Energy levels in magnetic field

This type of splitting of energy levels in magnetic fields for a nucleus (1 > 0) is called nuclear Zeeman splitting. 

Fig. 12.11. Energy levels in magnetic field H = (0, 0, H) for a nucleus with spin angular momentum I corresponding to spin quantum number I = j- The magnetic dipole moment equals M = yl. (a) At the zero field, the level is doubly degenerate, (b) For y > 0 (e.g., a proton), / and M have the same direction. In a nonzero magnetic field, the energy equals E = —M H = —M H = —ymiRH, where mj = j. Thus, the degeneracy is lifted the state withm/ = i.e., with the positive projection of...

A) Energy levels in magnetic field for spin S= 1 /2 (B) discoverers of NMR phenomenon and proton NMR signal of paraffin wax observed by Ed Purcell in 1945. 

Figure 8.39. Behaviour of the energy levels of HF in the J = 1 level in magnetic fields from 0 to 8 kG. The electric field was 2952 V cm-1. The vertical arrows indicate the five transitions measured by de Leeuw and Dymanus [89]. For the zero field energy level pattern, see figure 8.38.

The spin Hamiltonian for the hydrogen atom will be used to determine the energy levels in the presence of an external magnetic field. As indicated in Section II.A, the treatment may be simplified if it is recognized that the g factor and the hyperfine constant are essentially scalar quantities in this particular example. An additional simplification results if the z direction is defined as the direction of the magnetic field. For this case H = Hz and Hx = Hv = 0 hence,... 

When the magnetic field is large such that j(Ae + An)2 4a2, then C22 — 1 and C23 0 or 03) aej3n) similarly, C32 0 and C33 1 or 03) (3c n). These high-field approximations to the wavefunctions are shown along with their respective energy levels in Fig. 1. 

Hutchings, M.T. (1964) Point-charge calculations of energy levels of magnetic ions in crystalline electric. Fields Solid State Phys., 16, 227-273. 

The terms singlet" and triplet are used because a triplet state splits into three slightly different energy levels in a magnetic field, but a singlet state is not split. 

Zeeman effect Shifting of atomic energy levels in a magnetic field, zwitterion- A molecule with a positive charge localized at one position and a negative charge localized at another position. 

The splitting of atomic energy levels in a crystal field (CF) with the symmetry of one of the magnetic point groups has been considered in detail by Cracknell (1968). Consider an atomic 2P level (L = 1) in an intermediate field of 2mm or C2v symmetry and assume that Hs. L < Hcf. The degenerate 2P level is split into three components, T i T3 T4. But in a field of 4mm symmetry the two levels T3 and F4 stick together, that is, are degenerate, since 14 = r3 r4 (case (b)), while 14 is re-labeled as 14 (case (a)). (See Table 14.4 and... 

Fig. 3 Scheme of the calculation of energy levels in atoms, ions and unimetal complexes. The weak-field path (a) + (b) + (c). The strong-field path (b) + (a) + (c). The multiplet path (a) + (c) + (b). The crystal-field multiplets represent an appropriate basis for involvement of the Zeeman perturbation in the magnetic field... 

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