- High School Chemistry/The Wave Particle Duality.
- Matter wave.
- The Chemistry of Matter Waves!

He later described his interest for theoretical physics :. In , this division was exposed to doubt, when, investigating the theory of black body thermal radiation , Max Planck proposed that light is emitted in discrete quanta of energy. Light quanta are now called photons. The angular dependence of the diffracted electron intensity was measured, and was determined to have the same diffraction pattern as those predicted by Bragg for x-rays.

At the same time George Paget Thomson at the University of Aberdeen was independently firing electrons at very thin metal foils to demonstrate the same effect. Before the acceptance of the de Broglie hypothesis, diffraction was a property that was thought to be exhibited only by waves. Therefore, the presence of any diffraction effects by matter demonstrated the wave-like nature of matter. For this reason, it is proper to submit periodically to a very searching examination, principles that we have come to assume without any more discussion.

## Definition of matter wave in Physics.

The concept of matter waves in quantum mechanics reflects the wave—particle duality of matter. The waves became later known as de Broglie waves and in his theory, the scientist shows that the wavelength is inversely proportional to the momentum of a particle. Also, the frequency of matter waves , as deduced by de Broglie , is directly proportional to the total energy E sum of its rest energy and the kinetic energy of a particle [1,2].

Recently, it was also found that investigating the elementary process of diffusion gives the theoretical evidence of the relation of matter wave, regardless of the photon energy. In quantum mechanics, the concept of matter waves or de Broglie waves reflects the wave -particle duality of matter. Therefore, the presence of any diffraction effects by matter demonstrated the wave -like nature of matter. Just as the photoelectric effect demonstrated the particle nature of light, the Davisson—Germer experiment showed the wave -nature of matter , thus completing the theory of wave -particle duality.

Wave Nature of Matter Causes Quantization The wave nature of matter is responsible for the quantization of energy levels in bound systems.

To consider why wave nature of matter in bound systems leads to quantization, let's consider an example in classical mechanics. The wave nature of matter is responsible for the quantization of energy levels in bound systems.

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Just like a free string, the matter wave of a free electron can have any wavelength, determined by its momentum. Explain relationship between the wave nature of matter and the quantization of energy levels in bound systems Particle-Wave Duality Wave —particle duality postulates that all physical entities exhibit both wave and particle properties. Wave —particle duality postulates that all physical entities exhibit both wave and particle properties. De Broglie's wave matter wave : In , Louis-Victor de Broglie formulated the de Broglie hypothesis, claiming that all matter , not just light, has a wave -like nature.

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His hypothesis was soon confirmed with the observation that electrons matter also displays diffraction patterns, which is intuitively a wave property, as shown in. The wavelength of the matter wave associated with a baseball, say moving at 95 miles per hour, is extremely small compared to the size of the ball so that wave -like behavior is never noticeable.

Longitudinal Waves An example of a longitudinal wave is a sound wave.

Some longitudinal waves are also called compressional waves or compression waves. Like transverse waves , longitudinal waves do not displace mass. The most common pressure wave is the sound wave. After thinking for a while, de Broglie said to himself, "If mass is related to energy , and energy is related to frequency , then mass must be related to frequency! It's like saying "If I'm related to my brother , and my brother is related to my sister , then I must be related to my sister. If mass is related to frequency, then an object with mass must also have frequency. In other words, an object with mass must have wave-like properties!

This led de Broglie to propose the wave-particle duality of matter. But where were these so called matter waves? Why hadn't anybody seen them? If you're good at math, you may be able to derive the exact same formula yourself. When de Broglie looked at his equation, though, he realized that something was wrong. Why should the wavelength of an object like an electron, or a baseball, depend on the speed of light? Neither baseballs nor electrons travel at the speed of light — only light travels at the speed of light!

The problem, of course, was that de Broglie had derived his relationship using equations that applied to light, and not to matter. Luckily, the problem was easy to fix. All de Broglie needed to do was replace the speed of light, c , with some general speed, v. That way, the de Broglie relationship between mass and wavelength could be applied to any thing , traveling at any speed.

Let's try to find the wavelengths of a few common objects Figure 6. One of the fastest baseballs ever pitched traveled at a speed of If the average baseball has a mass of 0.

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Dividing by a fraction is the same as multiplying by its reciprocal. In order to account for units, you have to substitute basic units for compound units. Substituting these basic units into the equation in place of Joules yields:. Stock cars typically race at around a speed of If the average stock car has a mass of 1, kg, what is the stock car's wavelength? What do you notice about the wavelength of a typical baseball and the wavelength of a typical stock car?

## Wave-particle duality

They're both extremely small, aren't they? In fact, even the strongest microscope in the world today can't see down to sizes like 9. Well, that explains why we've never seen a matter wave — matter waves are just too small. If matter waves are too small to see, then how did scientists prove that they exist? After all, the scientific method requires experimental evidence before a theory is accepted — and certainly before a scientist is awarded a Nobel Prize for that theory!

Luckily, you can see matter waves. The only trick is to pick matter with waves that are big enough to see.

Take another look at the two example questions that we just did. Notice how the only two factors influencing the wavelength of an object are the object's mass and the object's speed. In our two examples, the car was more massive than the baseball, and it was traveling at a faster speed. What do you notice about the car's wavelength compared to the baseball's wavelength? The car's wavelength was a lot smaller, wasn't it? It turns out that the larger the mass of an object, and the faster the speed at which the object is traveling, the smaller the object's wavelength. Similarly, the smaller the mass of an object, and the slower the speed at which the object is traveling, the larger the object's wavelength.

This is a direct consequence of de Broglie's equation for the wavelength — because both mass, m , and speed, v , appear in the denominator the lower part of the fraction , they must both be big if you want a small wavelength, and small if you want a big wavelength.

### Examples of matter wave in the following topics:

Obviously, in order to see matter waves experimentally, it would be best to have a big wavelength. That means we need an object with a small mass and a slow speed. What's the smallest object that you know?