After our grand piano weighs 400 kilograms,

After watching this video, you will be able to explain the concept of wave-particle duality, give an example of an application of wave-particle duality, and complete simple calculations using the de-Broglie wavelength equation. A short quiz will follow.

Wave-Particle Duality

In the early 20th century, we discovered something amazing about particles and waves: light was both a particle and a wave. If that strikes you as impossible or hard to fathom, you wouldn’t be alone; it took a long time to convince a world of skeptical physicists.

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But the work of Albert Einstein and Max Planck had led to the realization that light didn’t always act like a wave. Light would indeed refract, reflect and diffract just as you would expect waves to. But Einstein’s photoelectric effect experiment showed that light also acts like it contains some sort of particle. Light, it turns out, contains packets of energy of a particular size called quanta, and these quanta can collide with atoms and be absorbed by them.But the full concept of wave-particle duality was introduced by Louis-Victor de Broglie in 1923 as part of his doctoral dissertation. He suggested that perhaps not only did waves, like light, behave as particles, but particles could also behave as waves. He suggested that matter had wave-like properties.

But, if that’s true, why don’t we see those properties in everyday life? Why don’t you see dogs bouncing off mirrors? Or, people spreading out and producing diffraction patterns when they walk through doors?

The de-Broglie Wavelength

To answer that question, we need to do some math. de Broglie suggested that matter had a wavelength, which was later called the de-Broglie wavelength. The de-Broglie wavelength, lambda, of an object or particle, measured in meters, would be equal to Planck’s constant, h, which is just a number that’s always equal to 6.

63 * 10^-34, divided by the momentum of the object or particle, p, measured in kilogram meters per second. And let’s also remember the basic equations for momentum, which is say 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.

Example Calculation

To test this out, let’s try calculating the wavelength of, say, a grand piano. Suppose our grand piano weighs 400 kilograms, and let’s roll it down the stairs, such that it’s moving at a speed of 2 meters per second. What is the wavelength of the grand piano?Well, 6.63 * 10^-34 divided by the momentum, mv, which is 400 multiplied by 2.

Type that all into a calculator and that gives us a wavelength of 8.3 * 10^-37. This is a tiny, tiny number. What this means is that for a grand piano to act like a wave, for example by diffracting as it goes around an obstacle, the obstacle would have to be just 8.3 * 10^-37 meters across – significantly bigger and nothing would happen.To put that into perspective, an electron is 10^-16 meters across. So, the obstacle would have to be one and twenty-one zeros smaller than an electron – no such object even exists.

So, when we do the math, it becomes pretty obvious why we never see a grand piano acting like a wave. It has a wavelength, it’s just much, much too small.

Application: The Electron Microscope

Although grand pianos might just be too large, electrons are still pretty tiny. The de-Broglie wavelength of an electron is small enough that you can observe wave properties. This is used most famously in the electron microscope.

This incredible piece of technology bounces electrons off the atom, observing diffraction effects as it does, and uses the paths of the electrons afterwards to create an image of the atom itself!

Lesson Summary

de Broglie was the first to suggest and show mathematically that not only could waves act like particles, but particles – matter – could also act like waves. He introduced it as part of his doctoral dissertation in 1923. This is the concept of wave-particle duality.

The only reason we don’t see matter act like a wave in everyday life is that the wavelength of everyday size objects is just too small.You can calculate this so-called de-Broglie wavelength using this equation. It says that the de-Broglie wavelength, lambda, of an object or particle, measured in meters, would be equal to Planck’s constant, h, which is always 6.63 * 10^-34, divided by the momentum of the object or particle, p, measured in kilogram meters per second.Probably the most famous application of this theory is the creation of the electron microscope, a device that uses the wave-properties of electrons to create an image of the atom itself!

Learning Outcomes

After this lesson is done, you should be able to:

  • Explain wave-particle duality and why we don’t see everyday items as waves
  • Describe and calculate the de-Broglie wavelength
  • Recall how an electron microscope functions

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