|MadSci Network: Physics|
Hi Robert, You ask some excellent questions, and I will do my best to answer them for you. The way a quantum system behaves is governed by what is called the Hamiltonian of the system. The Hamiltonian is the sum of the kinetic and potential energy operators, and so it's values correspond to the total energy of the system. In quantum mechanics the Hamiltonian can only give discrete values, and so the possible values of the total energy are quantized. The important thing to note is that this says nothing about the values of the kinetic or potential energies. Quantum mechanics is a little strange. It allows for particles to be in more than one state at a time (i.e. two or more places at the same time, or two or more energies). When you measure the particle, you will only ever see it in one of these states, but it is possible to show that it was in a superposition by indirect means (see the link concerning the double slit experiment below). Any thing we can observe (or measure) has what is called an operator associated with it. The operator is a mathematical device which describes what will happen to the particle when you measure it. If you can define the correct type of operator for something, then you can measure it. The Hamiltonian is the operator which correspond to measuring the total energy of a system. It is also possible to define a kinetic energy operator. The interesting thing here, however, is that what might be one of the allowed kinetic energy levels may correspond to a superposition of total energy levels, and vica versa. For experiments we are almost always only interested in the total energy level, as given by the Hamiltonian. One reason for this is because it defines the shells occupied by electrons (these are the clouds you mentioned in the title). I hope this goes someway towards answering the first part of your question. I'm afraid that to show this is true requires quite a bit of mathematics. I have included a link on Hamiltonians and on Operators in quantum mechanics below too, in case you do require further information. The second part you asked about was what happens if you add kinetic energy to an atom. The answer to this largely depends on how you add energy. If you add energy to both the nucleus and the electrons, then it is possible to simply accelerate the entire atom, with little or no effect on the electrons. This is what happens when you throw a baseball for example. If however the atom absorbs the energy internally, like when two atoms collide, or when an atom absorbs a photon (a particle of light), then the electrons are excited to higher energy levels. If you add enough energy, then it is possible for an electron to break free, with the atom becoming an ion. The energy required to achieve this is known as the ionisation energy. Electrons which are in excited states like this often decay into lower energy states by emitting a photon, through spontaneous emission. The probability of this happening within a given time period usually depend on how big a difference there is in energy levels between the initial energy level and the final energy level, although the can be added complications as not all transitions are possible (the laws governing these are known as selection rules). Any atom that can decay to a lower state through photon emission will, but the time taken for this to happen may be very long. Nuclear spins, for example, take a very long time to decay. While the exact time taken for a photon to be emitted is probabilistic (due to its quantum mechanical nature) there is a characteristic time associated with it known as the lifetime of the state. This is very similar to the concept of lifetimes (and half-lifes) in radioactivity. I hope this has answered your questions, Joe Useful Links: Operators in Physics Hamiltonians in Quantum Mechanics Hamiltonians in Quantum Mechanics Spontaneous Photon Emission Ionisation Energy
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