# The Quantum Mechanical Model: Definition & Overview

## Quantum Mechanical Model of Atom

The Quantum Mechanical Model of the Atom views electrons within an atom as waves, not as particles as previously believed. Because of this, electrons can be described as having a high probability of residing in specific orbitals, or regions of space, within the atom. This model doesn't represent an electron's motion but rather indicates the likelihood of finding an electron within a specific orbital within the atom at any given time. The quantum mechanical model of the atom is therefore based on probability and not certainty, unlike previous models of the atom.

### Who Discovered the Quantum Mechanical Model?

In his previous model of the atom, Neils Bohr proposed that electrons circle the nucleus in discrete orbits or shells. This model, however, did not account for the fact that electrons could behave as both waves and particles. Louis de Broglie had previously proposed that the electron shows wave properties in addition to particle properties. When mathematically describing electrons as standing waves, Austrian physicist Erwin Schr{eq}\ddot{o} {/eq}dinger developed an equation to determine a wave function that predicts an electron's likely position within the atom. By describing electrons as waves instead of particles, Schr{eq}\ddot{o} {/eq}dinger's quantum mechanical model revised previous models that characterized electrons as traveling along paths specific distances from the nucleus.

### Wave Functions

Wave functions describe an electron's probable location within an atom. Schr{eq}\ddot{o} {/eq}odinger's equation states {eq}\hat{H}\psi = E\psi {/eq}, where {eq}\psi {/eq} is the wave function, {eq}\hat{H} {/eq} is an operator, and E is the energy of the system. According to the Heisenberg uncertainty principle, it is impossible to know the exact energy and location of an electron at any given time. Therefore, this equation can be used to calculate specific wave functions called orbitals that correlate with a particular energy level, predicting the probable location of an electron rather than defining it with certainty.

### Electron Clouds

The location of the electrons in the quantum mechanical model of the atom is referred to as an electron cloud, which is simply a region of space. More specifically, this electron cloud can be referred to as a probability distribution. There are different probabilities of finding an electron at any given point in space within the region. More shaded regions indicate a higher likelihood of finding an electron region when visualizing electron clouds. In contrast, less shaded regions indicate a lower probability of finding an electron within this region.

### What is a Quantum Mechanical Orbital?

A quantum mechanical orbital is a three-dimensional region of space within an atom with a high probability of finding an electron. The probability density describes just how likely it is to find an electron within this region of space. A high probability density would indicate a high probability of locating an electron within this region. In contrast, a low probability density would indicate a low probability of finding an electron within this region.

## Definition of the Atom

Look around you. What do you see? Maybe you see a computer in front of you, a ceiling above you, the clothes you're wearing, or a tree outside a window. What do all of these things have in common? Not a lot, you might think. But, all matter in the universe, everything around you is made of the same basic stuff. Everything in the universe is made of the 118 elements discovered in chemistry—118 different types of atoms.

**Atoms** are the building blocks of the universe made up of protons and neutrons inside a central nucleus, surrounded by orbiting electrons. This model of the atom below is the one most people learn in chemistry classes at school, called the **planetary model**, which is a model of the atom that appears like a planetary system with the nucleus acting as the sun and the electrons acting as the planets.

It's a greatly simplified version of the model of what is now believed to be true, but the older model has been replaced more than once. It was replaced with a more detailed version first, called the **Bohr model** (named after physicist Neils Bohr), where electrons can only orbit with specific amounts of energy. And then later, it was replaced with the quantum mechanical model.

## Quantum Atom

The quantum atom can be described by the probability of finding electrons within given orbitals. To simplify this, four quantum numbers (n, l, {eq}m_l {/eq}, {eq}m_l {/eq}) were introduced to describe the characteristics of each electron within the quantum atom. Each electron within an atom has a unique set of four quantum numbers. The four quantum numbers are described below.

### Principal Quantum Number

The principal quantum number, n, describes the size and energy of an orbital within an atom. The value of n, which represents the principal shell number, can be a whole number integral (1, 2, 3,...), where larger numbers indicate larger orbitals with higher energy, as electrons in these orbitals are more likely to be found farther from the nucleus.

### Angular Momentum Quantum Number

The angular momentum quantum number, l, describes the shape of each orbital and can have a value of 0 to n-1. For example, for a principal quantum number of 3, the angular momentum quantum number can be 0, 1, or 2. Typically, letters are used to indicate common values of l where l = 0 is represented by s, l = 1 is represented by p, l = 2 is represented by d, l = 3 is represented by d, and l = 4 is represented by f, for example. These letters and values indicate the predicted subshell or shape of a region of probability where an electron is likely to be found.

### Magnetic Quantum Number

The magnetic quantum number, {eq}m_l {/eq}, describes how the orbital is oriented compared to other orbitals in the atom. Its value may range from -l to l. For example, for an angular momentum quantum number of 2, the magnetic quantum number can be -2, -1. 0, 1, or 2.

### Spin Quantum Number

When electrons spin, they produce magnetic fields. The spin quantum number, {eq}m_s {/eq}, describes the direction in which an electron spins. Its value can either be indicated by +1/2 or -1/2, meaning that electron pairs have the same spin magnitude but opposite directions. This also means that the same four quantum numbers can identify no two electrons.

## Lesson Summary

The quantum mechanical model of the atom was developed to describe the wave properties of electrons. This model characterizes electrons' properties using a set of four quantum numbers and represents the probability of locating an electron within specific orbitals, or regions of space, within an atom, rather than describing electrons as specific particles that can be located along a discrete path. The quantum mechanical model is not based on certainty but instead on the probability of finding electrons within regions of space in an atom.

## The Quantum Mechanical Model

The discovery that began quantum mechanics as a field of study was when physicists Albert Einstein and Max Planck proved that light and matter can behave both as particles and waves. This began the era of **quantum mechanics**, which is basically the physics of the very tiny. If particles like electrons can behave as waves, it means that they don't have an exact position the way we would imagine for a traditional particle. Quantum mechanics tells us that you can't precisely know both the position and velocity of an electron at the same time.

This means that we shouldn't imagine electrons as single objects going around the atom. Instead, all we know is the probability of finding an electron at a particular location. What we end up with is something called an electron cloud. An **electron cloud** is an area of space in which an electron is likely to be found. It's like a 3-D graph showing the probability of finding the electron at each location in space.

Quantum mechanics also tells us that a particle has certain numbers (called quantum numbers) that represent its properties. Just like how materials can be hard or soft, shiny or dull, particles have numbers to describe the properties. These include a particle's orbital quantum numbers, magnetic quantum number, and its spin. No two electrons in an atom can have exactly the same quantum numbers.

**Orbital quantum numbers** tell you what energy level the electron is in. In the Bohr model, this represents how high the orbit is above the nucleus; higher orbits have more energy. The first orbit is n=1, the second is n=2, and so on. The **magnetic quantum number** is just a number that represents which direction the electron is pointing. The other important quantum mechanical property, called **spin**, is related to the fact that electrons come in pairs. In each pair, one electron spins one way (with a spin of one half), and the other electron spins the other way (with a spin of negative one half). Two electrons with the same spin cannot exist as a pair. This might seem kind of random, but it has effects in terms of how magnetic material is. Materials that have unpaired electrons are more likely to be magnetic.

Although the quantum mechanical model of the atom is more abstract and complex, it's a much more accurate picture of how atoms work. Because of this, it allows us to make better predictions about how particles will behave when we try to interact with them. We use quantum mechanics to create flatscreen TVs, camera sensors, and computers, so knowing about quantum mechanics is very useful.

## Lesson Summary

Everything around you is made of **atoms**, which are the building blocks of the universe made up of protons and neutrons inside a central nucleus, surrounded by orbiting electrons. Those items contain smaller particles: protons and neutrons in the nucleus and electrons orbiting around the outside, like a model of the solar system, known as the **planetary model**. This classic model of the atom is simplified. After the **Bohr model**, in which electrons can only orbit with specific amounts of energy, **quantum mechanics** (the physics of the very tiny) entered the fray to tell us that knowing the exact position and movement of tiny particles is impossible. The best we can know are probabilities.

The quantum mechanical model of the atom tells us that electrons orbit the atom in random ways and pictures the atom as being surrounded by an electron cloud containing all the possible places that the electron might be. The **electron cloud**, an area of space in which an electron is likely to be found, represents the probability of finding an electron at different places in space, like a 3-D map. Quantum mechanics also gives electrons orbital quantum numbers, magnetic quantum numbers, and spins. The **orbital quantum numbers** tell you how high an orbit (which energy level) the electron is in, while the **magnetic quantum number** is just a number that represents which direction the electron is pointing. And we also know that electrons come in pairs, each with opposite **spins**, which is related to this fact that electrons come in pairs. Knowing this allows us to predict the properties of a material and build all kinds of impressive technology.

## Key Terms

**Atoms** - the building blocks of the universe; made up of protons and neutrons inside a central nucleus, surrounded by orbiting electrons

**Planetary model** - a model of the atom that appears like a planetary system with the nucleus acting as the sun and the electrons acting as the planets

**Bohr model** - a more detailed version of the planetary model in which electrons can only orbit with specific amounts of energy; named after physicist Neils Bohr

**Quantum mechanics** - the physics rules that govern the tiniest particles

**Electron cloud** - an area of space in which an electron is likely to be found

**Orbital quantum numbers** - numbers that can be used to determine the energy level the electron is in

**Magnetic quantum number** - a number that represents the direction in which the electron is pointing

**Spin** - an important quantum mechanical property; namely, that electrons come in pairs

## Learning Outcomes

Learn about the quantum mechanical model via this lesson so that you can:

- List the three major models that have been used to depict atoms
- Explain the rules that can help determine where the electrons of an atom are

To unlock this lesson you must be a Study.com Member.

Create your account

## Definition of the Atom

Look around you. What do you see? Maybe you see a computer in front of you, a ceiling above you, the clothes you're wearing, or a tree outside a window. What do all of these things have in common? Not a lot, you might think. But, all matter in the universe, everything around you is made of the same basic stuff. Everything in the universe is made of the 118 elements discovered in chemistry—118 different types of atoms.

**Atoms** are the building blocks of the universe made up of protons and neutrons inside a central nucleus, surrounded by orbiting electrons. This model of the atom below is the one most people learn in chemistry classes at school, called the **planetary model**, which is a model of the atom that appears like a planetary system with the nucleus acting as the sun and the electrons acting as the planets.

It's a greatly simplified version of the model of what is now believed to be true, but the older model has been replaced more than once. It was replaced with a more detailed version first, called the **Bohr model** (named after physicist Neils Bohr), where electrons can only orbit with specific amounts of energy. And then later, it was replaced with the quantum mechanical model.

## The Quantum Mechanical Model

The discovery that began quantum mechanics as a field of study was when physicists Albert Einstein and Max Planck proved that light and matter can behave both as particles and waves. This began the era of **quantum mechanics**, which is basically the physics of the very tiny. If particles like electrons can behave as waves, it means that they don't have an exact position the way we would imagine for a traditional particle. Quantum mechanics tells us that you can't precisely know both the position and velocity of an electron at the same time.

This means that we shouldn't imagine electrons as single objects going around the atom. Instead, all we know is the probability of finding an electron at a particular location. What we end up with is something called an electron cloud. An **electron cloud** is an area of space in which an electron is likely to be found. It's like a 3-D graph showing the probability of finding the electron at each location in space.

Quantum mechanics also tells us that a particle has certain numbers (called quantum numbers) that represent its properties. Just like how materials can be hard or soft, shiny or dull, particles have numbers to describe the properties. These include a particle's orbital quantum numbers, magnetic quantum number, and its spin. No two electrons in an atom can have exactly the same quantum numbers.

**Orbital quantum numbers** tell you what energy level the electron is in. In the Bohr model, this represents how high the orbit is above the nucleus; higher orbits have more energy. The first orbit is n=1, the second is n=2, and so on. The **magnetic quantum number** is just a number that represents which direction the electron is pointing. The other important quantum mechanical property, called **spin**, is related to the fact that electrons come in pairs. In each pair, one electron spins one way (with a spin of one half), and the other electron spins the other way (with a spin of negative one half). Two electrons with the same spin cannot exist as a pair. This might seem kind of random, but it has effects in terms of how magnetic material is. Materials that have unpaired electrons are more likely to be magnetic.

Although the quantum mechanical model of the atom is more abstract and complex, it's a much more accurate picture of how atoms work. Because of this, it allows us to make better predictions about how particles will behave when we try to interact with them. We use quantum mechanics to create flatscreen TVs, camera sensors, and computers, so knowing about quantum mechanics is very useful.

## Lesson Summary

Everything around you is made of **atoms**, which are the building blocks of the universe made up of protons and neutrons inside a central nucleus, surrounded by orbiting electrons. Those items contain smaller particles: protons and neutrons in the nucleus and electrons orbiting around the outside, like a model of the solar system, known as the **planetary model**. This classic model of the atom is simplified. After the **Bohr model**, in which electrons can only orbit with specific amounts of energy, **quantum mechanics** (the physics of the very tiny) entered the fray to tell us that knowing the exact position and movement of tiny particles is impossible. The best we can know are probabilities.

The quantum mechanical model of the atom tells us that electrons orbit the atom in random ways and pictures the atom as being surrounded by an electron cloud containing all the possible places that the electron might be. The **electron cloud**, an area of space in which an electron is likely to be found, represents the probability of finding an electron at different places in space, like a 3-D map. Quantum mechanics also gives electrons orbital quantum numbers, magnetic quantum numbers, and spins. The **orbital quantum numbers** tell you how high an orbit (which energy level) the electron is in, while the **magnetic quantum number** is just a number that represents which direction the electron is pointing. And we also know that electrons come in pairs, each with opposite **spins**, which is related to this fact that electrons come in pairs. Knowing this allows us to predict the properties of a material and build all kinds of impressive technology.

## Key Terms

**Atoms** - the building blocks of the universe; made up of protons and neutrons inside a central nucleus, surrounded by orbiting electrons

**Planetary model** - a model of the atom that appears like a planetary system with the nucleus acting as the sun and the electrons acting as the planets

**Bohr model** - a more detailed version of the planetary model in which electrons can only orbit with specific amounts of energy; named after physicist Neils Bohr

**Quantum mechanics** - the physics rules that govern the tiniest particles

**Electron cloud** - an area of space in which an electron is likely to be found

**Orbital quantum numbers** - numbers that can be used to determine the energy level the electron is in

**Magnetic quantum number** - a number that represents the direction in which the electron is pointing

**Spin** - an important quantum mechanical property; namely, that electrons come in pairs

## Learning Outcomes

Learn about the quantum mechanical model via this lesson so that you can:

- List the three major models that have been used to depict atoms
- Explain the rules that can help determine where the electrons of an atom are

To unlock this lesson you must be a Study.com Member.

Create your account

#### What are the main features of quantum mechanical model of an atom?

The quantum mechanical model of an atom describes the probability of finding electrons within given orbitals, or three-dimensional regions of space, within an atom. The properties of each electron within the quantum atom can be described using a set of four quantum numbers.

#### How was the quantum model created?

The quantum model was created when the Bohr model failed to account for the wave properties of electrons. By describing electrons as waves and not particles, Schrodinger utilized his equation to predict the probability of finding an electron within a specific orbital in the atom.

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