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Principles of quantum mechanics

   Uncertainty principle.
One of the most important concepts of quantum mechanics is the uncertainty principle, which states that there is always some uncertainty when trying to measure the posistion and momentum of a particle. More specifically, the product of the uncertainty in position, D x, and the uncertainty in momentum, Dmu, is always greater than or equal to h over 2p, where h is planck's constant. When trying to determine the position of an electron, for example, we cannot know exactly where it is and where it's going at the same time. The more accurately one is measured, the less accurately the other is known. To we measure the position of the electron, for example, we can only obtain the information through the collision of the electron with another subatomic particle, such as a photon. After the collision, the momentum of the photon changes--it "bounces" away, and from this change in momentum the position of the electron is calculated (this is how we see-photons bouncing off objects make possible vision). However, the photon also gives the electron a change in momentum, so that now the position and velocity of the electron has changed from what it was. Thus, we can't know precisely the position and velocity simultaneously.

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   Electron in the Bohr atom.
In the Bohr model, electrons revolved around the nucleus in orbits. According to classical physics, they should radiate energy as they move and ultimately fall to the center of the atom. Yet this is not so. The Quantum explanation is that electrons can only exist in predefined, discrete energy levels, and nowhere in between. The lowest energy level is not at the center of the atom, and electrons may go no closer than the lowest level. This explains why they don't collide into the nucleus. To move to another energy level, they must gain or lose exactly the energy difference between the levels. This explains spectral lines. Another explanation is that, if electrons crashed into the nucleus, their velovity would be zero and the uncertainty would also be zero. This would be a direct violation of the uncertainty principle, a fundamental property of nature.

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   Spin and Quantum Numbers.
It was discovered experimentally that subatomic particles have intrinsic angular momentum. That is, that angular momentum is not given by some interaction, but a property of the particles. This is a quantum property that classical physics has no explanation for. The closest thing on the macroscopic level is rotation (since angular momentum leads to rotating), so this property is called "spin". Subatomic particles, however, don't really spin; they just have the angular momenta. This property is quantatized since the particles may only have certain discrete values of spin and not any value in between. Electrons have spins of either +1/2 or -1/2.
In the quantum model, electrons in the atom are given four quantum numbers to distinguish them. The first three distinguish the energy level, the shape of the orbital, and in which orbital the electron is located (has 90% chance of being found), and the last one gives the spin. The Pauli Exclusion Principle states that no 2 electrons in the atom can have the same 4 quantum numbers. If they occupy the same energy level and orbital, then they must have opposite spin.

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