Chemistry Reference
In-Depth Information
integer numbers of l from 0 to (n−1) (Lide 2008). Consequently, each energy layer cor-
responding to a principal quantum number is made of a specific number of subshells
corresponding to the values of those orbitals. These subshells are represented with the
letters s, p, d, f, g corresponding to the secondary quantum numbers as follows:
l =
0
1
2
3
4
s
p
d
f
g
To specify the principal level, the letters s, p, d, f, and g are preceded by the
number that indicates the level to which that substrate belongs. The first energy level
contains a single subshell marked as 1s; the second principal energy level includes
two subshells marked as 2s and 2p; and so on.
The subshells also include a certain number of stable orbitals and a maximum
number of electrons. The difference in energy between different subshells deter-
mines the shape of the orbitals, and the orbital quantum number describes the orbital
shape.
For n = 1, we have l = 0 and the orbit is spherical. For n ≠ 1 and the values l = 1, 2, 3 …
the orbits are ellipses that look like nodal planes with each part forming a lobe. These
planes are similar, but perpendicular to each other for degenerate orbitals.
Since electrons are charged particles, they produce a magnetic field as they move.
Thus, the orbitals are, in turn, characterized by a magnetic quantum number (ml).
l
).
This number takes 2l + 1 values from −l to +l and reflects how many electrons can
exist on each orbital on each subshell, as well as their orientation in an exterior mag-
netic field. For example, there are four orbitals for n = 2, one in the sublevel s and
three in the sublevel l = 1 with ml
l
equal to +1, 0 and −1. Therefore, the s subshell has
only one orbital, the subshell p has three orbitals, the subshell d has five orbitals, and
the subshell f has seven orbitals.
The orbitals in a subshell have the same average (median) energy and are called
degenerate orbitals
. Consequently, the three p orbitals (p
x
, p
y
, and p
z
) have the same
energy; this also holds true for the five d orbitals or the seven f orbitals.
The fourth quantum number characterizes the movement or autorotation around
the electron's own axis. It is called the
spin motion
and is characterized by an angular
momentum and an inherent magnetic momentum, both of which can be quantified.
Accordingly, an electron has two spin states only, one in the clockwise state (↑ state)
and one in the counterclockwise state (↓ state). This quantitation is represented by
the magnetic quantum number of the spin and has only two values for an electron.
The number of electrons that rotate on a certain level around the nucleus is
determined by precise quantum laws. The filling of orbitals with electrons occurs
according to the Aufbau principle (in German the “construction principle”) so that
the electronic configuration leads to the lowest energy state. This principle uses the
rule of Hund and the rule of Pauli.
There are a maximum of 2 electrons for an orbital. Pauli's exclusion principle
shows that 2 electrons cannot exist in the same quantum state, that is, with 4 identical
numbers. They must differ at least by one quantum number. That means that there
will be a maximum of 2 electrons in each orbital that have different values of the
magnetic quantum number.
