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π= βπ π Wave Properties of Particles ( de Broglie Waves)
Remember photon case π= βπ π De Broglie: it is not only for photon but also for all particles π= ππ£ 1β π£ 2 / π 2 π= β 1β π£ 2 / π 2 ππ£
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Wave Equation π¦ π₯,π‘ =π΄ cos (ππ‘βππ₯)
Angular frequency of de Broglie waves π=2ππ=2ππ π 2 /β 1β π£ 2 / π 2 Note: βπ=π π 2 / 1β π£ 2 / π 2 Wave number of de Broglie waves π= 2π π = 2πππ£ β 1β π£ 2 / π 2
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de Broglie wave velocity
For a particle moves with velocity of v Group velocity π£ π = ππ ππ = ππ ππ£ / ππ ππ£ =v Phase velocity π£ π = π π
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Electron Diffraction Contoh:
Elektron dengan energi 54 eV menumbuk nikel. a. Hitung panjang gelombang de Broglie b. Bandingkan dengan pengukuran X-ray Berdasarkan x-ray diffraction, lattice spacing atom d= 0,91 A dan sudut diffraksi 65
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Particle in a box π π = 2πΏ π πΈ π = π 2 β 2 /8π πΏ 2
The quantization energy of trapped particle π π = 2πΏ π πΈπΎ= 1 2 π π 2 = (π π) 2 2π = β 2 /2π π 2 πΈ π = π 2 β 2 /8π πΏ 2
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Wave packet
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Uncertainty Principle
Ξπ₯= 1 2 π
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Uncertainty Formalism
Ξπ₯ Ξπ β₯ β/2 ΞπΈ Ξπ‘ β₯ β/2
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