2 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 2 Nuclear Binding Energy Magic numbers

3 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 3 Nuclear Binding Energy In general X Y + a S a (X) = (m a + m Y –m X ) c 2 = B X –B Y –B a The energy needed to remove a nucleon from a nucleus ~ 8 MeV average binding energy per nucleon (Exceptions???). Mass spectroscopy B. Nuclear reactions S. Nuclear reactions Q-value

4 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 4 Nuclear Binding Energy ~200 MeV Fission Fusion Coulomb effectSurface effect HWc 4 Think of a computer program to reproduce this graph.

5 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 5 Nuclear Binding Energy HW 15 A typical research reactor has power on the order of 10 MW. a) Estimate the number of 235 U fission events that occur in the reactor per second. b) Estimate the fuel-burning rate in g/s.

6 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 6 Nuclear Binding Energy Is the nucleon bounded equally to every other nucleon? C this presumed binding energy. B tot = C(A-1) A ½ B ave = ½ C(A-1) Linear ??!!! Directly proportional ??!!! Clearly wrong … ! wrong assumption finite range of strong force, and force saturation.

7 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 7 Nuclear Binding Energy Lead isotopes Z = 82 For constant Z S n (even N) > S n (odd N) For constant N S p (even Z) > S p (odd Z) Remember HW 14 (Krane 3.14). 208 Pb (doubly magic) can then easily remove the extra neutron in 209 Pb. Neutron Number N Neutron Separation Energy S n (MeV) 208 Pb

8 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 8 Nuclear Binding Energy Extra Binding between pairs of identical nucleons in the same state (Pauli … !) Stability (e.g. -particle, N=2, Z=2). S n (A, Z, even N) – S n (A-1, Z, N-1) This is the neutron pairing energy. even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei.

9 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 9 Abundance Systematics Odd NEven NTotal Odd Z Even Z Total Compare: even Z to odd Z. even N to odd N. even A to odd A. even-even to even-odd to odd-even to odd-odd. HWc 1 \

10 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 10 Neutron Excess Odd A Even A Z = N Asymmetry Remember HWc 1.

11 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 11 Neutron Excess Remember HWc 1. Asymmetry

12 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 12 Abundance Systematics

13 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 13 Abundance Systematics NEUTRON NUMBER MASS NUMBER ABUNDANCE NEUTRON CAPTURE CROSS SECTION r s Formation process Abundance

14 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 14

15 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 15 The Semi-empirical Mass Formula von Weizsäcker in 1935. Liquid drop. Shell structure. Main assumptions: 1.Incompressible matter of the nucleus R A. 2.Nuclear force saturates. Binding energy is the sum of terms: 1.Volume term.4. Asymmetry term. 2.Surface term.5. Pairing term. 3.Coulomb term.6. Closed shell term. …..

16 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 16 The Semi-empirical Mass Formula Volume Term B v = + a v A B v volume R 3 A B v / A is a constant i.e. number of neighbors of each nucleon is independent of the overall size of the nucleus. The other terms are corrections to this term. constant

17 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 17 The Semi-empirical Mass Formula Surface Term B s = - a s A Binding energy of inner nucleons is higher than that at the surface. Light nuclei contain larger number (per total) at the surface. At the surface there are: Nucleons. Remember t / R A -1/3

18 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 18 The Semi-empirical Mass Formula Coulomb Term B C = - a C Z(Z-1) / A Charge density Z / R 3. W 2 R 5. Why ??? W Z 2 / R. Actually: W Z(Z-1) / R. B C / A = - a C Z(Z-1) / A 4/3 Remember HW 8 … ?!

19 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 19 The Semi-empirical Mass Formula

20 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 20 The Semi-empirical Mass Formula Quiz 1 so far From our information so far we can write: For A = 125, what value of Z makes M(A,Z) a minimum? Is this reasonable…??? So …..!!!!


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