Explain Matter waves and their Characterist ic properties engineering physics

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Engineering-Physics-06PHY12--BE-I-Semester--VTU-Belagaum-Unit-1-Modern-physics-->View question

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All matter can exhibit wave-like behaviour. For example a beam of electrons can bediffracted just like a beam of light or a water wave. Matter waves are a central part of the theory of quantum mechanics, an example of wave–particle duality. The concept that matter behaves like a wave is also referred to as the de Broglie hypothesis due to having been proposed by Louis de Broglie in 1924.Matter waves are often referred to as de Broglie waves.

The de Broglie wavelength is the wavelength, λ, associated with a particle and is related to its momentum, p, through the Planck constant, h:

$Properties of Matter waves$

Wave-like behaviour of matter was first experimentally demonstrated in theDavisson–Germer experiment using electrons, and it has also been confirmed for other elementary particles, neutral atoms and even molecules. The wave-like behaviour of matter is crucial to the modern theory of atomic structure and particle physics.

λ=p

Since the wave vector k is defined as k=2πλ, we can rewrite this equation as

p=k
2πr=nλ

Now using the wavelength-momentum relationship λ=p to replace λ we get

rp=nh2π

Since rp equals the angular momentum, we have

M=n

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