a. Conceptually, discuss the particle-wave duality of light. Discuss the implications of this in combination with the de Broglie (pronounced “de Broy”) equation.

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Chapter7: Quantum Mechanics
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Problem 38P: Suppose an electron is confined to a region of length 0.1 nm (of the order of the size of a hydrogen...
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a. Conceptually, discuss the particle-wave duality of light. Discuss the implications of this in combination with the de Broglie (pronounced “de Broy”) equation.

b. The electron of a hydrogen atom is usually no further than 1.0 Å from the proton. We can therefore say the upper limit of the radius of an isolated hydrogen atom is roughly 1.0 Å. How does the de Broglie wavelength of the electron compare to this radius? (The velocity of an electron in the first principal energy level is about 2.2 x 106 m/s). Explain why wave-particle duality is so important for quantum mechanics, yet not required in macroscopic systems that are well described by classical mechanics.

c. Comment as to whether neutrons with velocity 4.14 x 103 m/s may be used to determine structures of molecules in a diffraction-based experiment. You may consider the relevant distance between atoms in molecules to be on the order of 1 Å.

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