MPS - Wave Nature of Matter
Wave Nature of Matter
We've seen how light behaves like a wave in some instances and like a particle in others. In 1923, Louis de Broglie proposed that if light can have this wave-particle duality, so might matter. Using the same relationship between the momentum of a photon and its wavelength he proposed that matter could have a wavelength given by:
where we have substituted the classical momentum equation, mv in for p. This wavelength is known as the de Broglie wavelength. As it turns out, the de Broglie wavelength is incredibly small for normal sized objects. A 0.20 kg ball moving at 15 m/s would have a de Broglie wavelength = 2.2 x 10-34 m. In order to observe wave phenomena like interference and diffraction, the size of the object or size of the slit the object passes through can't be much larger than the wavelength. This means that, if matter does have wave properties, it would be difficult to detect in normal sized objects. However, electrons, being significantly smaller, have a de Broglie wavelength around 10-10 m. This is still a small wavelength, but it is detectable. Within a few years experiments were done on electrons (and eventually protons, neutrons, and other particles) that showed diffraction patterns corresponding to the predicted de Broglie wavelength of the electrons. With these experiments, matter was proven to have a wave nature.
The Wave Function, Probability, and Uncertainty
One of the more fascinating consequences of the wave nature of matter is observed when electrons are shot at a double slit. As a wave, particles like electrons have what is known as a wave function that mathematically describes all of the possibilities of where the particle could be located given some basic information. Watch this video to see how this can create astonishing results at the quantum scale.
The wave function can describe the probability of an electron being at different places. When acting as a wave, the electron seems to exist at all of the possible locations described by the wave function! It's only when trying to observe the actual location of the electron that its wave function "collapses" and it ends up in one position. As was mentioned in the video at the beginning of the unit, the simple act of observing the electron means that we must interact with it. This not only causes the collapse of the wave function into a defined value, but also limits our ability to know everything there is to know about the electron. Werner Heisenberg's uncertainty principle describes this phenomenon. The uncertainty principle says that one cannot measure both the position and momentum (think velocity) of an object precisely at the same time.
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