The quantum numbers for the last electron added to a sulfur atom are n=3, l=1, m_l=1, and m_s=-1/2. This specific set uniquely describes the quantum state of this particular electron within the sulfur atom.
Understanding Quantum Numbers for Sulfur's Last Electron
Sulfur (S) is element number 16, possessing 16 electrons in a neutral atom. When considering "the quantum number of sulfur," it typically refers to the unique set of quantum numbers for a specific electron, most often the highest-energy electron or the last one added during the Aufbau filling process.
The electron configuration for sulfur is:
1s² 2s² 2p⁶ 3s² 3p⁴
From this configuration, it's evident that the 3p subshell is the outermost and highest-energy subshell to contain electrons. The "last electron added" refers to one of the four electrons residing in this 3p subshell.
The Four Quantum Numbers Defined for Sulfur's 3p Electron
Each electron within an atom is characterized by a unique set of four quantum numbers. For one of the 3p electrons in sulfur, specifically identified as the "last electron added," a possible and valid set of these numbers is:
| Quantum Number | Symbol | Value | Description |
|---|---|---|---|
| Principal Quantum Number | n |
3 | This number defines the electron's principal energy level or electron shell. Since the electron is in the 3p subshell, it belongs to the third energy shell, so n is 3. |
| Angular Momentum Quantum Number | l |
1 | Also known as the azimuthal or orbital shape quantum number, l determines the shape of the orbital and identifies the subshell (s, p, d, f). For a p-orbital, the value of l is always 1. |
| Magnetic Quantum Number | m_l |
1 | This number specifies the orientation of the orbital in three-dimensional space. For a p-subshell, the possible m_l values are -1, 0, or 1, each corresponding to a distinct p-orbital (e.g., px, py, pz). The value of 1 indicates one specific orientation. |
| Spin Quantum Number | m_s |
-1/2 | This describes the intrinsic angular momentum of the electron, often referred to as its "spin." Electrons can spin in one of two directions, yielding m_s values of +1/2 or -1/2. This value indicates a specific spin direction for the electron. |
Deriving Quantum Numbers for the 3p⁴ Configuration
The 3p subshell consists of three degenerate (equal energy) orbitals. According to Hund's Rule, electrons will first singly occupy each orbital within a subshell with parallel spins before pairing up.
For sulfur's 3p⁴ configuration:
- The first three electrons in the 3p subshell would each occupy a different 3p orbital (e.g.,
m_l= -1, 0, and 1), typically with an upward spin (m_s= +1/2). - The fourth electron, which is the "last added" in this context, must then pair up in one of these already partially filled orbitals. When it pairs, it will have an opposite spin. The provided set of quantum numbers indicates that this fourth electron occupies the 3p orbital with
m_l= 1 and has a spin ofm_s= -1/2. This represents a valid and specific set of quantum numbers for the last electron added to a sulfur atom.
Significance of Quantum Numbers
These four quantum numbers are crucial for understanding the quantum mechanical model of the atom. They define the unique quantum state of an electron, encompassing its energy, spatial distribution, and spin. This information is fundamental to predicting an atom's chemical behavior, including its reactivity, how it forms bonds, and its properties within the periodic table. The Pauli Exclusion Principle ensures that no two electrons in the same atom can share the exact same set of all four quantum numbers, highlighting the distinct identity of each electron's state.
For further exploration of electron configurations and quantum numbers, comprehensive resources such as Khan Academy's explanation of the Quantum Mechanical Model can provide additional insights.
