Modern Atomic Model (Quantum Mechanical Model - Introduction)

The modern atomic model, also called the quantum mechanical model of the atom, is a fundamental theory that provides a comprehensive understanding of atomic structure beyond older models such as Rutherford and Bohr. This model is largely based on the principles of quantum mechanics, a branch of physics that deals with the behavior of very small particles at the atomic and subatomic levels. In this lesson, we will understand this model in a simple and detailed manner, cover the basic concepts and explain its importance through examples.

Historical background

Before we dive into quantum mechanical models, let's start with a brief history of atomic theories. The idea of atoms comes from ancient Greece, where the philosopher Democritus first suggested that matter was composed of indivisible units called atoms. Since the early 20th century, scientists have been developing more detailed models as experimental data has become more sophisticated.

In the early 1900s, J.J. Thomson discovered the electron, leading to the "plum pudding" model, where electrons were scattered inside a positively charged substance. Then came Ernest Rutherford's gold foil experiment, which showed that atoms consisted of a small, dense, positively charged nucleus surrounded by electrons in empty space. Niels Bohr further refined this view by introducing quantized energy levels, which allowed electrons to occupy definite orbitals.

Despite the accuracy of Bohr's model in explaining electron transitions in hydrogen atoms, it could not adequately explain the more complex spectra of larger atoms. This limitation paved the way for the development of the quantum mechanical model.

Quantum mechanical model

The quantum mechanical model is based on the work of many brilliant scientists, including Max Planck, Louis de Broglie, Werner Heisenberg, and Erwin Schrödinger. This model includes several key principles and concepts, which we will explore in detail.

Wave–particle duality

A fundamental idea in quantum mechanics is that particles such as electrons exhibit both wave and particle characteristics, known as wave-particle duality. This means that electrons can behave like particles in some experiments or exhibit wave-like properties in others.

λ = h / (mv)

In the above equation, λ represents the wavelength of the electron, h is Planck's constant, m is the mass, and v is the velocity. This equation, called de Broglie's equation, shows how moving particles have wave properties.

Heisenberg uncertainty principle

An essential principle of the quantum mechanical model is the Heisenberg uncertainty principle. This principle states that it is impossible to simultaneously accurately determine both the position and momentum of an electron. This uncertainty means that electrons cannot be placed in specific locations as previously thought, which is in contrast to the earlier Bohr model where the orbits of electrons were fixed.

Atomic orbitals

Rather than considering specific paths for electrons, quantum mechanics describes regions around the nucleus where electrons are likely to be found, known as orbitals. Atomic orbitals are characterized by different shapes and energy levels, and they can accommodate up to two electrons each.

Schrödinger's equation

Erwin Schrödinger developed a mathematical equation that describes how the quantum state of a quantum system changes over time. This equation, known as the Schrödinger equation, is fundamental in determining the behavior of electrons in atoms.

ĤΨ = EΨ

Here, Ĥ is the Hamiltonian operator, which describes the total energy of the system, Ψ is the wave function, and E is the energy eigenvalue. The wave function Ψ gives us information about the probability distribution of the electron.

Visualization of atomic orbitals

To better understand orbitals, it is helpful to visualize them. Let's learn about some of the basic types of orbitals that electrons can occupy in an atom.

s-orbitals

S-orbitals are spherical. The shape of the s-orbital increases as the energy level increases. Below is an illustration of the s-orbital:

Here, the circle represents the range within which there is a high probability of finding an electron.

p-orbitals

p-orbitals are dumbbell-shaped and oriented along the x, y, and z axes. There are three p-orbitals for each energy level, starting at n=2:

The above shapes are an indication of how the electron density is distributed along the axes.

d-orbitals and f-orbitals

d-orbitals are more complex, typically cloverleaf shaped, and appear at the third energy level and beyond. Meanwhile, f-orbitals, which have even more complex shapes, appear at the fourth energy level and beyond.

Electron configuration

Understanding how electrons fill these orbitals is important for understanding chemical behavior. Electrons fill orbitals based on the "Aufbau Principle", the "Pauli Exclusion Principle" and "Hund's Rule".

Aufbau principle

According to the Aufbau principle, electrons fill orbitals starting from the lowest energy level to the highest energy level. For example, after filling the 1s orbital, the electrons will move to the 2s and then to the 2p orbital:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s

Pauli exclusion principle

The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers, i.e. an orbital can hold a maximum of two electrons with opposite spins.

Hund's rule

Hund's rule states that electrons will fill degenerate orbitals (orbitals with the same energy level) singly before they pair up. This reduces electron repulsion by spreading out the electrons.

Examples of electron configurations

Let's look at some examples to reinforce this concept:

Hydrogen

Hydrogen has one electron, so its electron configuration is the simplest:

1s¹

Oxygen

Oxygen has eight electrons. Let's follow the rules:

1s² 2s² 2p⁴ ↑ ↑ ↑ ↑

The arrows indicate spin; note that each p orbital fills singly according to Hund's rule before any pairing occurs.

Importance of quantum mechanical models

The quantum mechanical model represents a significant shift in our understanding of atoms:

• This brings clarity about atomic spectra and also explains why elements emit different wavelengths.
• It explains the chemical properties of atoms, which are important for bonding and reactivity.
• It forms the foundation of quantum chemistry and modern physics, and influences fields such as materials science, nanotechnology, and quantum computing.

Conclusion

The modern atomic model, or quantum mechanical model, is a cornerstone in the study of chemistry and physics. It advances from earlier models by providing a microscopic view of where and how electrons exist within atoms. By incorporating wave-particle duality, probability distributions, and quantized energy states, this model enhances our understanding of atomic structure and chemical properties, which is essential for technological advancement and research in many fields.

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