Les nombres quantiques n, l et m1 peuvent-ils avoir ensemble...

Les nombres quantiques $n, l$ et $m_1$ peuvent-ils avoir ensemble les valeurs suivantes? Si oui, quelle sous-couche caractérisent-elles? $$ \begin{array}{lrrr} & n & l & m_1 \\ \text { a) } & 2 & 0 & 0 \\ \text { b) } & 4 & 1 & -2 \\ \text { c) } & 3 & 1 & -1 \\ \text { d) } & 4 & -1 & 0 \\ \text { e) } & 2 & 0 & -1 \end{array} $$$$ \begin{array}{lllr} & n & l & m_1 \\ \text { f) } & 5 & 3 & -3 \\ \text { g) } & 4 & 2 & 2 \\ \text { h) } & 2 & 3 & 3 \\ \text { i) } & 3 & 0 & 0 \\ \text { j) } & 5 & 2 & -2 \end{array} $$

Les nombres quantiques $n, l$ et $m_1$ peuvent-ils avoir ensemble les valeurs suivantes? Si oui, quelle sous-couche caractérisent-elles?
$$
\begin{array}{lrrr}
& n & l & m_1 \\
\text { a) } & 2 & 0 & 0 \\
\text { b) } & 4 & 1 & -2 \\
\text { c) } & 3 & 1 & -1 \\
\text { d) } & 4 & -1 & 0 \\
\text { e) } & 2 & 0 & -1
\end{array}
$$$$
\begin{array}{lllr}
& n & l & m_1 \\
\text { f) } & 5 & 3 & -3 \\
\text { g) } & 4 & 2 & 2 \\
\text { h) } & 2 & 3 & 3 \\
\text { i) } & 3 & 0 & 0 \\
\text { j) } & 5 & 2 & -2
\end{array}
$$

Key Concepts

Allowed Quantum Number Ranges

Quantum numbers must satisfy specific rules: n is any positive integer, l can only take integer values from 0 up to n–1, and for any given l, m can only be any integer between –l and +l. These restrictions underlie the structure of atomic orbitals and determine which sets of quantum numbers represent physically allowed states.

Magnetic Quantum Number m

The magnetic quantum number, commonly denoted as m or m?, specifies the orientation of the orbital in space. For a given l, its possible values range from –l to +l in integer steps. This quantum number is responsible for the splitting of energy levels when an external magnetic field is applied.

Subshell Notation

The subshell notation is a labeling system for electron orbitals based on the angular momentum quantum number l. Common designations are s for l = 0, p for l = 1, d for l = 2, and f for l = 3. This notation helps in identifying the type and shape of the orbital in which an electron is found.

Quantum Number n

The principal quantum number, n, defines the main energy level of an electron in an atom. It is a positive integer (n = 1, 2, 3, ...) and essentially determines the size and energy of the orbital. As n increases, the electron is found on average further from the nucleus and in a higher energy state.

Quantum Number l

The angular momentum quantum number, l, describes the shape of the electron orbital. Its allowed values are integers from 0 to n-1 for a given principal quantum number n. Each value of l corresponds to a specific type of orbital (e.g., l = 0 corresponds to s, l = 1 to p, l = 2 to d, and l = 3 to f orbitals).

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