Magnetic momentum

Quantum numbers The four quantum numbers—principal, angular momentum, magnetic, and spin—arise from solutions to the wave equation and govern the electron configuration of atoms. 

The atom comprises a nucleus surrounded by electrons. Each element has a specific number of electrons that are bound to the atomic nucleus in an orbital structure which is unique for each element. In the structure of the atom, each electron is characterised by the principal, angular momentum, magnetic and spin quantum numbers that define its energy level at no time do they simultaneously have the same value for two electrons of the same atom (Pauli s exclusion principle). 

Principal Angular momentum Magnetic Spin n f m s Any positive integer 0,. n — 1 in integer steps 0 -I-Zmintcgcr steps i 4.1 2- +2... 

K L ko) Atomic absorption edge Atomic absorption edge Fourier transform of total atomic orbital angular momentum Magnetic modulation wave vector... 

Electrons and most other fiindamental particles have two distinct spin wavefunctions that are degenerate in the absence of an external magnetic field. Associated with these are two abstract states which are eigenfiinctions of the intrinsic spin angular momentum operator S... 

Most instruments are configured with a fixed value for the radius of curvature, r, so changing the value of B selectively passes ions of particular values of momentum, mv, tlirough tlie magnetic sector. Thus, it is really the momentum that is selected by a magnetic sector, not mass. We can convert this expression to one involving the accelerating potential. 

If the angular momentum of a free electron is represented by a spin vector S=(S, S, S ), the magnetic moment... 

Now, consider the case of spinless particles not subject to external electronic and magnetic fields. We may now choose the unitai7 operator U as the unit operator, that is, T = K. For the coordinate and momentum operators, one then obtains... 

Magnetic analyzer. A direction-focusing device that produces a magnetic field perpendicular to the direction of ion travel. The effect is to bring to a common focus all ions of a given momentum with the same mass-to-charge (m/z) ratio. 

Accelerating voltage (high voltage) scan. An alternative method of producing a momentum (mass) spectrum in magnetic-deflection instruments. This scan can also be used, in conjunction with a fixed radial electrical field, to produce an ion kinetic energy spectrum. 

Magnetic-field scan. The usual method of producing a momentum (mass) spectrum in instruments. 

Momentum spectrum. A spectrum obtained when a beam of ions is separated according to the momentum-to-charge (m/z) ratios of the ionic species present. A magnetic-sector analyzer achieves separation of the various ionic species in this way. If the ion beam is homogeneous in translational energy, as is the case with sector instruments, separation according to the m/z ratios is also achieved. 

An effect of space quantization of orbital angular momentum may be observed if a magnetic field is introduced along what we now identify as the z axis. The orbital angular momentum vector P, of magnitude Pi, may take up only certain orientations such that the component (Pi) along the z axis is given by... 

For 5 states there is no orbital angular momentum and therefore no resulting magnetic field to couple S to the intemuclear axis. The result is that a 5 state has only one component, whatever the multiplicity. 

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