Wave-Particle Duality (Introduction to Quantum Mechanics)

Introduction

Wave-particle duality is a central idea to the study of quantum mechanics, which deals with the behavior of light and matter at a subatomic scale. In very simple terms, wave-particle duality explains how all forms of matter can behave both as a wave and a particle.

Properties of Light

1. Double-Slit Experiment

For centuries, scientists have been puzzled by the true nature of light. In 1807, English physicist Thomas Young came to the conclusion that light was a wave from the double-slit experiment. Here is the description of the double slit experiment:

A light is shined from the light source through a small opening in the first plate.
The light waves will travel in a way, as shown in the figure above.
The light then passes through the second plate through two small openings this time.
A new wave pattern is created in each two slits.
As the two waves interfere with each other, some waves will be added together to generate a larger wave while others will cancel each other out in a way that makes the some waves disappear.

The bright portion of the screen is where the waves have been added together whereas the dark portion of the screen is where the waves have cancelled each other out. This can only be explained if light is a wave since if the double-slit experiment were to be conducted using particles, it will just produce two huge lumps adjacent to the slits.

2. Photoelectric Effect

Consider a case where you have a metal plate (which could be made of say, sodium). When light rays are shined to the metal surface, they limit electrons (also called photoelectrons) from the atoms in the metal plate. The photoelectric effect was first discovered by German physicist Heinrich Hertz in 1887. The results of this experiment, however, contradicted the conclusion made by the double-slit experiment that light is a wave. If light were a wave, increasing the intensity of light will produce an electric field with more energy and thus there will be more electrons ejected from the metal plate with higher kinetic energy (in other words, the electrons will have more speed when they are ejected). Increasing the frequency of the light would not have any effect. If light behaved as a particle, the photons will transfer the energy to the electrons for them to fly off from the metal surface. In order to achieve this however, the energy must overcome the strength of the attraction between the electron and the nucleus (this is called the Work Function). The remaining energy will give electrons kinetic energy. All of this can be written as [hf = W + KE, h = planck’s constant, f = frequency]. This equation tells us that if the frequency of light is increased, the kinetic energy of the electrons will increase. Moreover, increasing the intensity of the light will increase the number of electrons being emitted, but it will not affect the kinetic energy of the electrons. The experiment on the photoelectric effect confirmed the latter, meaning that light behaves as a particle. This however, contradicted the results of the double-slit experiment, which led to physicists believe that light can behave as a wave and a particle, also called wave-particle duality.

Wave-Particle Duality

Physicists soon began to suspect that other matters had a wave-particle duality-like property as well. When the double slit experiment was tested using other forms of matter (e.g. electrons and atoms), they produced similar diffraction patterns that were produced for light. This led physicists to conclude that everything in the universe is a wave. In our daily lives however, we are unable to see these wavelengths with our naked eyes. The wavelength is given by the following equation: [wavelength = (Planck’s constant)/Momentum, Momentum = mass * velocity]. If a person with a mass of 60 kg was moving with a velocity of 5 m/s, its momentum will be 300 kg m/s. Take Planck’s constant to be 6.626 * 10^-34, and the wavelength turns out to be 2.209 * 10^-36 m. For comparison, the radius of an electron is about 2.82*10^-15 m. Obviously, this wavelength is far too small to be seen by the naked eye.

Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle is another core theory in quantum mechanics and it states that regardless of how advanced measuring devices become, there will always be some uncertainty in the position and the momentum of matter. The reason for this has to do with wave-particle duality. When finding out the momentum of matter, the equation [wavelength = (Planck’s constant)/Momentum, Momentum = mass * velocity] is used. The wave property of matter is used to find the momentum, and as waves do not have a definite position in space, the accuracy for the position of the matter is lost when finding its momentum. Likewise, when finding the position of matter, the particle property of matter is used. As particles do not have wavelengths, one can find the position of matter but not its momentum. Therefore, if a physicist wishes to find the position and the momentum to about an equal level of uncertainty, they will “collect” wavelengths into a small area. One can achieve this by combining different waves of different wavelengths to create an overall wave that has a greater wavelength and the region between the two peaks are separated by a straight line. If we take the wavy region of the wave, it is possible to know the position and momentum to a certain degree of accuracy. It is also important to note however, that in order to get to this form of matter, it must have lost some precision of momentum and precision:

The accuracy of position has been lost since there is a range of probability where the quantum object could be
As the quantum object has been created by adding waves with different wavelengths, the calculated momentum could be any one of these waves that have been combined, and therefore we lose accuracy for its momentum

If one wishes to increase the accuracy for the matter’s position it has to make the wavy region smaller by adding more waves to it and thus losing accuracy for its position. Likewise, if one wishes to increase the accuracy of the matter’s momentum, it can “subtract” waves to make a larger region of the wavy region and lose accuracy for its momentum as a result.

Note that this uncertainty is of little significance in our daily lives since the error would be too small to have a major effect. From the equation below, if say that the uncertainty of the position is 10 m, the uncertainty in momentum will be greater than or equal to 5.2728 * 10^-36 kg m/s.

Sources

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