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De Broglie Hypothesis (Deriving the de Broglie Wavelength ((Since de…
De Broglie Hypothesis
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General rule
whenever the de Broglie wavelength of an object is in the range of, or exceeds, its size, the wave nature of the objects is detectable and hence cannot be neglected.
if de Borglie wavelength is much too small compared to its size, the wave behavior of this object is undetectable.
Microscopic systems - the wavelength are finite and display easily detectable wave-like patterns
Macroscopic systems - the wavelength are infinitesimally small and display no discernible wave-like behavior
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1) Electron are not wave, how can they diffract??
2) Electron is not acting like our concept of a particle
3) It is acting more like our concept of a wave.
Hypothesis
De Broglie - think of matter (including electron) as having an associated wavelength which describe their wavelike properties. When they behave like wave, they act like they have certain wavelength.
λ = h/p
But, why we did not notice this wavelike before??
It is because the wavelike behavior is only evident when the aperture the electron passes through is approximately the size of the De Broglie wavelength which is about 10^-8 metres(very small).
This wavelike behavior can be observed in crystals
1) In crystals, the spacing between atoms is very small. It is small enough that it can behave like an aperture ~ the size of De Broglie wavelength of an electron
If we shoot electron into crystals, we can get diffraction of electron.
This behavior of electron behaving like waves is exist when the aperture is very small on the order of the De Broglie wavelength.
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