fixed for any given transition and whether a transition will occur is again governed by selection rules. In other words, although an electron is given a quantum of energy sufficient to raise it to an adjacent higher state, it will not go up to that state if the transition is not permitted. In that case, it is theorized that if the electron absorbs the quantum, it will most probably go up to the excited state, remain there for a time allowed by the uncertainty principle, reradiate the quantum, and return to its original state. If an electron is given a sufficiently large quantum of energy, it will completely leave the atom. The electron will carry off as kinetic energy the difference between the input quantum and the energy required to ionize. The remaining atom will now become a positively charged ion, and the stripped electron will become a free electron. This electron may have sufficient energy when it leaves the atom (or it may acquire sufficient energy from an external field) to collide with another atom and strip it of an electron. This is the basis for electric discharge where free electrons are accelerated by an applied field and, as they collide with neutral atoms, generate additional free electrons. This process avalanches as the electrons approach the positive electrode. At the same time, the positively charged ions are accelerated toward the negative electrode. In a vacuum, when a voltage is applied between two electrodes, electrons will move from the cathode to the anode. Of course, in a vacuum there will be no avalanching effects. Electrons are emitted from the cathode by a number of mechanisms:

• Thermionic Emission - Because of. the nonzero temperature of the cathode, free electrons are continuously bouncing inside. Some of these have sufficient energy to overcome the work function of the material and can be found in the vicinity of the surface. The cathode may be heated to increase this emission. Also to enhance this effect, cathodes are usually made of, or coated with, a low work-function material such as thorium.

• Shottky Emission - This is also a thermionic type of emission except that in this case, the applied electric field effectively decreases the work function of the material, and more electrons can then escape.

• High Field Emission - In this case, the electric field is high enough to narrow the work-function barrier and allow electrons to escape by tunneling through the barrier.

• Photoemission - Electromagnetic radiation of energy can cause photoemission of electrons whose maximum energy is equal to or larger than the difference between the photon energy and the work function of the material.

• Secondary Emission - Electrons striking the surface of a cathode could cause the release of some electrons and, hence, a net amplification in the number of electrons. This principle is used in the construction of photomultipliers where light photons strike a photoemitting cathode releasing photoelectrons. These electrons are subsequently amplified striking a number of electrodes (called dynodes) before they are finally collected by the anode.

Electromagnetism - In a high-gradient magnetic separator, the force on a magnetized particle depends on the intensity of the magnetizing field and on the gradient of the field. When a particle is magnetized by an applied magnetic field, the particle develops an equal number of north and south poles. Hence, in a uniform field, a dipolar particle experiences a torque, but not a net tractive force. In order to develop a net tractive force, a field gradient is required; that is, the induced poles at the opposite ends of the particle must view different magnetic fields. In a simplified, one-dimensional case, the magnetomotive force on a particle is given by:

where ¡jl is the magnetic moment of the particle under field intensity, HdH/dx is the field gradient. The magnetic moment n is the product of the magnetization of the particle and its volume (/m = MV). And magnetization is the product of the particle susceptibility, x> and the field intensity, H. In water purification, this magnetic force may be used to separate magnetizable particles.

Direct and Alternating Currents - Electrolytic treatment is achieved when two different metal strips are dipped in water and a direct current is applied from a rectifier. The higher the voltage, the greater the force pushing electrons across the gap between the electrodes. If the water is pure, very few electrons cross the path between the electrodes. Impurities increase conductivity, hence decreasing the required voltage. Additionally, chemical reactions occur at both the cathode and the anode. The major reaction taking place at the cathode is the decomposition of water with the evolution of hydrogen gas. The anode reactions are oxidations by four major means: (1) oxidation of chloride to chlorine and hypochlorite, (2) formation of highly oxidative species such as ozone and peroxides, (3) direct oxidation by the anode, and (4) electrolysis of water to produce oxygen gas.

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