Multi-electron atoms orbital energy

In the lithium atom, and for all other multi-electron atoms, orbitals in different energy sublevels differ in energy. 

In a multi-electron atom, the energy sublevels within a principal energy level have different energies. For example, the three 2p orbitals are of higher energy than the 2s orbital. 

The Quantum-Mechanical Model The quantum-mechanical model for the atom describes electron orbitals, which are electron probability maps that show the relative probability of finding an electron in various places surrounding the atomic nucleus. Orbitals are specified with a number (n), called the principal quantum number, and a letter. The principal quantum number (n = 1,2,3. . . ) specifies the principal shell, and the letter (s, p, d, or f) specifies the subshell of the orbital. In the hydrogen atom, the energy of orbitals depends only on n. In multi-electron atoms, the energy ordering is Is 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s. 

Figure Al.l Approximate energy level diagram for electronic orbitals in a multi-electron atom. Each horizontal line can accommodate two electrons (paired as so-called spin-up and spin-down electrons), giving the rules for filling the orbitals - two in the s-levels, 6 in the p-levels, 10 in the d-levels. Note that the 3d-orbital energy is lower than the 4p, giving rise to the d-block or transition elements. (From Brady, 1990 Figure 7.10. Copyright 1990 John Wiley Sons, Inc. Reprinted by permission of the publisher.)...

Chapter 3 is devoted to atoms. One-electron atom and multi-electron atoms of chemical elements are considered. The probability density functions (orbitals) for electrons are illustrated. The Hartree theory is presented as a first method of approximation that has been proposed in order to calculate wave functions and energies of electrons in atoms. The covalently bonded diatomic molecules are subject of the consequent consideration. 

FIGURE 9.23 Energy ordering of orbitals for multi-electron atoms... 

List all of the quantum-mechanical orbitals through 5s, in the correct energy order for multi-electron atoms. What is the Pauli exclusion principle Why is it important when writing electron configurations ... 

The electron s wave function (iK atomic orbital) is a mathematical description of the electron s wavelike behavior in an atom. Each wave function is associated with one of the atom s allowed energy states. The probability density of finding the electron at a particular location is represented by An electron density diagram and a radial probability distribution plot show how the electron occupies the space near the nucleus for a particular energy level. Three features of an atomic orbital are described by quantum numbers size (n), shape (/), and orientation (m/). Orbitals with the same n and / values constitute a sublevel sublevels with the same n value constitute an energy level. A sublevel with / = 0 has a spherical (s) orbital a sublevel with / = 1 has three, two-lobed (p) orbitals and a sublevel with / = 2 has five, multi-lobed (d) orbitals. In the special case of the H atom, the energy levels depend on the n value only. 

Energy states for which L = 0, 1, 2, 3, 4... are known as S, P, D, F,G... terms, respectively. These are analogous to the s, p, d,f, g... labels used to denote atomic orbitals with / = 0,1, 2, 3,4... in the 1-electron case. By analogy with equation 21.8, equation 21.9 gives the resultant orbital angular momentum for a multi-electron system. 

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