What is the designation for the subshell with n = 5 and l = 1? b. How many orbitals are in this subshell? c. Indicate the values of ml for each of these orbitals.
The Correct Answer and Explanation is:
Correct Answers:
a. The designation for the subshell with n = 5 and l = 1 is 5p.
b. There are 3 orbitals in this subshell.
c. The values of ml (magnetic quantum number) for these orbitals are –1, 0, and +1.
Explanation
In quantum mechanics, the structure of atoms is described using four quantum numbers: n, l, ml, and ms. These determine the energy, shape, orientation, and spin of atomic orbitals.
Let’s break down each part of the question using this framework:
a. Subshell Designation:
The principal quantum number (n = 5) represents the energy level or shell. The azimuthal quantum number (l = 1) describes the subshell and shape of the orbital. The values of l correspond to subshell letters:
- l = 0 → s
- l = 1 → p
- l = 2 → d
- l = 3 → f
- l = 4 → g (less common in known elements)
So, when n = 5 and l = 1, the subshell is designated 5p.
b. Number of Orbitals:
The number of orbitals in a subshell is determined by the number of possible values of the magnetic quantum number (ml), which ranges from –l to +l, including 0.
For l = 1, ml can be: –1, 0, and +1 — which means there are 3 orbitals.
c. ml Values:
As stated, the ml values for a p subshell (l = 1) are:
- ml = –1
- ml = 0
- ml = +1
Each orbital can hold 2 electrons with opposite spins (ms = ±½), so the 5p subshell can accommodate 6 electrons total (3 orbitals × 2 electrons).
Understanding these quantum numbers helps explain the periodic table’s structure, electron configurations, and the chemical behavior of elements. For example, the 5p subshell begins filling in elements like iodine (I), which influences their reactivity and placement in the periodic table.
