Subshells letter designation

Electrons having the same value of n in an atom are said to be in the same shell. Electrons having the same value of n and the same value of / in an atom are said to be in the same subshell. (Electrons having the same values of n, /, and m in an atom are said to be in the same orbital.) Thus, the first two electrons of magnesium (Table 17-3) are in the first shell and also in the same subshell. The third and fourth electrons are in the same shell and subshell with each other. They are also in the same shell with the next six electrons (all have n = 2) but a different subshell (/ = 0 rather than 1). With the letter designations of Sec. 17.3, the first two electrons of magnesium are in the Is subshell, the next two electrons arc in the 2s subshell, and the next six electrons are in the 2p subshell. The last two electrons occupy the 3s subshell. 

The shell number is represented by 1, 2, 3, and so forth, and the letters designate the subshells. The superscript numbers tell how many electrons occupy each subshell. Thus, in this example, there are two electrons in the Is subshell, two electrons in the 2s subshell, six electrons in the 2p subshell, and only one electron in the 3s subshell. (The 3s subshell can hold a maximum of two electrons, but in this atom this subshell is not filled.) The total number of electrons in the atom can easily be determined by adding the numbers in all the subshells, that is, by adding all the superscripts. For sodium, this sum is 11, equal to the atomic number of sodium. 

Because only n and values affect the energies of electrons, the electrons with the same n value and the same value all have the same energy. In other words, all the electrons in a given subshell are degenerate. Each subshell is denoted by its principal quantum number and the letter designation for . For example, for neon, with atomic number 10, the sets of quantum numbers for the 10 electrons are listed in Table 4.2. We can group them as follows ... 

The symbols used to indicate the number of electrons in a subshell include the number of the principal shell (1,2, 3...), the letter designation of the subshell (s, p, d, f), with a superscript number indicating the number of electrons. 

Sublevel. The atom s levels contain sublevels, or subshells, which designate the orbital shape. Each sublevel has a letter designation ... 

The letters derive from the names of spectroscopic lines 5harp, principal, diffuse, and fundamental. Sublevels with I values greater than 3 are designated alphabetically g sublevel, h sublevel, etc.) Sublevels are named by joining the n value and the letter designation. For example, the sublevel (subshell) with n = 2 and / = 0 is called the 2s sublevel. 

Plan To name the sublevel (subshell), we combine the n value and Z letter designation. We know Z, so we can find the possible wi values, whose total number equals the number of orbitals. 

The first four levels of orbitals in the hydrogen atom are listed with their quantum numbers in Table 7.2. Note that each set of orbitals with a given value of (sometimes called a subshell) is designated by giving the value of n and the letter for . Thus an orbital where n = 2 and = 1 is symbolized as 2p. There are three 2p orbitals, which have different orientations in space. We will describe these orbitals in the next section. 

The collection of orbitals with the same value of n is called an electron shell. AU the orbitcds that have n = 3, for example, are said to be in the third shell. The set of orbitals that have the same n and / values is called a subsheU. Each subshell is designated by a number (the value of n) and a letter (s, p, d, or/, corresponding to the value of /). For excunple, the orbiteds that have n = 3 and 1 = 2 rue cedled 3d orbitals and are in the 3d subshell. 

The origin of these letters is from the language used to describe the lines seen in early studies of atomic spectra s was sharp, p was principal, was diffuse, and/was fundamental. Beyond/ the letter designations proceed in alphabetical order. There is no known atom that has electrons in any subshell higher than / when it is in its ground state, but higher orbitals may be occupied in excited states, and additional superheavy elements in which these orbitals are populated may yet be discovered. 

Solution As we saw earlier, the number given in the designation of the subshell is the principal quantum number, so in this case = 4. The letter designates the type of orbital. Because we are dealing with d orbitals, = 2. The values of m( can vary from... 

The letters s, p, d, and/, corresponding to values of Z = 0,1,2, and 3, respectively, are conventionally used to designate sublevels. The number of electrons present in a given sublevel is limited to 2,6,10, and 14 for s, p, d, and/, sublevels, respectively. It follows that, since each orbital can be occupied by a maximum of 2 electrons, Aere is only 1 orbital in the 5 sublevel, 3 orbitals in the p sublevel, 5 in the d and 7 in the /. The value of the principal quantum number and the letter designating the azimuthal quantum number are written in sequence to designate both the shell and subshell. For example. Ad represents the d subshell of the fourth shell. 

Each shell is made up of subshells that are designated by a letter from the group s, p, d, and f. Because all subshells are designated by one of these letters regardless of the shell in which the subshell is found, a combination of both shell number and subshell letter is used to identify subshells clearly. Thus, a p subshell in shell number 2 is referred to as a 2p subshell. The number of subshells found in a shell is the same as the value of n for the shell. Thus, shell number 2 (n = 2) contains two subshells. The subshells are the 2p mentioned earlier and a 2s. Electrons located in specific subshells are often referred to in terms of the same number and letter as the subsheU. Eor example, we might refer to an atom as having three 2p electrons. All electrons within a specific subshell have the same energy. 

Plan We name the sublevel (subshell) with the n value and the letter designation of the / value. From the I value, we find the number of possible values, which equals the number of orbitals in that sublevel. 

To denote a subshell within a particular shell, we write the value of the n quantum number for the shell, followed by the letter designation for the subshell. For example, 2p denotes a subshell with quantum numbers n = 2 and / = 1. ... 

Give the notation (using letter designations for /) for the subshells denoted by the following quantum numbers. 

Subshell nThe electrons within the same shell (energy level) of the atom are characterized by the same principal quantum number (n), and are further divided into groups according to the value of their azimuthal quantum numbers (1) the electrons which possess the same azimuthal quantum number for the same principal quantum number are considered to occupy the same subshell (or sublevel). The individual subshells are designated with the letters s,p,d,f,g, and hm as follows ... 

The second quantum number is called the angular momentum quantum number. It is designated by the letter f and can be thought of as representing a subshell within a principal energy... 

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