An atom’s electrons are organized into shells, subshells, and orbitals. The shell and subshell designations depend on the quantum mechanical characteristics of a bound electron. Each shell has one or more subshells, each of which can contain orbitals. The sum of subshell orbitals gives us the number of possible orbitals in each shell type.
A subshell is an area within the electron shell of an atom that contains one type of electron orbital. Each atom consists of a central nucleus of one or more positive protons and zero or more uncharged neutrons, with electrons surrounding it. The electrons of an atom are not free to travel at random, but are, to some extent, bound. Just as books are organized in the format of chapters, pages, and lines, an atom’s electrons are organized into shells, subshells, and orbitals. Unless the electrons are energetically excited, they stay in those orbitals.
Assignments to shell and subshell designations depend on the quantum mechanical characteristics of a bound electron. There are four such quantum numbers: “n”, “l”, “m” and “s”. These are the energy-related primary quantum number (n) – associated with the Bohr model of the atom, the angular momentum quantum number (l), the angular momentum component vector (m), and the spin quantum number ( s). The value n defines the shell and must be an integer no less than one. If the primary quantum number n=1, the number of shells is 1, also called shell K; if n=2, the shell number is 2, shell L; if n=3, the shell M; n=4, the shell N; n=5, the O shell; and so on.
Bypassing, momentarily, the description of the next level of order – subshells – the orbitals of the electrons depend on the magnitude and angular momentum of the electron. The values of the angular momentum quantum number, l, can be zero or whole numbers greater than zero; if l=0, the orbital is an s orbital; if l=1, it is a p-; if l=2, a d-; l=3, an f- and if the orbital has a value l=4, the orbital is a g-orbital. It is the value l which determines the probability that an electron is located within a certain region of space, a region which has a definite shape. An s orbital is spherical, while a p orbital has two flattened spheres with their flat surfaces facing each other. The d orbital shape can have four closely associated spheres, or two spheres above and below a ring: higher values of l lead to other shapes of orbital probabilities.
Each shell has one or more subshells, each of which can contain orbitals. The letters that identify the subshells correspond to the types of orbitals they contain: a d-subshell contains d-orbitals, an f-subshell, f-orbitals. The number of possible angular momentum component or m-values, multiplied by the number of possible spin quanta or s-values, determines the maximum number of orbitals that can exist within a particular subshell. Values for m can be any integer between -1 and +1, including 0, while s must be +1/2 or -1/2. The calculation gives us, in the case of an f-subshell (l=3), seven m values and two s values, resulting in a maximum of 7×2=14 possible orbitals.
The sum of subshell orbitals gives us the number of possible orbitals in each shell type. In a K-shell, there is only one s-subshell, which itself contains up to two s-orbitals. Two subshells, s- and p-, are contained in the L-shell and each subshell contains up to 2+6=8 orbitals. The three subshells of an M-shell, s-, p- and d-, can contain 2+6+10=18 orbitals, while the s-, p-, d- and f subshells of an N-shell contain up to 2 +6+10+14=32 orbitals. The g-shells include s-, p-, d-, f- and g-subshells and can contain up to 2+6+10+14+18=50 orbitals.
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