Dans un atome, combien d'électrons peuvent-ils être caractérisés par les valeurs suivantes d'un

Dans un atome, combien d'électrons peuvent-ils être...

Key Concepts

Quantum Numbers

Quantum numbers are sets of numerical values that describe the properties and behavior of electrons in an atom. They include numbers associated with energy levels, orbital shapes, orbital orientations, and electron spins. These values uniquely specify the state of an electron and are foundational in understanding atomic structure and electron configuration.

Principal Quantum Number (n)

The principal quantum number, denoted by n, indicates the energy level or shell in which an electron resides. It determines the overall size and energy of an orbital, with higher values of n corresponding to orbitals that are larger and of higher energy. This number is a key factor in organizing electrons into shells around the nucleus.

Orbital Angular Momentum Quantum Number (l)

The orbital angular momentum quantum number, l, defines the shape of an electron’s orbital and takes on integer values from 0 up to n-1. This number is important for distinguishing among subshells (s, p, d, f, etc.) and plays a crucial role in the spatial distribution of the electron’s probability density within the atom.

Magnetic Quantum Number (m_l)

The magnetic quantum number, m_l, specifies the orientation of an orbital in space relative to an external magnetic field. Its values range from -l to +l in integer steps, defining the different possible angular orientations (or degeneracy) within a given subshell. This quantum number is essential for understanding how orbitals split in magnetic fields.

Spin Quantum Number (m_s)

The spin quantum number, m_s, characterizes the intrinsic angular momentum, or spin, of an electron. It can take on one of two values, generally represented as +1/2 or -1/2. These two orientations are central to the electron pairing mechanism and influence how electrons populate orbitals while obeying the Pauli exclusion principle.

Pauli Exclusion Principle

The Pauli exclusion principle states that no two electrons in an atom can have the same set of all four quantum numbers. This principle is fundamental in determining the electron configuration of atoms and explains why electrons must occupy different quantum states, leading to the structured filling of orbitals.

Quantum State Degeneracy

Quantum state degeneracy refers to the phenomenon where multiple quantum states share the same energy. In the context of atomic orbitals, degeneracy is determined by the number of allowable values of m_l for a given l, meaning that several orbitals can exist at the same energy level. This concept is critical when counting the number of electrons that can be found under specific quantum conditions.

Transcript

00:02 Hi, this is problem number 84, and in problem number 84, we are given sets of quantum numbers and ask the maximum number of electrons that we could put into the orbital, where orbitals describe those quantum numbers.

00:18 So let's go ahead and get started.

00:20 With letter a, we are given a principal quantum number of n equals 3, and an angular momentum quantum number of l equals 1.

00:30 When l equals 1, we have p orbitals.

00:36 And any time we have p orbitals, there are three of those.

00:41 We also know that the maximum number of electrons we can put into any orbital is two.

00:47 So if we take each of those p orbitals, remember there are three because there's three orientations in space along the x axis, along the y axis, and along the z axis.

00:57 So if we multiply three times two electrons in each of those, we get a maximum number of electrons of six.

01:05 So we could place six electrons in the orbitals described by this pair of quantum numbers.

01:15 For letter b, we have n equals three again, but now l equals two.

01:23 When l equals two, these are d -orbital.

01:31 And if you think about the pictures of the de -orbital, there are five of those.

01:36 Again, we can put a maximum of two electrons in each of those.

01:39 So that gives us a total maximum count of 10 electrons.

01:49 All right, for letter c, we have n equals 3, l equals 0, and m sub l.

02:00 So now they're also giving us the magnetic quantum number of negative 1.

02:13 Okay, looking at this, technically, this orbital does not exist.

02:21 Because l equals 0.

02:23 Remember, m sub l ranges from negative l to positive l.