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The Nucleus

The Nucleus. PHY 3101 D. Acosta. Rutherford Scattering. Experiments by Geiger & Marsden in 1909. Rutherford Model of the Atom. Conclusion: the atom contains a positive nucleus < 10 fm in size (1 fm = 10 -15 m). The Neutron. The neutron was discovered in 1932 by James Chadwick

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The Nucleus

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  1. The Nucleus PHY 3101 D. Acosta

  2. Rutherford Scattering Experiments by Geiger & Marsden in 1909 PHY 3101 -- D. Acosta

  3. Rutherford Model of the Atom Conclusion: the atom contains a positive nucleus < 10 fm in size (1 fm = 10-15 m) PHY 3101 -- D. Acosta

  4. The Neutron • The neutron was discovered in 1932 by James Chadwick • -particles accelerated in a small accelerator and collided with Be nuclei • Neutral, very penetrating radiation • Found by elastic scattering off protons in paraffin wax • By the way, the positron (anti-electron) also was discovered in 1932 by Carl Anderson in cosmic rays • Anti-matter predicted by P.A.M. Dirac in his relativistic version of the Schrodinger Equation PHY 3101 -- D. Acosta

  5. The Periodic Table • All elements composed of just electrons, neutrons, and protons • Elements of the same group have nearly the same chemical property • Chemical periodicity depends on the atomic number Z • Any other fundamental particles? Next chapter… PHY 3101 -- D. Acosta

  6. Nomenclature • X is the element • A is the atomic mass (Z+N) • Z is the atomic number (number of protons) • N is the number of neutrons • Atoms are neutral. Number of electrons equals number of protons = Z • Chemical properties depend on Z • Ordering of Periodic Table given by valence configuration of electrons • Isotopes: • Same Z, different A • Isobars: • Same A, different Z • Isotones: • Same N, different A PHY 3101 -- D. Acosta

  7. Atomic Mass Units (u) • The atomic mass is the mass of an atomic isotope, including electrons • Note that mass of 12C is 6 mp+ 6mn + 6me = 12.1 u > 12.0 u • The nucleus is bound • Binding energy is 0.1 u = 90 MeV • It takes energy to liberate all particles • Should not think of mass as measuring the number of particles, only the rest energy of the system: • Mass is a measure of inertia (a = F/m)not contents PHY 3101 -- D. Acosta

  8. Binding Energy • Take the mass of all particles individually, including electrons, and subtract the mass of the combined system • A system is bound if the binding energy is positive. • Example: Deuterium • Note that e- mass cancels • If the binding energy is negative, the system will decay. The energy released is PHY 3101 -- D. Acosta

  9. Atomic Binding Energies • The Coulomb potential for an electron in a hydrogen-like atom can be written in terms of the dimensionless fine structure constant • The energy levels are given by • Hydrogen: • Positronium (e+e-): • These are the binding energies! • e.g. mass of H is less than mass of e+p • The Bohr radii are PHY 3101 -- D. Acosta

  10. Nuclear Binding Energies • Consider the binding energy of the deuteron • proton–neutron bound state • The binding potential is roughly similar to that of the Coulomb potential, but with a dimensionless constant characteristic of the Strong Nuclear Force rather than EM • The energy levels are given by • Agrees with measured value of 2.2 MeV • 1 million times larger than atomic energies! • Nuclear radius is 10,000 times smaller: PHY 3101 -- D. Acosta

  11. Nuclear Potential Well • Rutherford concludes from Geiger and Marsden that the range of the Strong Nuclear Force is < 10-14 m • No deviation in the scattering rate of the highest-energy -particles off nuclei from that predicted by electromagnetic Coulomb scattering • Thus, the Strong Nuclear Force is short-ranged, and does not extend to infinity • To probe the size of nuclei, need higher energies than -particles from radioactive decay • The nuclear potential well resembles a semi-infinite potential well • -particles inside the nucleus must tunnel to escape! Higher rate for higher energy -particles PHY 3101 -- D. Acosta

  12. Size of Nuclei • Robert Hofstadter performs experiment at Stanford using a new linear accelerator for electrons in 1950s • E = 100 -- 500 MeV •  = h / p = 2.5 fm • The proton is not a point! (Deviation of elastic scattering rate from Rutherford Scattering prediction) • Proton and nuclei have extended charge distributions • Nobel prize in 1961 nucleus PHY 3101 -- D. Acosta

  13. Nuclear Spin • neutrons and protons have s = ½ (ms =  ½)so they are fermions and obey the Pauli-Exclusion Principle • The nuclear magnetic dipole moment is • But actually, • Thus, the neutron and proton have complicated charge distributions • They are not fundamental particles… PHY 3101 -- D. Acosta

  14. Zeeman Effect • In the atom, the orbital angular momentum of the electrons gives rise to a magnetic dipole moment which interacts with external magnetic fields • In the normal Zeeman effect, atomic states with angular momentum have split energy levels in the presence of a magnetic field: • Similarly, a single particle with intrinsic angular momentum (spin) can interact with an external magnetic field, with different energy configurations • There can be transitions between these different energy levels. A photon is emitted or absorbed in the process PHY 3101 -- D. Acosta

  15. Nuclear Magnetic Resonance • Now consider an H-atom nucleus (proton) in a 1 T magnetic field. Since the nuclear magnetic moment is smaller than the Bohr magneton, the transition energy is smaller • The frequency of emission/absorption is • A sample of protons (like the human body) will resonate at this frequency. • Radio waves at this frequency induce transitions • Strong absorption of radio waves if there is a population difference between the two energy states (thermal distribution) • Studied by I.I.Rabi in 1938 (Nobel in 1944) • Now applied to medical imaging: • Magnetic Resonance Imaging (MRI) PHY 3101 -- D. Acosta

  16. Nuclear Shell Model • Recall the electron configuration of atoms: • Closed subshells occur after the following number of electrons:Z = 2, 10, 18, 36, 54, 80, 86 • Refer to these as atomic magic numbers • Configuration is very stable • Large ionization energy  inert gases • Similar behavior is seen in the binding energy of nuclei • Plot of B.E./A • Since neutrons and protons are fermions, the Pauli-Exclusion Principle applies • Nuclei also have shell structure PHY 3101 -- D. Acosta

  17. Nuclear Structure • The Pauli-Exclusion Principle applies to neutrons and protons separately • Not together because n, p are distinguishable from each other • Ground state configurations • Tend to want to have equal numbers of neutrons and protons to minimize the total energy of the nucleus • Too many n’s or p’s causes binding energy to be negative -- unstable EF E n=3 n=2 n=1 PHY 3101 -- D. Acosta

  18. Nuclear Magic Numbers PHY 3101 -- D. Acosta

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