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Phys 2D soln3 - 1a de Broglie postulated that even a...

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1a de Broglie postulated that even a massive particle of energy E has wave-like property with frequency f = E/h , whereas Einstein postulated that light of frequency f is quan- tized (like particles) with energy E = hf . 1b Newton’s law requires a set of initial conditions on the precise position and velocity (or momentum) of a particle, and determines the exact position and momentum of the par- ticle for all times afterwards. However, according to Heisenberg’s uncertainty principle, it is impossible to simultaneously know the position and momentum of a particle with infinite precision. 1c The electron spirals in closer to the nucleus, the uncertainty in its distance from the nucleus decreases. As a result, the uncertainty in momentum of the electron increases. The increase in uncertainty in momentum means increased energy cost (since p 2 = p ) 2 + p 2 ) for approaching the nucleus. 1d What’s waving in a matter wave is known as a wavefunction, the amplitude square of which gives the probability density of finding the particle according to Max Born.
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