4.2 Multi-electron atoms and electron configurations
4 min read•august 7, 2024
Multi-electron atoms are complex systems where electron interactions shape atomic properties. Electron-electron repulsion and shielding affect energy levels, while the and guide electron configurations.
Understanding these concepts helps explain periodic trends in atomic properties. Atomic radius, , and patterns across the periodic table stem from the interplay between nuclear charge and .
Electron Interactions and Shielding
Electron-Electron Repulsion and Shielding
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- Electrons in an atom repel each other due to their negative charges
- This electron-electron repulsion affects the energy and stability of the atom
- Inner shell electrons shield the outer shell electrons from the full positive charge of the nucleus
- Shielding effect reduces the experienced by the outer electrons
- Effective nuclear charge () is the net positive charge experienced by an electron in a multi-electron atom
- is calculated as the nuclear charge () minus the shielding constant ():
- Shielding constant represents the number of inner shell electrons that shield the outer electron from the nucleus
- Example: In a carbon atom, the two 1s electrons shield the 2s and 2p electrons from the full +6 nuclear charge
- Example: The effective nuclear charge experienced by the 2s electron in lithium is +1.26, reduced from the +3 nuclear charge due to shielding by the 1s electrons
Electron Configurations and Energy
- Electron configuration describes the arrangement of electrons in an atom's orbitals
- Electron configurations are written using the notation: 1s²2s²2p⁶3s²3p³
- The superscript numbers indicate the number of electrons in each orbital
- Electrons fill orbitals in order of increasing energy, following the Aufbau principle
- Electrons in the same subshell have parallel spins, as stated by Hund's rule, to minimize electron-electron repulsion
- Example: The electron configuration of nitrogen is 1s²2s²2p³, with three unpaired electrons in the 2p subshell
- Example: The electron configuration of calcium is 1s²2s²2p⁶3s²3p⁶4s², with all orbitals filled up to 4s
Electron Configuration Principles
Aufbau Principle and Hund's Rule
- The Aufbau principle states that electrons fill orbitals in order of increasing energy
- The order of filling is: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f
- Electrons occupy orbitals singly before pairing up, as stated by Hund's rule
- Hund's rule minimizes electron-electron repulsion by keeping electrons with parallel spins in different orbitals within a subshell
- Example: The electron configuration of carbon (1s²2s²2p²) has two unpaired electrons in the 2p subshell, following Hund's rule
- Example: The electron configuration of chromium (1s²2s²2p⁶3s²3p⁶4s¹3d⁵) has six unpaired electrons, maximizing the number of parallel spins
Slater Determinants and Term Symbols
- Slater determinants are a way to represent the wavefunction of a multi-electron system
- Slater determinants ensure that the wavefunction is antisymmetric with respect to the exchange of any two electrons
- The determinant is constructed using the one-electron wavefunctions (orbitals) as the rows and the electron coordinates as the columns
- Term symbols are used to describe the electronic state of an atom or molecule
- Term symbols have the format , where is the total spin angular momentum, is the total orbital angular momentum, and is the total angular momentum
- Example: The term symbol for the ground state of carbon is , indicating a triplet state with L=1 and J=0
- Example: The term symbol for the first excited state of helium is , indicating a triplet state with L=0 and J=1
Periodic Trends
Trends in Atomic Properties
- The periodic table arranges elements based on their atomic number and electron configuration
- Periodic trends describe the regular patterns in atomic properties across the periodic table
- Atomic radius generally decreases from left to right across a period and increases down a group
- Ionization energy increases from left to right across a period and decreases down a group
- Electron affinity generally increases from left to right across a period and decreases down a group
- Electronegativity increases from left to right across a period and decreases down a group
- These trends arise from the interplay between the increasing nuclear charge and the shielding effect of inner electrons
- Example: Lithium has a larger atomic radius than beryllium because the 2s electron in lithium is less tightly bound to the nucleus
- Example: Fluorine has a higher electron affinity than oxygen because the added electron experiences a greater effective nuclear charge in fluorine
Anomalies and Exceptions
- Some elements deviate from the general periodic trends due to their unique electron configurations
- The lanthanides and actinides, known as the f-block elements, have similar properties within each series due to the filling of the 4f and 5f orbitals
- The d-block elements (transition metals) exhibit less regular trends due to the complex interplay between the s and d electrons
- Example: The atomic radius of potassium is larger than that of argon, despite being in the same period, due to the presence of the 4s electron in potassium
- Example: The electron configuration of chromium (1s²2s²2p⁶3s²3p⁶4s¹3d⁵) deviates from the expected pattern due to the greater stability of the half-filled 3d subshell
Key Terms to Review (16)
Aufbau Principle: The Aufbau Principle is a fundamental concept in quantum chemistry that describes the process by which electrons fill atomic orbitals in order of increasing energy. According to this principle, electrons occupy the lowest energy orbitals first before filling higher energy levels, which helps in predicting electron configurations of multi-electron atoms and understanding molecular orbital diagrams. This systematic approach ensures that the most stable arrangements of electrons are achieved, influencing chemical properties and bonding behavior.
Bohr Model: The Bohr Model is a theoretical representation of the hydrogen atom proposed by Niels Bohr in 1913, which describes the atom as a nucleus surrounded by electrons that occupy specific, quantized orbits. This model introduced the idea that electrons can only exist in certain energy levels, and when they transition between these levels, they absorb or emit energy in the form of light. The Bohr Model laid the groundwork for understanding atomic structure and behavior, influencing the study of multi-electron atoms, atomic spectra, and quantum mechanics.
Effective Nuclear Charge: Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi-electron atom, accounting for both the attraction from the nucleus and the repulsion from other electrons. This concept is crucial for understanding electron configurations, as it helps explain trends in atomic size, ionization energy, and electronegativity across the periodic table.
Electron Shielding: Electron shielding is the phenomenon where inner-shell electrons reduce the effective nuclear charge experienced by outer-shell electrons in multi-electron atoms. This reduction occurs because the inner electrons repel outer electrons, making it easier for these outer electrons to be influenced by other atoms or removed from the atom altogether, which significantly impacts their energy levels and chemical behavior.
Electronegativity: Electronegativity is a measure of the tendency of an atom to attract a bonding pair of electrons. It plays a crucial role in determining the type of bond that forms between atoms, influencing the molecular structure and properties of compounds, especially in multi-electron systems where electron configurations are more complex.
Hund's Maximum Multiplicity: Hund's Maximum Multiplicity is a principle in quantum chemistry that states that for a given electron configuration, the most stable arrangement of electrons will have the maximum number of unpaired electrons in degenerate orbitals. This principle is crucial for understanding the behavior of multi-electron atoms and helps explain the energy levels and electron configurations of these atoms, leading to insights about their chemical properties and bonding behavior.
Hund's Rule: Hund's Rule states that for degenerate orbitals (orbitals with the same energy), electrons will fill each orbital singly before pairing up in any one orbital. This rule helps minimize electron-electron repulsion and leads to a more stable electron configuration. Understanding this concept is essential when determining the electron configurations of multi-electron atoms and in constructing molecular orbital diagrams, as it influences the arrangement of electrons and the overall energy of the system.
Ionization Energy: Ionization energy is the amount of energy required to remove an electron from an atom or ion in its gaseous state. This concept is essential for understanding how atoms interact with one another, especially in the context of electron configurations and the stability of multi-electron systems, as well as for examining the simpler hydrogen atom and its derivatives, known as hydrogenic systems.
Magnetic quantum number: The magnetic quantum number, denoted as $$m_l$$, describes the orientation of an atomic orbital in space relative to an external magnetic field. It is one of the four quantum numbers that specify the state of an electron in an atom, connecting to angular momentum, the arrangement of electrons in multi-electron atoms, and the solutions to eigenvalue equations that represent quantum systems.
Noble Gas Configuration: Noble gas configuration refers to the electron configuration of an atom that matches the electron arrangement of the nearest noble gas, resulting in a stable and low-energy state. This configuration is significant in understanding how multi-electron atoms interact and bond, as atoms strive to achieve stability by gaining, losing, or sharing electrons to resemble the electron structure of noble gases, which are known for their lack of reactivity.
P orbital: A p orbital is a type of atomic orbital that can hold a maximum of two electrons and is characterized by a dumbbell shape. These orbitals are essential for understanding the electron configurations of multi-electron atoms, as they arise after the s orbitals and can accommodate electrons in specific energy levels and sublevels.
Pauli Exclusion Principle: The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of quantum numbers. This fundamental principle helps explain the arrangement of electrons in atoms, which in turn influences their angular momentum and plays a critical role in determining the electron configurations of multi-electron atoms, molecular orbitals, and the behavior of fermions in quantum statistics.
Principal Quantum Number: The principal quantum number is a quantum mechanical value that denotes the energy level of an electron in an atom, typically represented by the symbol 'n'. It plays a crucial role in determining the size and energy of atomic orbitals, influencing how electrons are arranged in multi-electron atoms, how atomic spectra are produced, and the eigenvalues associated with electron wave functions in quantum mechanics.
Quantum Mechanical Model: The quantum mechanical model describes the behavior of electrons in atoms using quantum mechanics principles, emphasizing their wave-particle duality and probabilistic nature. Unlike earlier models that portrayed electrons as particles in fixed orbits, this model uses wave functions to represent the likelihood of finding an electron in a specific region around the nucleus. This approach provides a more accurate understanding of atomic structure, particularly in complex multi-electron systems.
S orbital: An s orbital is a type of atomic orbital that is spherical in shape and can hold a maximum of two electrons with opposite spins. It is the simplest type of orbital and serves as the foundation for understanding the electron configurations of multi-electron atoms. The presence and arrangement of s orbitals in an atom's electron configuration directly influence its chemical properties and behavior.
Valence Electrons: Valence electrons are the outermost electrons in an atom that are involved in forming chemical bonds. These electrons play a crucial role in determining how an element interacts with others, including its reactivity, bonding behavior, and the types of compounds it can form. Understanding valence electrons is essential for comprehending the electron configurations of multi-electron atoms and their overall chemical properties.