A) Combien d'électrons peut accueillir au maximum une...

a) Combien d'électrons peut accueillir au maximum une sous-couche $l$ ? b) Combien d'électrons peuvent contenir, au maximum, les couches K, L, M. Pouvez-vous généraliser ces résultats? c) Combien d'électrons peut décrire au maximum une orbitale d ? d) Combien de cases quantiques peut-on prévoir relativement à $n=4$ ?

a) Combien d'électrons peut accueillir au maximum une sous-couche $l$ ?
b) Combien d'électrons peuvent contenir, au maximum, les couches K, L, M. Pouvez-vous généraliser ces résultats?
c) Combien d'électrons peut décrire au maximum une orbitale d ?
d) Combien de cases quantiques peut-on prévoir relativement à $n=4$ ?

Key Concepts

Orbitals and the Pauli Exclusion Principle

An orbital is a region in space where there is a high probability of finding an electron, and each orbital is defined by a specific set of quantum numbers (n, l, m). According to the Pauli Exclusion Principle, each orbital can host a maximum of 2 electrons with opposite spins. This rule applies to all types of orbitals, such as d orbitals.

Atomic Shells and Their Electron Capacity

An atomic shell is specified by the principal quantum number n and comprises all subshells with l ranging from 0 to (n – 1). The overall capacity of a shell is the sum of the electrons in all its subshells. This total is given by the formula 2n², which shows, for instance, that the first three shells (K, L, M corresponding to n = 1, 2, 3) can hold 2, 8, and 18 electrons, respectively.

Degeneracy of Quantum States

Degeneracy in this context refers to the number of quantum states (or cases) available for a given energy level, which is determined by the different possible combinations of quantum numbers. For example, for a principal quantum number n=4, the total number of orbitals is calculated by summing (2l + 1) for l = 0 to 3, resulting in 16 orbitals. When each orbital is capable of holding 2 electrons, the shell can accommodate up to 32 electrons.

Quantum Numbers

Electrons in atoms are characterized by a set of quantum numbers, primarily the principal quantum number (n), the azimuthal or orbital angular momentum quantum number (l), and the magnetic quantum number (m). These numbers determine the energy level, shape, and orientation of the electron orbitals and are essential in calculating how many electrons can occupy a given subshell or shell.

Subshells

A subshell is defined by a particular value of the azimuthal quantum number, l. For each subshell, the magnetic quantum number, m, takes values from –l to +l, which gives a total of (2l + 1) orbitals. Since each orbital can hold 2 electrons, the maximum number of electrons in a subshell with quantum number l is 2(2l + 1).

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