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Spin

Spin. Electronic charge in motion - A current loop behaves as a magnetic dipole and has a magnetic moment. - Note the current direction is opposite to the electron velocity, and also the angular momentum direction is opposite to the magnetic moment

edward-saunders
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Spin

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  1. Spin • Electronic charge in motion • - A current loop behaves as a • magnetic dipole and has a • magnetic moment. • - Note the current direction is • opposite to the electron • velocity, and also the angular • momentum direction is opposite • to the magnetic moment • Two contributions to the • electronic magnetic moment • -An orbital magnetic moment due to • orbital angular momentum • -A spin magnetic moment due to • electron spin

  2. Electronic Magnetic Moments -Orbital Contribution • The orbital motion of an electron around the nucleus • may correspond to a current in a loop of wire having • no resistance where m=(area of loop) (current) • Note that the angular momentum is continuous (not • quantized), indicating a classical treatment of the • problem

  3. Electronic Magnetic Moments -Spin Contribution • Spin? • - Was postulated in 1925 by Paul Dirac in order to explain • certain features of optical spectra of hot gases subjected to • a magnetic field(Zeeman effect) and later theoretical • confirmation in wave mechanics • - The root cause of magnetism and an intrinsic • property, together with charge and mass, of subatomic • particles of fermions (eg.electrons, protons and neutrons) • and bosons (photons, pions) • It was found, theoretically and experimentally, that • the magnetic moment due to electron spin is equal • to,m0

  4. Electronic Magnetic Moments -m vs. p • For a given angular momentum, the spin gives • twice the magnetic moment of orbit

  5. Electronic Magnetic Moments -Total Moments • The total magnetic moment per electron is the • vector sum of the orbital and spin magnetic moments • The term ‘g’ is called the Lande splitting factor • — g=2 for spin only components • — g=1 for orbital only components

  6. Electronic Magnetic Moments -Lande’Equation • Orbital is quenching : L=0, J=S  g=2 • Spin =0 : S=0, J=L  g=1

  7. Schrodinger Equation

  8. Schrodinger Equation m=hml ml= l(l+1)

  9. Schrodinger Equation

  10. Electronic Magnetic Moments -Quantum Mechanical • The orbital angular momentum quantum number (l) • The spin angular momentum quantum number (l) • The spin angular momentum quantum number (l)

  11. Hund’s Rule • Empirical rules which determine the occupancy • of the Available electronics within an atom • Used to calculate L, S and J for an unfilled shell • 1. Maximum total S=max Sz with Sz=imsi • Obeying the Pauli exclusion principle • 2. Maximum total L=maxLz with Lz= imli • Minimizing the Coulomb interaction energy • 3. Spin-orbit interaction: • L -S  if less than half-filled • J= L+S  if more than half-filled

  12. Hund’s Rule - Examples • Sm3+ ion having 5 electrons in its 4f shell • (n=4, l=3)  S=5/2, L=5, J=L-S=5/2 • ml 3 2 1 0 –1 –2 –3 • ms • occupancy s • Fe2+ ion having 6 electrons in its 3d shell • (n=3, l=2)  S=2, L=2, J=L+S=4. • Actually, however, S=2, L=0 (quenched) • J=S=2 • ml 2 1 0 –1 –2 2 1 0 -1 -2 • ms • occupancy s

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