91Ó°ÊÓ

To understand the quantum numbers associated with magnesium, we first need to look at its electron configuration. Magnesium, which has the atomic number 12, houses 12 electrons. The electron configuration describes how these electrons are organized within the atom's shells and subshells. For magnesium, this arrangement can be denoted as \( [\text{Ne}] \, 3s^2 \). To express it in a more detailed manner, we consider it as \( 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \).
This configuration shows us that:
\(1s\) subshell holds 2 electrons, \(2s\) subshell contains another 2 electrons, \(2p\) subshell has 6 electrons, and the \(3s\) subshell carries the last 2 electrons.
This arrangement relates directly to the effective distribution of quantum numbers, which are characteristics that describe each electron's position and behavior.

The principal quantum number, expressed as \( n \), plays a pivotal role in atomic structure. It indicates the electron shell level or the energy level in which electrons reside. Increasing \( n \) means electrons are situated further from the atomic nucleus.
For magnesium:

• The electrons in the \(1s\) orbital have a principal quantum number \(n = 1\).
• Those in the \(2s\) and \(2p\) orbitals have \(n = 2\).
• The electrons in the \(3s\) orbital have \(n = 3\).

As \(n\) increases, the energy level ascends, meaning electrons in higher levels require more energy to be removed from the atom.

The azimuthal quantum number, symbolized by \( l \), defines the subshell or the shape of the orbital in which the electron is located. Its values range from \(0\) to \(n-1\).

• For \(s\) orbitals, like \(1s\), \(2s\) and \(3s\), the azimuthal quantum number \(l\) is \(0\). These are spherical.
• For \(2p\) orbitals, the quantum number \(l\) is \(1\). These have a dumbbell shape.

Each different value of \( l \) pertains to a specific subshell (\(s, p, d, f\)), delineating the shape and energy level differences within a principal level.

The spin quantum number, denoted as \( s \), represents the intrinsic angular momentum of the electrons, commonly known as 'spin' and can either be \( +\frac{1}{2} \) or \( -\frac{1}{2} \). This characteristic describes the orientation of an electron's spin in its magnetic field.
Considering magnesium's electron configuration:

• Each orbital can hold 2 electrons, with opposing spins, making use of \(s = +\frac{1}{2}\) and \(s = -\frac{1}{2}\).
• This is true for all orbitals: \(1s, 2s, 2p,\) and \(3s\).

The pairing of opposite spins in an orbital reduces repulsion between electrons due to their negative charges, thus stabilizing the atom's structure.