The quantum mechanical model revolutionized our understanding of atoms. It describes electrons as waves, with their positions determined by probability. This model introduces atomic orbitals - mathematical functions that represent the likelihood of finding electrons in specific regions around the nucleus.
Atomic orbitals come in various shapes and sizes, each with unique properties. The s, p, and d orbitals differ in shape, energy, and electron capacity. Understanding these orbitals is crucial for grasping electron configurations and chemical bonding.
Quantum Mechanical Model and Atomic Orbitals
Wave functions and orbitals
Represents electrons as wave functions (Ψ) describe probability of finding an electron in a given region of space
Obtained by solving for a particular atom or molecule (hydrogen atom)
Atomic orbitals are mathematical functions describe probability distribution of electrons in an atom
Associated with specific energy level and shape (1s, 2p, 3d)
Electrons occupy orbitals in order of increasing energy following (1s < 2s < 2p < 3s)
Square of (Ψ2) at a given point represents of finding an electron at that location
Orbitals designated by (n), (l), and (ml)
Shapes of s, p, and d orbitals
s orbitals (l = 0)
Spherically symmetric around nucleus (1s, 2s, 3s)
Hold maximum of 2 electrons
Exist in every principal energy level (n = 1, 2, 3, etc.)
p orbitals (l = 1)
with two lobes (2p, 3p)
Hold maximum of 6 electrons with 2 electrons per orbital
Exist in principal energy levels n ≥ 2
Three types: px, py, and pz, oriented along x, y, and z axes
d orbitals (l = 2)
More complex shapes including and (3d, 4d)
Hold maximum of 10 electrons with 2 electrons per orbital
Exist in principal energy levels n ≥ 3
Five types: dxy, dxz, dyz, dx2−y2, and dz2
Spatial orientation of p orbitals
Three p orbitals (px, py, and pz) oriented perpendicular to each other along x, y, and z axes
Each p orbital consists of two lobes with opposite algebraic signs (+ and -)
Opposite signs indicate phase difference of 180° between two lobes
Algebraic signs do not represent positive or negative charge
is a region in an orbital where probability of finding an electron is zero
p orbitals have that passes through nucleus, separating two lobes
Presence of nodes is consequence of wave-like nature of electrons
When orbitals overlap during bonding, phase of lobes (+ or -) determines whether constructive (bonding) or destructive (antibonding) interference occurs
Electron Configuration and Orbital Filling
describes the arrangement of electrons in atomic orbitals
states that no two electrons in an atom can have the same set of quantum numbers
Limits each orbital to a maximum of two electrons with opposite spins
dictates that electrons occupy singly with parallel spins before pairing
is an intrinsic angular momentum of an electron, represented as +1/2 or -1/2
Degenerate orbitals are orbitals with the same energy level (e.g., 2px, 2py, and 2pz)
provides the theoretical framework for understanding atomic structure and electron behavior
is a mathematical description of the quantum state of an electron in an atom
Key Terms to Review (33)
Angular Momentum Quantum Number: The angular momentum quantum number, denoted as $l$, is a quantum number that describes the angular momentum of an electron within an atom. It is one of the principal quantum numbers that determine the allowed energy levels and spatial distributions of electrons in an atom.
Atomic Orbital: An atomic orbital is a mathematical function that describes the wave-like behavior of an electron in an atom. It defines the region of space where an electron is likely to be found around the nucleus of an atom.
Aufbau principle: The Aufbau principle is a guideline used in organic chemistry to determine the electron configuration of an atom, molecule, or ion. It states that electrons occupy the lowest energy orbitals first before filling higher energy levels.
Aufbau Principle: The Aufbau principle is a fundamental concept in quantum mechanics that describes the order in which electrons occupy atomic orbitals. It is a crucial principle that governs the electron configurations of atoms and is closely tied to the understanding of atomic structure and chemical bonding.
Cloverleaf: A cloverleaf is a type of atomic orbital in quantum mechanics, specifically a p-orbital, that has a distinctive three-lobed shape resembling a clover leaf. This orbital configuration is crucial in understanding the behavior and properties of atoms and molecules.
Constructive Interference: Constructive interference is a phenomenon that occurs when two or more waves, such as light or sound waves, interact in a way that reinforces or amplifies the resulting wave. This happens when the crests of the waves align, causing the amplitudes to add together, resulting in a larger overall wave.
D-orbital: The d-orbital is a type of atomic orbital that is found in the electron shells of atoms. It is characterized by a more complex shape and higher energy level compared to the s-orbital and p-orbital, and plays a crucial role in the electronic structure and bonding of certain elements, particularly transition metals.
Degenerate Orbitals: Degenerate orbitals are a set of atomic orbitals that have the same energy level, or are energetically equivalent, within a given atom or molecule. These orbitals can be occupied by electrons without any increase in the overall energy of the system.
Destructive Interference: Destructive interference is a phenomenon that occurs when two waves, such as sound or light waves, interact in a way that results in the cancellation or reduction of the wave amplitude at certain points. This happens when the crests of one wave align with the troughs of another wave, causing them to cancel each other out.
Double-Dumbbell: The double-dumbbell is a structural feature in atomic orbitals where two distinct lobes or regions of high electron density are present. This arrangement is particularly relevant in the context of understanding the spatial distribution and shape of atomic orbitals, a key aspect of atomic structure.
Dumbbell-shaped: Dumbbell-shaped refers to the characteristic shape of certain atomic orbitals, where the electron density is concentrated in two lobes or bulges connected by a narrower region. This unique shape arises from the specific mathematical functions that describe the behavior of electrons within an atom's quantum mechanical framework.
Electron configuration: Electron configuration describes the distribution of electrons in an atom's atomic orbitals. It follows a set of rules, including the Pauli exclusion principle and Hund's rule, to show how these electrons are arranged around the nucleus.
Electron Configuration: Electron configuration refers to the arrangement of electrons in an atom's orbitals, which determines the atom's chemical properties and behavior. This concept is central to understanding the structure and behavior of atoms, as well as the formation of chemical bonds and the properties of molecules.
Electron shells: Electron shells are layers around the nucleus of an atom where electrons reside, determined by their energy level. The number of electron shells and their occupancy by electrons govern the chemical properties of an atom.
Electron Spin: Electron spin is a fundamental property of electrons that describes their intrinsic angular momentum. It is a quantum mechanical property that arises from the behavior of electrons at the subatomic level, and it is a crucial concept in understanding the structure and behavior of atoms and molecules.
F-orbital: An f-orbital is a type of atomic orbital in an atom's electron configuration. It is the fifth principal energy level and is characterized by a high angular momentum quantum number, which results in a complex spatial distribution of the electron density.
Hund's Rule: Hund's rule is a fundamental principle in quantum mechanics that describes the electronic configuration of atoms. It states that when electrons occupy degenerate orbitals, they will occupy these orbitals singly with parallel spins before pairing up.
Magnetic Quantum Number: The magnetic quantum number is a quantum number that describes the orientation of an atomic orbital in space. It is one of the four quantum numbers used to fully describe the state of an electron in an atom.
Nodal Plane: A nodal plane is a plane within an atomic orbital where the probability density of finding an electron is zero. It represents a region where the wave function of an electron changes sign, indicating the location where the wave function is equal to zero.
Node: A node is a fundamental concept in various fields, including atomic structure, molecular orbital theory, and the stability of conjugated dienes. It represents a specific point or location within a system, where important properties or interactions occur.
P-orbital: A p-orbital is one of the possible shapes of electron orbitals in an atom. It is a higher energy orbital that can hold up to six electrons and has a more complex shape compared to the s-orbital.
Pauli exclusion principle: The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers. This principle helps determine electron configurations within atoms, crucial for understanding chemical bonding and molecular structure in organic chemistry.
Pauli Exclusion Principle: The Pauli exclusion principle is a fundamental principle in quantum mechanics that states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. This principle has far-reaching implications for the structure of atoms, the organization of the periodic table, and the behavior of chemical bonds.
Principal Quantum Number: The principal quantum number is a fundamental concept in atomic structure that describes the energy level or shell of an electron within an atom. It is a key parameter that determines the overall energy and spatial distribution of electrons in an atom.
Probability Density: Probability density is a fundamental concept in quantum mechanics that describes the likelihood of finding a particle in a specific region of space. It is a measure of the probability per unit volume of a particle being present at a given location.
Quantum Mechanics: Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy on the atomic and subatomic scale. It is the foundation for understanding the properties and interactions of particles at the quantum level.
S-orbital: An s-orbital is a type of atomic orbital that has a spherical shape and is the lowest energy level orbital in an atom. It is characterized by a quantum number of 0 and is the simplest and most symmetrical of the atomic orbitals.
Schrödinger equation: The Schrödinger equation is a fundamental equation in quantum mechanics that describes the wave-like behavior of particles. It is used to determine the quantum state of a particle and how it evolves over time.
Spherical: Spherical refers to the shape of an object or entity that is perfectly round, like a sphere. In the context of atomic structure and orbitals, this term describes the spatial distribution of electrons around the nucleus of an atom.
Wave equation: The wave equation in the context of organic chemistry and specifically within the topic of atomic structure and orbitals is a mathematical formula used to describe the behavior of electrons in atoms as waves, rather than just particles. It helps predict where an electron is likely to be found around a nucleus.
Wave function: A wave function is a mathematical description of the quantum state of an isolated quantum system, representing the probability amplitude of a particle's position and other variables. In organic chemistry, it particularly helps in understanding the behavior of electrons within atomic orbitals.
Wave Function: The wave function is a mathematical function that describes the quantum state of an object, such as an electron or a particle. It is a fundamental concept in quantum mechanics that provides a complete description of the behavior and properties of a particle or system.
Wavefunction: The wavefunction is a mathematical function that describes the quantum state of an electron or other particle in an atomic or subatomic system. It is a fundamental concept in quantum mechanics that provides a complete description of the particle's behavior and properties.