Principal quantum number assigned

The close-packed-spheron theory of nuclear structure may be described as a refinement of the shell model and the liquid-drop model in which the geometric consequences of the effectively constant volumes of nucleons (aggregated into spherons) are taken into consideration. The spherons are assigned to concentric layers (mantle, outer core, inner core, innermost core) with use of a packing equation (Eq. I), and the assignment is related to the principal quantum number of the shell model. The theory has been applied in the discussion of the sequence of subsubshells, magic numbers, the proton-neutron ratio, prolate deformation of nuclei, and symmetric and asymmetric fission. 

The structure of a neutral atom consists of a positively charged nucleus with a number of electrons moving about it—the number being such that their total negative charge is equal to the positive charge on the nucleus. These electrons may be assigned to various shells, characterized by different principal quantum numbers. 

To define the region in which electrons can be found, scientists have assigned four quantum numbers to each electron. Table 5 lists the quantum numbers for the first 30 atomic orbitals. The principal quantum number, symbolized by n, indicates the main energy level occupied by the electron. Values of n are positive integers, such as 1, 2, 3, and 4. As n increases, the electron s distance from the nucleus and the electron s energy increases. 

Recall that the Bohr atomic model assigns quantum numbers to electron orbits. In a similar maimer, the quantum mechanical model assigns principal quantum numbers ( ) that indicate the relative sizes and energies of atomic... 

Let us now consider the two configurations 2/>3p and 2p2. In the first case, our freedom to assign quantum numbers mt and ms to the two electrons is unrestricted by the exclusion principle since the electrons already differ in their principal quantum numbers. Thus microstates such as (1+, 1+) and (0, 0 ) are permitted. They are not permitted for the 2p2 configuration, however. Secondly, since the two electrons of the 2p3p configuration can be... 

Letters are assigned to the various values of as shown. If, for example, the electron has a principal quantum number n equal to 3, the possible I values are 0, I, and 2. 

When procedures such as this are adopted, it is still possible to assign to each orbital four quantum numbers n, I, m, and 5, the latter being for spin. However, whereas for hydrogen-like atoms the energy of the electron depends only on the principal quantum number n, for atoms containing more than one electron the energy depends also on I This is illustrated in Figure 1.8, which shows schematically the relative... 

The first four principal energy levels in the hydrogen atom. Each level is assigned a principal quantum number n. 

The sequence of nucleon energy levels (overlapping ranges), with assignment to successive layers (inner core, outer core, mantle) on the basis of the principal quantum number. 

Strategy Use the Aufbau principle discussed in Section 6.8. Start writing each electron configuration with principal quantum number n = 1, and then continue to assign electrons to orbitals in the order presented in Figure 6.23 until all the electrons have been accounted for. 

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