1 / 22

Nuclear Chemistry and Mass-Energy Relationships

Nuclear Chemistry and Mass-Energy Relationships. Chapter 3. The Nuclear Radius. Nucleus is very small single nucleon ~ 1x10 -15 m or 1 fm fm: femtometer, fermion, fermi nucleus ~ 1 – 10 fm atom ~ 1 Å = 1 x10 -10 m = 100,000 fm All experiments suggest that R = r 0 A 1/3

basil-sanford
Download Presentation

Nuclear Chemistry and Mass-Energy Relationships

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Nuclear Chemistry and Mass-Energy Relationships Chapter 3

  2. The Nuclear Radius Nucleus is very small • single nucleon ~ 1x10-15 m or 1 fm • fm: femtometer, fermion, fermi • nucleus ~ 1 – 10 fm • atom ~ 1 Å = 1 x10-10 m = 100,000 fm All experiments suggest that R = r0A1/3 r0 = constant 1.1-1.6 fm; A-mass number • Measure scattered radiation from an object; λ = h/p • For nuclei with diameter of about 10 fm λ<10 fm, corresponding to p >100 MeV/c

  3. Nuclear Shapes R(θ,φ) = R0(1 + βYλμ(θ,φ)) λ=2; β= 0spherical; β < 0oblate (disk-like) ; β > 0 prolate (football-like) λ=3; triaxial, octupole deformed 3:1 2:1

  4. Nuclear Size and Density The nuclear radius and volume as a function of A. Density profile of three nuclei.

  5. Potential Center of the nucleus n O p Distance R Nucleus with radius R Nuclear Potential

  6. Nuclear Properties Angular momentum and Nuclear Spin • Intrinsic spin +1/2 or -1/2 • Orbital angular momentum l • Total angular momentum of a single nucleon is: j = l+s = l + (+_ 1/2) • The total angular momentum of all nucleons is I = Σj For all even-A nuclei I = 0 or integral For all odd-A nuclei I is half integral Even – even nuclei have I = 0

  7. Magnetic Moment • Any moving electrical charged object gives rise to a magnetic moment • μ = (pole strength) x (distance between poles)

  8. Parity • Parity involves a transformation that changes the algebraic sign of the coordinate system. Parity is an important idea in quantum mechanics because the wavefunctions, Ψ, which represent particles can behave in different ways upon transformation of the coordinate system which describes them. Under the parity transformation: • The parity transformation changes a right-handed coordinate system into a left-handed one or vice versa. Two applications of the parity transformation restores the coordinate system to its original state.

  9. Parity • The value we measure for the observable quantities depend on • The we have the following assertion: • If V(r) = V(-r) then

  10. Parity Consequence 1 ψ(r) = ± ψ(-r) ψ(-r) = + ψ(r) positive (even) parity ψ(-r) = - ψ(-r) negative (odd) parity

  11. Parity The parity of a single particle moving in a fixed potential is (-1)ℓ, where ℓ is the orbital angular momentum. π(nucleus) = π1π2π3π4… πA multiply parity of every nucleon to get final parity – We don’t know the wavefunction (ψ) for every nucleon – but since nucleons pair up, every pair has even parity, π = + • even-even π = + • odd-A π = π of last nucleon, πp or πn • odd-odd π = πpπn Just as outer electrons determine atomic, molecular properties, outer nucleons determine nuclear properties

  12. Fermi-Dirac • Bose-Einstein • Pauli exclusion principle

  13. Pauli Exclusion Principle Applications

  14. Models of Nuclear Structure • Shell Model (Single Particle Model) • Fermi Gas Model • Liquid Drop Model • Optical Model • Collective Models

  15. Relative Abundance of The Elements Solar system

  16. Magic Numbers and Shell Model 184 • a nucleon moves in a common potential • generated by all the other nucleons 126 82 50 Maria Goeppert Mayer and Hans Jensen Nobel Prize Physics 1963 "for their discoveries concerning nuclear shell structure" 28 20 8 2 M.G. Mayer, Phys. Rev. 75, 1969 (1949)

  17. Energy required to remove proton or neutron (SP or SN, or a pair S2P, S2N) more difficult for Z,N of certain values atomic ionization energy: nuclear S2N: Energy to remove neutron pair Energy to remove electron (note similar pattern)

  18. large change in nuclear radius when 2 nucleons are added to Z,N of certain values change when adding 2 neutrons: atomic radii: Normalized to Rstd = r0A1/3

  19. The Pauli principle operates independently for Protons and Neutrons Only strong interaction In reality

  20. Fermi Gas Model • Fermi gas model – also called statistical model • treat nucleus as a statistical assembly of particles – in gas state • calculate their momentum distribution and therefore other nuclear properties • The nuclear forces are expressed as a nuclear potential • The nucleons are in the possible lowest energy states • The highest filled energy level is called Fermi level • Nuclear excitation are obtain by promoting nucleons above the Fermi level • Thermodynamic properties of excited nuclei (temperature, entropy, etc)

  21. V r 8 MeV 8 MeV 37 MeV 43 MeV neutrons protons V Fermi level 8 MeV 43 MeV Fermi sea neutrons For states – highest occupied level is Fermi level lower states constitute Fermi sea

  22. Masses Far From Stability

More Related