Orbitals and Quantum Numbers

Energy level diagram of the sodium atom. The energy levels are denoted by the values for the principal quantum number , the orbital quantum number/, and the spin quantum number s. Levels with 1 = 0 are not split for / = 1 two separate levels are drawn (s = 1/2) for/> 1 the splitting is too small to be shown in the figure. Wavelengths of a few special transitions are given in nanometers. 

See also Orbitals Quantum Number and Pauli Exclusion Principle. 

For configurations with one electron or hole above closed shells the moments of the spectrum are conditioned in the single-configuration approach by only one-electron spin-orbit interaction, and then the dimensionless quantities skewness jci and excess K2 (formulas (32.7)) as well as orbital quantum number and, therefore, do not depend on the accuracy of radial orbitals, namely,... 

Since the energy levels have different shapes, secondary quantum numbers are used in order to represent the shape of the electron clouds and divisions of the energy levels. The secondary quantum number is also called the orbital quantum number and denoted by 1. The values of the secondary quantum number are the positive numbers from zero to n-1, depending on the principal quantum number. The secondary quantum numbers are also represented by letters such as s,p,d and f... starting from the least energetic. 

In a free multielectron atom or ion, the spin and orbital angular moments of the electrons couple to give a total angular momentum represented in the Russell-Saunders scheme by the quantum number J. Since J arises from vectorial addition of L (the total orbital quantum number) and 5 (total spin quantum number), it may take integral (or half-integral... 

Do the three 4p atomic orbitals possess the same or different values of (a) principal quantum number, (b) the orbital quantum number and (c) the magnetic quantum number Write down a set of quantum numbers for each 4p atomic orbital to illustrate your answer. 

If. in an atom, two electrons have the same three orbital quantum numbers / , /, and / ), their spins must be coupled (i.e., the spin quantum number of one must be +5, the other... 

This set includes not only the three orbital quantum numbers, , / and ntp but also the spin quantum number m, which was discussed in Chapter 5. The spin quantum number is restricted to one of two values +J, corresponding to spin-up, and -4, corresponding to spin-down. This leads to an alternative formulation of the Pauli exclusion principle as ... 

Two more quantum numbers, / and W/, appear when the angular part of the wavefunction is solved. The quantum number / is called the orbital quantum number and has allowed values of 0,1,2... (n — 1). The value of I determines the shape... 

Electronic states are conveniently classified in terms of the electronic configuration, as described by the principal and orbital quantum numbers, and the interactions between orbital and spin momenta of the electrons... 

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