spin

Examples of spin in the following topics:

• Diamagnetism and Paramagnetism

  • In other words, one of the electrons has to be "spin-up," with $m_s = +\frac{1}{2}$, while the other electron is "spin-down," with $m_s = -\frac{1}{2}$.
  • In order to decide whether electron spins cancel, add their spin quantum numbers together.
  • Think of spins as clockwise and counterclockwise.
  • If one spin is clockwise and the other is counterclockwise, then the two spin directions balance each other out and there is no leftover rotation.
  • If even one orbital has a net spin, the entire atom will have a net spin.

• Introduction

  • The nuclei of many elemental isotopes have a characteristic spin (I).
  • Some nuclei have integral spins (e.g.
  • I = 1, 2, 3 ....), some have fractional spins (e.g.
  • The resulting spin-magnet has a magnetic moment (μ) proportional to the spin.
  • For spin 1/2 nuclei the energy difference between the two spin states at a given magnetic field strength will be proportional to their magnetic moments.

• Spin-Spin Splitting

  • If an atom under examination is perturbed or influenced by a nearby nuclear spin (or set of spins), the observed nucleus responds to such influences, and its response is manifested in its resonance signal.
  • They may actually be spin-coupled, but the splitting cannot be observed directly.
  • If there are 2 neighboring, spin-coupled, nuclei the observed signal is a triplet ( 2+1=3 ); if there are three spin-coupled neighbors the signal is a quartet ( 3+1=4 ).
  • Spin 1/2 nuclei include 1H, 13C, 19F & 31P.
  • Spin coupling with nuclei having spin other than 1/2 is more complex and will not be discussed here.

• Magnetic Properties

  • Since the configuration of Fe3+ has five d electrons, we would expect to see five unpaired spins in complexes with Fe.
  • In order for this to make sense, there must be some sort of energy benefit to having paired spins for our cyanide complex.
  • This is referred to as low spin, and an electron moving up before pairing is known as high spin.
  • As a result, they have either have too many or too few d electrons to warrant worrying about high or low spin.
  • This shows the comparison of low-spin versus high-spin electrons.

• Detection and Observation of Radicals

  • The same unpaired or odd electron that renders most radical intermediates unstable and highly reactive may be induced to leave a characteristic "calling card" by a magnetic resonance phenomenon called "electron spin resonance" (esr) or "electron paramagnetic resonance" (epr).
  • Just as a proton (spin = 1/2) will occupy one of two energy states in a strong external magnetic field, giving rise to nmr spectroscopy; an electron (spin = 1/2) may also assume two energy states in an external field.
  • Because the magnetic moment of an electron is roughly a thousand times larger than that of a proton, the energy difference between the spin states falls in the microwave region of the spectrum (assuming a moderate magnetic field strength).
  • The lifetime of electron spin states is much shorter than nuclear spin states, so esr absorptions are much broader than nmr signals.
  • This complexity is the result of hyperfine splitting of the resonance signal by protons and other nuclear spins, an interaction similar to spin-spin splitting in nmr spectroscopy.

• The Pauli Exclusion Principle

  • The Pauli exclusion principle governs the behavior of all fermions (particles with half-integer spin), while bosons (particles with integer spin) are not subject to it.
  • Atoms can have different overall spin, which determines whether they are fermions or bosons—for example, helium-3 has spin 1/2 and is therefore a fermion, in contrast to helium-4 which has spin 0, making it a boson.
  • In contrast, particles with integer spin (bosons) have symmetric wave functions; unlike fermions, bosons may share the same quantum states.
  • However, there are only two distinct spin values for a given energy state.
  • When a state has only one electron, it could be either spin-up or spin-down.

• Hund's Rule

  • All of the electrons in singly occupied orbitals have the same spin.
  • Therefore, spins that are aligned have lower energy.
  • Technically speaking, the first electron in a sublevel could be either "spin-up" or "spin-down."
  • Once the spin of the first electron in a sublevel is chosen, the spins of all of the other electrons in that sublevel depend on that first choice.
  • Keeping with convention, all of the unpaired electrons are drawn as "spin-up."

• Physical Properties and Atomic Size

  • Some d-d transitions are spin forbidden.
  • An example occurs in octahedral, high-spin complexes of manganese(II) in which all five electrons have parallel spins.
  • The color of such complexes is much weaker than in complexes with spin-allowed transitions.
  • In octahedral complexes with between four and seven d electrons, both high spin and low spin states are possible.
  • Tetrahedral transition metal complexes, such as [FeCl4]2−, are high-spin because the crystal field splitting is small.

• Conservation of Angular Momentum

  • An example of conservation of angular momentum is seen in an ice skater executing a spin, as shown in .
  • (Both F and r are small, and so $\vec \tau = \vec r \times \vec F$ is negligibly small. ) Consequently, she can spin for quite some time.
  • She can also increase her rate of spin by pulling in her arms and legs.
  • An ice skater is spinning on the tip of her skate with her arms extended.
  • In the next image, her rate of spin increases greatly when she pulls in her arms, decreasing her moment of inertia.

• Quantum Numbers

  • Mulliken, which incorporates Bohr energy levels as well as observations about electron spin.
  • The fourth quantum number describes the spin (intrinsic angular momentum) of the electron within that orbital and gives the projection of the spin angular momentum (s) along the specified axis.
  • An electron has spin s = ½, consequently ms will be ±, corresponding with spin and opposite spin.
  • The fourth quantum number, the spin, is a property of individual electrons within a particular orbital.
  • Each orbital may hold up to two electrons with opposite spin directions.