MPS - Quantum Mechanics and the Photon

Quantum Mechanics and the Photon

At around the time Einstein was turning the world of classical physics on its head, another revolution in our understanding of our universe was occurring. Discoveries were being made in the early 1900s that revolutionized our understanding of the makeup of atoms. The following assignment will introduce you to the fundamentals of atoms and the beginnings of quantum mechanics.

The idea that atoms consisted of electrons orbiting nuclei at specific, quantized, energy levels proved to be an excellent foundation for explaining certain observations as well as opening the door to new questions.

Photon Theory of Light

In 1905, building on a discovery made by Max Planck, Albert Einstein introduced the idea of the light "quanta", which we know today as the photon. A photon is a massless packet of light with a discrete, or quantized, energy. The energy of a photon can be given as:

Where E is the energy of a photon, f is the frequency of the light, and h is known as Plancks constant and has a value of

This particle theory of light seemed to be at odds with the well-established wave theory of light (as evidenced by phenomena such as light diffraction and interference). However, Einstein felt it was an appropriate explanation for several new observations associated with the structure and interaction of atoms. To test his theory, Einstein applied the photon theory of light to explain the photoelectric effect. It had been shown that when light shines on a metal surface, electrons would be ejected and could provide a current to a circuit. This phenomenon could be explained by the wave theory of light, but the particle theory made very different predictions as to how the electron flow would be affected by changes to light intensity and frequency. When observations were made, the predictions made by the photon theory of light were verified.

Photoelectric Effect

According to Einsteins theory an electron was ejected from the metal by a collision with a single photon. During the collision, all of the energy of the photon was conserved and converted into a) the energy necessary to get the electron out of the atom, and b) the final kinetic energy of the electron. The minimum amount of energy necessary to eject the electron is known as the work function (ϕ). For the least tightly held electrons in the atom this gives us the mathematical relation:

Some electrons are more tightly held and therefore require energy greater than the work function to be ejected. The work function, and other energies associated with atoms and subatomic particles, is a very small value when measured in the SI energy units of joules, so the unit of electron volts (eV) is a common replacement. 1 eV = 1.6 x10^-19 J.

Photoelectric Effect Practice

What is the kinetic energy and the speed of an electron from a sodium surface whose work function is ϕ = 2.28 eV when illuminated by light of wavelength 410 nm?

SOLUTION Links to an external site.

Photon Momentum

Because a photon always travels at the speed of light, it must be considered a relativistic particle. A consequence of this is that photons, though massless, have momentum that can be calculated based on their energy and the speed of light.

Where E is the energy of the photon, p is the momentum, and c is the speed of light in a vacuum. Relating this to the equation we already have for the energy of a photon we get:

This equation allows you to relate the momentum of a photon to its wavelength.

Wave-particle Duality

It might seem like we have a conundrum: is light a wave or a particle? Diffraction and interference results suggest light is a wave. The photoelectric effect and having a momentum suggest light is a particle. Neils Bohr proposed that light is, in fact, both. Since both the wave nature and particle nature explain the results of different experiments, rather than being mutually exclusive, these competing theories must compliment one another. Today we now embrace the wave-particle duality of light.

Photon Interactions

Since photons are basically packets of pure energy, they can react in different ways when they interact with matter. This includes, but is not limited to:

1. The photoelectric effect.
2. The photon may not have enough energy to eject an electron so instead gives its energy to the electron in order to jump to a higher energy state. This is called being in an excited state and will be discussed more in the next lesson.
3. The photon could disappear and actually create matter. In this case two particles must be produced, one of matter and one of anti-matter. Anti-matter has the same properties of its matter counterpart but an opposite electric charge.

In this final way we see how pure energy can be converted into matter. Often, when a particle/anti-particle pair is created the two particles come back together and annihilate each other, converting the matter back to energy. The minimum energy needed to create such matter from energy can be calculated using the equation E = mc².

Extra Resources

Visit this resource to read about Quarks:

Hyper Physics: Quarks Resource Links to an external site.

Visit the following resource to read about Quantum Mechanical Model of the Atom.

Quantum Mechanical Model Links to an external site.

IMAGES AND VIDEOS SOURCED FROM PUBLIC DOMAIN