Chapter 3: Problem 39

What does Hund's rule for maximum multiplicity state?

Short Answer

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Question: Explain Hund's rule for maximum multiplicity and its three main principles in determining the ground state electron configuration of an atom. Answer: Hund's rule for maximum multiplicity is a set of guidelines used to determine the ground state electron configuration of an atom. The three main principles are: 1. Principle of maximum multiplicity, which states that the electron configuration with the highest multiplicity should be selected as the ground state, 2. Principle of equal spins, which states that electrons should occupy unoccupied orbitals with the same spin before pairing up with opposite spins, and 3. Principle of energy order, which states that electrons fill orbitals in the order of increasing energy. These principles help to arrange electrons in an atom to minimize its overall energy while maximizing its multiplicity.

Step by step solution

1. Definition of Hund's rule for maximum multiplicity

Hund's rule for maximum multiplicity is a set of guidelines that determine the electron configuration of an atom in its ground state. The rule helps to arrange the electrons in an atom so that they occupy the lowest energy orbitals first (in ascending order of energy), with a preference for maximizing the total spin angular momentum, which in turn maximizes the atom's multiplicity.

2. Principle of maximum multiplicity

The first principle of Hund's rule states that the state with the maximum multiplicity should be selected as the ground state configuration. The multiplicity is given by the formula: \(Multiplicity = 2S + 1\), where \(S\) denotes the total spin of the system. If there is more than one way to assign electrons to the orbitals, the configuration with the highest multiplicity will correspond to the lowest energy state.

3. Principle of equal spins

The second principle of Hund's rule is that, for a given multiplicity, the electron configuration that has the maximum number of unpaired electrons with parallel spins should be selected. This means that electrons will preferentially occupy unoccupied orbitals with the same spin before pairing up in a single orbital with opposite spins. This principle also follows from the requirement to maximize the total spin angular momentum of the atom.

4. Principle of energy order

The third principle of Hund's rule is that electrons fill orbitals in the order of increasing energy. If there are multiple orbitals with the same energy (degenerate orbitals), electrons will fill them according to the first two principles. In the case of non-degenerate orbitals, electrons will occupy the lower energy orbitals first and then progress to higher energy orbitals as needed. To summarize, Hund's rule for maximum multiplicity states that electrons should be arranged in an atom in such a way that the least amount of energy is required, achieved by maximizing the atom's multiplicity, having unpaired electrons with parallel spins, and filling orbitals in the order of increasing energy.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electron Configuration

Understanding the arrangement of electrons within an atom is fundamental to chemistry and physics, and this is where electron configuration comes into play. It represents how electrons are distributed among the orbitals of an atom. The configuration is typically noted by a shorthand notation that indicates the number of electrons in each orbital (e.g., 1s² 2s² 2p⁶).

The rules governing electron configuration are designed to minimize the energy of the atom. Electrons fill the lowest energy orbitals first—a principle known as the Aufbau principle. However, within the same energy level, there are often multiple orbitals available, such as the p or d orbitals. Here Hund's rule helps guide the process: electrons distribute across these degenerate orbitals to maximize the total spin, as parallel spins have lower energy due to reduced electron repulsion.

Spin Angular Momentum

Spin angular momentum is a quantum property of electrons that relates to their intrinsic spin. Each electron behaves like a tiny magnet and can have one of two possible spin states: up or down. In terms of quantum mechanics, we describe these as spin quantum numbers, which can be either +1/2 or -1/2.

When dealing with multiple electrons in an atom, their spins can be either aligned (parallel) or opposed (antiparallel). Hund's rule promotes arrangements where electrons maintain parallel spins as much as possible before filling orbitals with electrons of opposite spin. This tendency maximizes the overall spin of the atom and is linked to the stability of the electron configuration.

Ground State Configuration

The most stable arrangement of electrons in an atom is known as its ground state configuration. It describes the electron configuration with the lowest possible energy. Determining this configuration involves applying Hund's rule alongside the Aufbau principle and the Pauli exclusion principle, ensuring that no two electrons in the same orbital have the same set of quantum numbers.

When electrons are in their ground state configuration, the atom is in its most stable and unexcited state. Any addition of energy may lead to an excited state where electrons occupy higher energy levels. The ground state, therefore, represents the starting point for understanding an atom's chemical behavior and how it interacts with other atoms.

Principle of Equal Spins

Hund's rule includes the principle of equal spins which emphasizes that electrons in degenerate orbitals (orbitals with the same energy within a subshell) will occupy separate orbitals with parallel spins as much as possible. This arrangement is energetically favorable, as it minimizes electron-electron repulsion and is a reflection of the electrons behaving as if they are 'aware' of each other's presence, avoiding pairing until necessary.

For instance, when filling p orbitals, each of the three p orbitals will receive one electron with the same spin before any orbital receives a second electron with the opposite spin. This results in the maximum number of unpaired electrons and maximizes the total spin angular momentum, which is a key component in achieving the atom's lowest energy configuration.

Orbital Energy Order

The energy levels of orbitals increase from lower to higher principal quantum numbers and from s to f subshells, a concept known as orbital energy order. This sequence is partially depicted by the Aufbau diagram and occurs because electrons further from the nucleus experience less electrostatic pull, allocating them to higher energy levels.

In a multi-electron atom, the energy of orbitals also depends on their effective nuclear charge and electron-electron repulsion. Therefore, within the same energy level, the s orbital is filled before the p orbitals, which in turn is filled before the d orbitals. Understanding this order is crucial when applying Hund's rule to determine the ground state electron configuration as it dictates the order in which electrons are distributed across available orbitals.

What does Hund's rule for maximum multiplicity state?

Short Answer

Step by step solution

1. Definition of Hund's rule for maximum multiplicity

2. Principle of maximum multiplicity

3. Principle of equal spins

4. Principle of energy order

Key Concepts

Electron Configuration

Spin Angular Momentum

Ground State Configuration

Principle of Equal Spins

Orbital Energy Order

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