* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download zeeman effect
Franck–Condon principle wikipedia , lookup
Magnetoreception wikipedia , lookup
Casimir effect wikipedia , lookup
Tight binding wikipedia , lookup
Hydrogen atom wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Wave–particle duality wikipedia , lookup
Spin (physics) wikipedia , lookup
Chemical bond wikipedia , lookup
Atomic orbital wikipedia , lookup
Nitrogen-vacancy center wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Mössbauer spectroscopy wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Atomic theory wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
The Zeeman Effect o Atoms in magnetic fields: o Normal Zeeman effect o Anomalous Zeeman effect Zeeman Effect o First reported by Zeeman in 1896. Interpreted by Lorentz. o Interaction between atoms and field can be classified into two regimes: o Weak fields: Zeeman effect, either normal or anomalous. o Strong fields: Paschen-Back effect. o Normal Zeeman effect agrees with the classical theory of Lorentz. Anomalous effect depends on electron spin, and is purely quantum mechanical. Norman Zeeman effect o Observed in atoms with no spin. o Total spin of an N-electron atom is Sˆ sˆi N i1 o Filled shells have no net spin, so only consider valence electrons. Since electrons have spin 1/2, not possible to obtain S = 0 from atoms with odd number of valence electrons. o Even number of electrons can produce S = 0 state (e.g., for two valence electrons, S = 0 or 1). o All ground states of Group II (divalent atoms) have ns2 configurations => always have S = 0 as two electrons align with their spins antiparallel. o Magnetic moment of an atom with no spin will be due entirely to orbital motion: ˆ B ˆ L Norman Zeeman effect o Interaction energy between magnetic moment and a uniform magnetic field is: ˆ Bˆ E o Assume B is only in the z-direction: o 0 Bˆ 0 Bz The interaction energy of the atom is therefore, E z Bz B Bz ml where ml is the orbital magnetic quantum number. This equation implies that B splits the degeneracy of the ml states evenly. Norman Zeeman effect transitions o But what transitions occur? Must consider selections rules for ml: ml = 0, ±1. o Consider transitions between two Zeeman-split atomic levels. Allowed transition frequencies are therefore, h h 0 B Bz ml 1 h h 0 ml 0 ml 1 h h 0 B Bz o Emitted photons also have a polarization, depending on which transition they result from. Norman Zeeman effect transitions o Longitudinal Zeeman effect: Observing along magnetic field, photons must propagate in zdirection. o Light waves are transverse, and so only x and y polarizations are possible. o The z-component (ml = 0) is therefore absent and only observe ml = ± 1. o Termed -components and are circularly polarized. o Transverse Zeeman effect: When observed at right angles to the field, all three lines are present. o ml = 0 are linearly polarized || to the field. o ml = ±1 transitions are linearly polarized at right angles to field. Norman Zeeman effect transitions o Last two columns of table below refer to the polarizations observed in the longitudinal and transverse directions. o The direction of circular polarization in the longitudinal observations is defined relative to B. o Interpretation proposed by Lorentz (1896) (ml=-1 ) (ml=0 ) + (ml=+1 ) Anomalous Zeeman effect o Discovered by Thomas Preston in Dublin in 1897. o Occurs in atoms with non-zero spin => atoms with odd number of electrons. o In LS-coupling, the spin-orbit interaction couples the spin and orbital angular momenta to give a total angular momentum according to Jˆ Lˆ Sˆ o In an applied B-field, J precesses about B at the Larmor frequency. o L and S precess more rapidly about J to due to spin-orbit interaction. Spin-orbit effect therefore stronger. Anomalous Zeeman effect o Interaction energy of atom is equal to sum of interactions of spin and orbital magnetic moments with B-field: E z Bz (zorbital zspin )Bz Lˆ z gsSˆ z B Bz where gs= 2, and the < … > is the expectation value. The normal Zeeman effect is obtained by setting Sˆz 0 and Lˆ z ml . o In the case of precessing atomic magnetic in figure on last slide, neither Sz nor Lz are constant. Jˆz m Only j is well defined. o Must therefore project L and S onto J and project onto z-axis => Jˆ Jˆ B ˆ | Lˆ | cos1 2 | Sˆ | cos 2 ˆ ˆ |J | |J | Anomalous Zeeman effect o The angles 1 and 2 can be calculated from the scalar products of the respective vectors: Lˆ Jˆ | L || J | cos1 Sˆ Jˆ | S || J | cos 2 which implies that o ˆ Lˆ Jˆ Sˆ Jˆ B ˆ 2 J | Jˆ |2 | Jˆ |2 Now, using Sˆ Jˆ Lˆ implies that (1) Sˆ Sˆ (Jˆ Lˆ ) (Jˆ Lˆ ) Jˆ Jˆ Lˆ Lˆ 2Lˆ Jˆ ˆ therefore L Jˆ (Jˆ Jˆ Lˆ Lˆ Sˆ Sˆ ) /2 so that j( j 1) l(l 1) s(s 1) 2 /2 Lˆ Jˆ j( j 1) 2 | Jˆ |2 o Similarly, j( j 1) l(l 1) s(s 1) 2 j( j 1) Sˆ Jˆ (Jˆ Jˆ Sˆ Sˆ Lˆ Lˆ ) /2 and Sˆ Jˆ j( j 1) s(s 1) l(l 1) 2 j( j 1) | Jˆ |2 Anomalous Zeeman effect o We can therefore write Eqn. 1 as j( j 1) l(l 1) s(s 1) ˆ 2 j( j 1) o This can be written in the form ˆ g j 2 j( j 1) s(s 1) l(l 1)B Jˆ 2 j( j 1) B ˆ J where gJ is the Lande g-factor given by o This implies that g j 1 j( j 1) s(s 1) l(l 1) 2 j( j 1) z g j B m j and hence the interactionenergy with the B-field is o E z Bz g j B Bz m j Classical theory predicts that gj = 1. Departure from this due to spin in quantum picture. Anomalous Zeeman effect spectra o Spectra can be understood by applying the selection rules for J and mj: j 0,1 m j 0,1 o Polarizations of the transitions follow the as for normal Zeeman effect. same patterns o For example, consider the Na D-lines at right produced by 3p 3s transition.