![]() The energy of an electron in the 2 s-state is lower than in a 2 p-state, and hence the 2 s-states will be filled first. Here l may take the value 0 or 1, and therefore electrons can be in either a 2 s- or a 2 p-state. Once the two 1 s-states have been filled, the next lowest energy state must have n=2. Thus when n=1, only s-states can exist and these can be occupied by only two electrons. It follows, therefore, that there are only two electrons in any one atom which can be in a 1 s-state, and that these electrons will spin in opposite directions. Such a state can only have a single value of the inner quantum number m=0 but can have values of + 1 2 or − 1 2 for the spin quantum number s. 1 When the principal quantum number n=1, l must be equal to zero, and an electron in this state would be designated by the symbol 1 s. These letters, which are derived from the early days of spectroscopy, are s, p, d and f, which signify that the orbital quantum numbers l are 0, 1, 2 and 3, respectively. ![]() The principal quantum number is simply expressed by giving that number, but the orbital quantum number is denoted by a letter. The energy of an electron is mainly determined by the values of the principal and orbital quantum numbers. This is the so-called “bus seat rule,” analogous to the filling of a bus where double seats tend to fill with single individuals before double occupancy occurs. Each electron has a spin quantum number, s, that is represented as “up” or “down.” The orbitals in the subshells are typically filled singly with electrons of parallel spin before double occupancy begins. Each subshell (s, p, d, f) is typically filled with the requisite number of electrons before filling the remaining subshells. This order of filling is shown in Figure 1.4.2. The sequential filling of these orbitals accounts for the periodic chemical behavior of the elements with their atomic number. The s subshell is spherically symmetrical and holds only 2 electrons each set of p orbitals holds 6 electrons, the d orbitals hold 10, and the f orbitals hold 14. Each subshell has a structure and a capacity for electrons that is described by the magnetic quantum number, m, and the spin quantum number, s. These orbitals are described by the azimuthal quantum number, l=(0,1,2,3) for (s,p,d,f), respectively. There are four major subshells: s, p, d, and f, whose names derive from spectroscopic descriptions of sharp, principal, diffuse, and fundamental. There are eight main “shells,” referring to the principal quantum number, n=(1,2,3,4,5,6,7,8) that describes atomic orbitals.
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