Give One Permissible Set Of Four Quantum Numbers For Each Of The Outermost Electrons In A Single As Atom When It Is In Its Ground State.
The correct answer and explanation is :
Answer:
For a single arsenic (As) atom in its ground state, the outermost electron is located in the 4p orbital. The quantum numbers for one of these electrons can be:
- Principal quantum number (n): 4
- Azimuthal quantum number (l): 1 (since it is in a p orbital)
- Magnetic quantum number (mₗ): -1, 0, or +1 (any of the three possible orientations of the p orbital)
- Spin quantum number (mₛ): +½ or -½ (since electrons can have either spin up or spin down)
A valid set of quantum numbers for one of the outermost electrons in arsenic:
(4, 1, -1, +½)
Explanation:
- Understanding the electron configuration of As (Z = 33):
The full ground-state electron configuration of arsenic is:
1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p³
The outermost electrons are in the 4p subshell, which contains three electrons. - Defining quantum numbers:
- Principal quantum number (n):
It describes the energy level of the electron. Since the outermost electron is in the 4p orbital, n = 4. - Azimuthal quantum number (l):
It defines the shape of the orbital. For a p orbital, l = 1. - Magnetic quantum number (mₗ):
It determines the specific orbital within the subshell. For p orbitals (l = 1), possible values are -1, 0, +1. - Spin quantum number (mₛ):
It describes the electron’s spin, which can be either +½ (spin-up) or -½ (spin-down).
Since arsenic has three electrons in the 4p orbital, each electron will occupy a separate p orbital (Hund’s Rule). One valid set is (4, 1, -1, +½), but other valid combinations exist.