Question

Explain what each quantum number in a quantum number set tells you about the electron. Compare and contrast the locations and properties of two electrons within an atom that have the quantum number sets (3, 2, -1, +½) and (3, 1, -1, +½).

Answer 1

Quantum Numbers
The allowed values and general meaning of each of the four quantum numbers of an
electron in an atom are as follows:
1. Principal Quantum Number (n) This quantum number is the one on which
the energy of an electron in an atom principally depends; it can have any positive
value: 1, 2, 3, and so on. The energy of an electron in an atom depends principally
on n. The smaller n is, the lower the energy. In the case of the hydrogen
atom or single-electron atomic ions, such as Li2 and He, n is the only quantum
number determining the energy (which is given by Bohr’s formula, discussed in
Section 7.3). For other atoms, the energy also depends to a slight extent on the l
quantum number.
The size of an orbital also depends on n. The larger the value of n is, the larger
the orbital. Orbitals of the same quantum state n are said to belong to the same shell.
Shells are sometimes designated by the following letters:
Letter K L M N . . .
n 1 2 3 4 . . .
2. Angular Momentum Quantum Number (l ) (Also Called Azimuthal Quantum
Number) This quantum number distinguishes orbitals of given n having different
shapes; it can have any integer value from 0 to n 1. Within each shell of
quantum number n, there are n different kinds of orbitals, each with a distinctive shape
denoted by an l quantum number. For example, if an electron has a principal quantum
number of 3, the possible values for l are 0, 1, and 2. Thus, within the M shell
(n 3), there are three kinds of orbitals, each having a different shape for the region
where the electron is most likely to be found. These orbital shapes will be discussed
later in this section.
Although the energy of an orbital is principally determined by the n quantum
number, the energy also depends somewhat on the l quantum number (except for the
H atom). For a given n, the energy of an orbital increases with l.
Orbitals of the same n but different l are said to belong to different subshells of
a given shell. The different subshells are usually denoted by letters as follows:
Letter s p d f g . . .
l 0 1 2 3 4 . . .
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 l 1. <
3. Magnetic Quantum Number (ml) This quantum number distinguishes orbitals
of given n and l—that is, of given energy and shape but having a different orientation
in space; the allowed values are the integers from l to l. For l 0 (s subshell),
the allowed ml quantum number is 0 only; there is only one orbital in the s subshell.
For l 1 ( p subshell), ml 1, 0, and 1; there are three different orbitals in the
p subshell. The orbitals have the same shape but different orientations in space. In