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# Quantum Energy

Let's say that you have a car that has a velocity of 5 miles per hour (ca. 8 km/h) in neutral, 15 miles per hour (ca. 24 km/h) in first gear, and 30 mph (ca. 48 km/h) in second gear. If you were driving in first gear and changed it to second gear, your car would instantaneously go from 15 to 30 mph without passing through any of the velocities in the middle.

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However, this is not the case in real life, or even at the atomic level! According to quantum chemistry and physics, certain things, such as the energy of an electron, are quantized.

So, if you are interested in learning about quantum energy, keep reading!

• First, we will talk about the quantum energy theory.
• Then, we will look at the definition of quantum energy.
• After, we will explore quantum energy.
• Lastly, we will look at quantum vacuum energy.

## Quantum Energy Theory

The beginning of quantum theory was the discovery of the electromagnetic energy quanta emitted by a blackbody. This discovery was published by Max Planck in 1901, in which he stated that heated objects emit radiation (such as light) in small, discrete amounts of energy called quanta. Planck also proposed that this emitted light energy was quantized.

An object is considered a blackbody if it is capable of absorbing all the radiation that strikes it.

• A blackbody is also considered a perfect emitter of radiation at a particular energy.

Then, in 1905, Albert Einstein published a paper explaining the photoelectric effect. Einstein explained the physics of the emission of electrons from a metal surface when a beam of light was shone upon its surface Moreover, he noticed that the brighter the light, the more electrons were ejected from the metal. However, these electrons would only be ejected if the light energy was above a certain threshold frequency (figure 1). These electrons emitted from a metal's surface were called photoelectrons.

By using Planck's theory, Einstein proposed the dual nature of light, which was that light had wave-like characteristics, but was made of streams of tiny energy bundles or particles of EM radiation called photons.

A photon is referred to as a particle of electromagnetic radiation with no mass that carries a quantum of energy.

• A photon = a single quantum of light energy.

Photons possess the following characteristics:

• They are neutral, stable and have no mass.

• Photons are able to interact with electrons.

• The energy and speed of photons depend on their frequency.

• Photons can travel at the speed of light, but only in a vacuum, such as space.

• All light and EM energy are made of photons.

## Quantum Energy Definition

Before diving into quantum energy, let's review electromagnetic radiation. Electromagnetic radiation (energy) is transmitted in the form of a wave (figure 2), and these waves are described based on frequency, and wavelength.

• Wavelength is the distance between a wave's two adjacent peaks or troughs.

• Frequency is the number of complete wavelengths that pass at a specific point per second.

Electromagnetic radiation is a kind of energy that behaves like a wave as it travels through space.

There are different types of EM radiation around us, such as X-rays and UV lights! The different forms of EM radiation are shown in an electromagnetic spectrum (figure 3). Gamma rays possess the highest frequency and smallest wavelength, indicating that frequency and wavelength are inversely proportional. In addition, notice that visible light only makes up a tiny part of the electromagnetic spectrum.

All electromagnetic waves moves at the same speed in a vacuum, which is the speed of light 3.0 X 108 m/s

Let's look at an example.

Find the frequency of a green light that has a wavelength of 545 nm.

To solve this problem, we can use the following formula: $$c=\lambda \text{v}$$, where $$c = \text{speed of light (m/s) , } \lambda = \text{wavelength (m), and }\text{v = frequency (nm)}$$

We already know the wavelength (545 nm) and the speed of light ( $$2.998 \times 10^{8} m/s$$ ). So, all that's left to do is to solve for frequency!

$$\text{v} = \frac{c}{\lambda} = \frac{2.99\times10^{8} \text{ m/s }}{5.45 \times10^{-7} \text{ m }} = 5.48\times10^{14} \text{ 1/s or Hz }$$

Now, let's look at the definition of quantum energy.

A quantum is the smallest quantity of electromagnetic (EM) energy that can be emitted or absorbed by an atom. In other words, it is the minimum amount of energy that can be gained or lost by an atom.

## Quantum Energy Formula

The formula below can be used to calculate the energy of a photon:

$$E =h\text{v}$$

Where:

• E is equal to the energy of a photon (J).
• $$h$$ is equal to planck's constant ( $$626.6\times10 ^{-34}\text{ Joules/s}$$ ).
• v is the frequency of light absorbed or emitted (1/s or s-1).

Remember that, according to Planck's theory, for a given frequency, matter can emit or absorb energy only in whole-number multiples of hv.

Calculate the energy transferred by a wave that has a frequency of 5.60×1014 s-1.

This question asks us to calculate the energy per quantum of a wave with a frequency of 5.60×1014 Hz. So, all we need to do is use the formula above and solve for E.

$$E = (626.6\times10 ^{-34}\text{ J/s } ) \times (5.60\times10 ^{14}\text{ 1/s } ) = 3.51 \times10 ^{-17}\text{ J }$$

Another way of solving for quantum energy is by using an equation that included the speed of light. This equation is as follows:

$$E = \frac{hc}{\lambda}$$

Where,

• E = quantum energy (J)
• $$h$$ = planck's constant ( $$626.6\times10 ^{-34}\text{ Joules/s}$$ )
• $$c$$ = speed of light ( $$2.998 \times 10^{8} m/s$$ )
• $$\lambda$$ = wavelength

## Quantum Energy Chemistry

Now that we know that definition of quantum energy and how to calculate it, let's talk about the energy of electrons in an atom.

In 1913, the Danish physicist Niels Bohr's model of the atom was developed using Planck's quantum theory and Einstein's work. Bohr created a quantum model of the atom in which the electrons orbit the nucleus, but in distinct and fixed orbits with a fixed energy. He called these orbits "energy levels" (figure 4) or shells, and each orbit was given a number called the quantum number.

The Bohr model also aimed to explain the electron's ability to move by suggesting that electrons moved between different energy levels through the emission or absorption of energy.

When an electron in a substance is promoted from a lower shell to a higher shell, it undergoes the process of the absorption of a photon.

When an electron in a substance moves from a higher shell to a lower shell, it undergoes the process of the emission of a photon.

However, there was a problem with Bohr's model: it suggested that energy levels were at specific, fixed distances from the nucleus, analogous to a miniature planetary orbit, which we now know is incorrect.

So, how do electrons behave? Do they act like waves or are they more like quantum particles? Enter three scientists: Louis de Broglie, Werner Heisenberg and Erwin Schrödinger.

According to Louis de Broglie, electrons had both wave-like and particle-like properties. He was able to prove that quantum waves could behave like quantum particles, and quantum particles could behave like quantum waves.

Werner Heisenberg further proposed that, when behaving like a wave, it is impossible to know the exact location of an electron within its orbit around the nucleus. His proposal suggested that Bohr's model was wrong because the orbits/energy levels were not fixed at a distance from the nucleus and did not have fixed radii.

Later, Schrödinger hypothesized that electrons could be treated as matter waves, and proposed a model called the quantum mechanical model of the atom. This mathematic model, called the Schrödinger equation, rejected the idea that electrons existed in fixed orbits around the nucleus, and instead described the likelihood of finding an electron at different locations around the atom's nucleus.

Today, we know that atoms have quantized energy, meaning that only certain discrete energies are allowed, and these quantized energies can be represented by energy level diagrams (figure 5). Basically, if an atom absorbs EM energy, its electrons can jump up to a higher energy ("excited") state. On the other hand, if an atom emits/gives off energy, electrons jump down to a lower energy state. These jumps are called quantum jumps, or energy transitions.

## Quantum Vacuum Energy

In modern physics, there is a term called the vacuum energy, which is the measurable energy of an empty space. So, it turns out that an empty space is not empty at all! Vacuum energy is sometimes called the zero-point energy, meaning that it is the lowest quantized energy level of a quantum mechanical system.

Vacuum energy is referred to as the energy associated with the vacuum, or empty space.

## Quantum Energy - Key takeaways

• A quantum is the smallest quantity of electromagnetic (EM) energy that can be emitted or absorbed by an atom.
• Electromagnetic radiation is a kind of energy that behaves like a wave as it travels through space.
• Vacuum energy is referred to as the energy associated with the vacuum, or empty space.

## References

1. Jespersen, N. D., & Kerrigan, P. (2021). AP chemistry premium 2022-2023. Kaplan, Inc., D/B/A Barron’s Educational Series.
2. Zumdahl, S. S., Zumdahl, S. A., & Decoste, D. J. (2019). Chemistry. Cengage Learning Asia Pte Ltd.
3. Openstax. (2012). College Physics. Openstax College.
4. Theodore Lawrence Brown, Eugene, H., Bursten, B. E., Murphy, C. J., Woodward, P. M., Stoltzfus, M. W., & Lufaso, M. W. (2018). Chemistry : the central science (14th ed.). Pearson.

#### Flashcards in Quantum Energy 15

###### Learn with 15 Quantum Energy flashcards in the free StudySmarter app

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What is quantum energy?

A quantum is the smallest quantity of electromagnetic (EM) energy that can be emitted or absorbed by an atom.

What is quantum chemistry used for?

Quantum chemistry is used to study the energy states of atoms and molecules.

How is quantum energy created?

Remember that energy cannot be created or destroyed, only converted into different forms.

How much is a quantum of energy?

A quantum of energy is smallest quantity of electromagnetic (EM) energy that can be emitted or absorbed by an atom.

How do you calculate quantum energy?

The energy of a photon ( a quantum of light) can be calculated by multiplying Planck's constant times the frequency of light absorbed or emitted.

## Test your knowledge with multiple choice flashcards

In the photoelectric effect, electrons emitted from a metal's surface are called ______.

When an electron in a substance is promoted from a lower shell to a higher shell, it undergoes the process of the ____ of a photon.

When an electron in a substance moves from a higher shell to a lower shell, it undergoes the process of the ____ of a photon.

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