Concept of quantum number:
Using wave mechanics, every electron in an atom is characterized by four parameters
called quantum numbers. The size, shape, and spatial orientation of an electron’s
probability density are specified by three of these quantum numbers. Furthermore,
Bohr energy levels separate into electron subshells, and quantum numbers dictate the
number of states within each subshell. Shells are specified by a principal quantum
number n, which may take on integral values beginning with unity; sometimes these
shells are designated by the letters K, L, M, N, O, and so on, which correspond,
respectively, to n = 1,2,3,4,5.... as indicated in Table . Note also that this quantum
number, and it only, is also associated with the Bohr model.This quantum number
is related to the distance of an electron from the nucleus, or its position.
The second quantum number, l, signifies the subshell, which is denoted by a
lowercase letter—an s, p, d, or f; it is related to the shape of the electron subshell.
In addition, the number of these subshells is restricted by the magnitude of n.
Allowable subshells for the several n values are also presented in Table 2.1. The
number of energy states for each subshell is determined by the third quantum number,
For an s subshell, there is a single energy state, whereas for p, d, and f subshells,
three, five, and seven states exist, respectively. In the absence of
an external magnetic field, the states within each subshell are identical. However,
when a magnetic field is applied these subshell states split, each state assuming a
slightly different energy.
Associated with each electron is a spin moment, which must be oriented either
up or down. Related to this spin moment is the fourth quantum number, for
which two values are possible ( and ), one for each of the spin orientations.
Thus, the Bohr model was further refined by wave mechanics, in which the introduction
of three new quantum numbers gives rise to electron subshells within
each shell.
A complete energy level diagram for the various shells and subshells using the
wave-mechanical model is shown in Figure below. Several features of the diagram are
worth noting. First, the smaller the principal quantum number, the lower the energy
level; for example, the energy of a 1s state is less than that of a 2s state, which in
turn is lower than the 3s. Second, within each shell, the energy of a subshell level increases
with the value of the l quantum number. For example, the energy of a 3d
state is greater than a 3p, which is larger than 3s. Finally, there may be overlap inenergy of a state in one shell with states in an adjacent shell, which is especially true
of d and f states; for example, the energy of a 3d state is greater than that for a 4s.
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