Quantum 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.

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.

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.

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.

Let's look at an example.

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

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).

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.

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.