PHY100H1 Lecture Notes - Matter Wave, Bohr Model

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6 Feb 2013
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Quantum Physics: Planks Constant
If Planck’s constant is zero:
- First, energy of radiation would be zero.
E = h x f. So, h = E/f where h is Plancks constant, E is energy and f is the frequency
of the particle. If that is 0=E/f that means that E= 0
- Second, particles would not have wave properties.
Matter wave length (m) = h / mv where h is Plancks constant, m is mass and v is
velocity. When h equals 0, matter wave length would be zero as well.
- Third, the uncertainty principle would be meaningless.
(Δx)·(Δv) h/m whereΔx is uncertainty in position, Δv is uncertainty in
velocity, h is Planks constant and m is mass. If h equals 0, (Δx)·(Δv) would
equals 0. Then, there would be no uncertainty because we could predict both
velocity and position with pinpoint accuracy.
- Forth, when h = 0, there would be no quantum physics and Newtonian physics
would be valid.
Comments about Planck's Constant
1) Planck's constant proves to have a very small value.
2) The quantity, h, is the central constant of quantum physics.
3) In a universe in which h = 0, there would be no quantum physics and classical
physics would be valid in the sub-atomic domain.
4) [for the Bohr model of the hydrogen atom, in the equation of the angular
momentum of the electron电子动量] ... Planck's constant appears again in a
fundamental way.
5) Planck's constant, h, probably appears nowhere that has more, deep-seated
significance than in the Uncertainty Principle.
6) We can always tell whether a particular theory is a classical or a quantum theory
by inspecting its results to see whether Planck's constant, h, enters. If it contains h,
either explicitly or hidden in a numerical factor with other constants, the theory is a
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