The following is a representation of the orbital diagram of Al. What are the four quantum numbers of the electron highlighted in the 3s subshell? 1s 2s 2p 3s
The correct answer and explanation is :
The four quantum numbers for the highlighted electron in the 3s subshell of aluminum (Al) are:
- Principal quantum number (n): 3
- Azimuthal quantum number (ℓ): 0
- Magnetic quantum number (mₗ): 0
- Spin quantum number (mₛ): +½ (or -½ depending on which of the two electrons in the 3s orbital is highlighted)
Explanation (Approx. 300 Words):
Quantum numbers describe the properties and location of an electron in an atom. Aluminum (Al) has an atomic number of 13, meaning it has 13 electrons in its neutral state. These electrons fill orbitals in the following order:
1s² 2s² 2p⁶ 3s² 3p¹
The orbital diagram for aluminum can be represented as:
1s ↑↓
2s ↑↓
2p ↑↓ ↑↓ ↑↓
3s ↑↓
3p ↑We are focusing on an electron in the 3s subshell, which has two electrons.
Each electron is characterized by four quantum numbers:
- Principal Quantum Number (n):
This indicates the main energy level or shell.
For the 3s subshell, n = 3. - Azimuthal Quantum Number (ℓ):
This defines the subshell or orbital shape.
For s-orbitals, ℓ = 0. - Magnetic Quantum Number (mₗ):
This defines the orientation of the orbital.
For ℓ = 0, the only possible value is mₗ = 0. - Spin Quantum Number (mₛ):
This indicates the spin of the electron, which can be either +½ (spin-up) or -½ (spin-down).
The 3s orbital contains two electrons: one with mₛ = +½ and one with mₛ = -½.
Since the question mentions a “highlighted” electron but doesn’t specify which of the two in the 3s orbital is meant, both spins are possible. If the diagram shows the first (spin-up) electron, the spin is +½. If it’s the second, it’s -½.
Therefore, one possible set of quantum numbers for the 3s electron is:
(n = 3, ℓ = 0, mₗ = 0, mₛ = +½)