*David Wood*Show bio

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

Lesson Transcript

Instructor:
*David Wood*
Show bio

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you should be able to explain what wave-particle duality is, explain how the Davisson-Germer experiment contributed to our evidence for it, and use the de Broglie equation to solve problems. A short quiz will follow.

**Wave-particle duality** is the idea that light and sub-atomic particles can behave both as waves but also as particles. Therefore, the two states are not mutually exclusive. A scientist called de Broglie introduced the idea in 1923, and it formed his doctoral dissertation.

This might be hard to imagine. How could light be both a wave AND a particle? And indeed, physicists found it difficult to accept, too. What we needed to be sure of wasn't just mathematics, but we needed actual experimental evidence. We already knew from the 19th century that light could behave as a wave -- that it exhibited reflection, refraction, and diffraction. These features couldn't be explained any other way. Then, Einstein's photoelectric effect experiment showed that light could also behave like a particle -- it turned out that light contains packets of energy, or 'quanta,' of a particular size. These days we call these packets 'photons.'

But that's just about light. To really pin down the more fundamental idea of wave-particle duality, we needed to also show that not only could light behave as a particle, but particles could also behave as waves.

In 1928, Clinton Davisson did exactly that in what would later be named the Davisson-Germer experiment. In his experiment, he fired electrons at a solid crystal lattice. Some electrons would reflect off the outermost layer of the crystal, while others would reflect off layers further inside the crystal. The electrons that reflected from the lattice were analyzed and turned out to have light and dark fringes in this pattern:

What did the pattern mean? Well, the electrons that bounced off different layers had interfered with each other, just like waves. By different electrons penetrating at different distances, this created a path difference between them. Wherever a peak met a peak or a trough met a trough, he saw a bright spot, called constructive interference. Where a peak met a trough, he saw a dark spot, called destructive interference. Electrons, it seemed, could behave as waves.

Now that it had been shown that particles and waves were one and the same thing, it was time to put some mathematics to it. De Broglie did this as part of his dissertation. He suggested that if something was a particle and a wave, then it must have both a wavelength (like a wave) and a momentum (like a particle), and that these things must be related to one another.

According to his equation, the **de Broglie wavelength**, or lambda, of an object or particle, measured in meters, would be equal to Planck's constant, *h*, which is just a number that is always equal to 6.63 x 10^-34, divided by the momentum of the object or particle, *p*, measured in kg m/s.

We can also expand on this by remembering the basic equation for momentum, an equation which states that the momentum of an object or particle is equal to the mass, measured in kilograms, multiplied by the velocity, measured in meters per second.

We can try this experiment by calculating the wavelength of an everyday object. For example, a Mini Cooper. What is the wavelength of a 1,000 kilogram Mini Cooper moving at 30 m/s?

First of all, we should write out what we know. We have the mass, *m*, which is 1,000, and the velocity, *v*, which is 30. We also know that Planck's constant is always 6.63 x 10^-34. So, we can just divide 6.63 x 10^-34 by the momentum *mv*, which is 1,000 multiplied by 30. That gives us a wavelength of 2.21 x 10^-38. This is a minuscule number.

So for a Mini Cooper to act like a wave -- to diffract, for example -- the obstacle it diffracted around would have to be a mere 2.21 x 10^-38 meters in size. Any bigger and nothing would happen. This is unbelievably tiny, as 1,000 trillion trillion objects this size would reach the width of an electron. As far as we know, no such object even exists. So, that's why a Mini Cooper doesn't appear to act like a wave.

**Wave-particle duality** is the idea that light and subatomic particles can behave both as waves but also as particles. It means that the two states are not mutually exclusive. We knew from the 19th century that light could reflect, refract, and diffract like a wave, and Einstein's photoelectric effect experiment showed us that light could also behave like a particle.

But then the Davisson-Germer experiment showed that particles like electrons could also behave like waves. In his experiment, Davisson fired electrons at a crystal lattice. Some electrons reflected from the outer layer of the crystal, and some reflected off layers further inside the crystal. The light that reflected from the lattice was analyzed and turned out to have light and dark fringes in a specific pattern. This was an interference pattern, showing that the different beams of electrons had interfered with each other just like a wave, creating constructive and destructive interference.

De Broglie put some math to wave-particle duality as part of his dissertation. He suggested that if something was a particle and a wave, then it would have to have both a wavelength (like a wave) and a momentum (like a particle), and that these things would be related to each other.

According to his equation, the **de Broglie wavelength**, or lambda, of an object or particle, measured in meters, would be equal to Planck's constant, *h*, which just a number that is always equal to 6.63 x 10^-34, divided by the momentum of the object or particle, *p*, measured in kg m/s. We should also note that the momentum of an object or particle is equal to the mass, measured in kilograms, multiplied by the velocity, measured in meters per second.

You should have the ability to do the following after watching this video lesson:

- Recall what wave-particle duality is
- Describe the Davisson-Germer experiment and the impact of the results of the experiment
- Explain de Broglie's mathematical representation of wave-particle duality and identify the de Broglie wavelength

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