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Monday, 16 November 2009 07:44 |
- early
 quantum physics did not ask the question of `why' quantum effects are found in the microscopic world
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Perhaps one of the key questions when Bohr offered his quantized orbits as an explanation to the UV catastrophe and spectral lines is, why does an electron follow quantized orbits? The response to this question arrived from the Ph.D. thesis of Louis de Broglie in 1923. de Broglie argued that since light can display wave and particle properties, then perhaps matter can also be a particle and a wave too.
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- One way of thinking of a matter wave (or a photon) is to think of a wave packet. Normal waves look with this:
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- having no beginning and no end. A composition of several waves of different wavelength can produce a wave packet that looks like this:
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- the wave packet interpretation requires the particle to have no set position
- momentum of a particle is proportional to the wavelength of the particle
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So a photon, or a free moving electron, can be thought of as a wave packet, having both wave-like properties and also the single position and size we associate with a particle. There are some slight problems, such as the wave packet doesn't really stop at a finite distance from its peak, it also goes on for every and every. Does this mean an electron exists at all places in its trajectory?
de Broglie also produced a simple formula that the wavelength of a matter particle is related to the momentum of the particle. So energy is also connected to the wave property of matter.
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- Lastly, the wave nature of the electron makes for an elegant explanation to quantized orbits around the atom. Consider what a wave looks like around an orbit, as shown below
- only certain wavelengths will fit into orbit, so quantiziation is due to wavelike nature of particles
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The electron matter wave is both finite and unbounded (remember the 1st lecture on math). But only certain wavelengths will `fit' into an orbit. If the wavelength is longer or shorter, then the ends do not connect. Thus, de Broglie explains the Bohr atom in that on certain orbits can exist to match the natural wavelength of the electron. If an electron is in some sense a wave, then in order to fit into an orbit around a nucleus, the size of the orbit must correspond to a whole number of wavelengths.
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- wavelike nature also means that a particles existence is spread out, a probability field
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Notice also that this means the electron does not exist at one single spot in its orbit, it has a wave nature and exists at all places in the allowed orbit. Thus, a physicist speaks of allowed orbits and allowed transitions to produce particular photons (that make up the fingerprint pattern of spectral lines). And the Bohr atom really looks like the following diagram:
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- the idea of atoms being solid billiard ball type objects fails with quantum physics
- quantum effects fade on larger scales since macroscopic objects have high momentum values and therefore small wavelengths
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While de Broglie waves were difficult to accept after centuries of thinking of particles are solid things with definite size and positions, electron waves were confirmed in the laboratory by running electron beams through slits and demonstrating that interference patterns formed.
How does the de Broglie idea fit into the macroscopic world? The length of the wave diminishes in proportion to the momentum of the object. So the greater the mass of the object involved, the shorter the waves. The wavelength of a person, for example, is only one millionth of a centimeter, much to short to be measured. This is why people don't `tunnel' through chairs when they sit down.
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