Drift speed

When ions move under equilibrium conditions in a gas and an external electric field, the energy gained from the electric field E between collisions is lost to the gas upon collision so that the ions move with a constant drift speed v = KE. The mobility K of ions of charge e in a gas of density N is given in tenns of the collision integral by the Chapman-Enskog fomuila [2]... 

Charge carriers in a semiconductor are always in random thermal motion with an average thermal speed, given by the equipartion relation of classical thermodynamics as m v /2 = 3KT/2. As a result of this random thermal motion, carriers diffuse from regions of higher concentration. Applying an electric field superposes a drift of carriers on this random thermal motion. Carriers are accelerated by the electric field but lose momentum to collisions with impurities or phonons, ie, quantized lattice vibrations. This results in a drift speed, which is proportional to the electric field = p E where E is the electric field in volts per cm and is the electron s mobility in units of cm /Vs. 

Ohm s law assumes that the drift speed of electrons in an electric field, is small compared to thek average speed, in a... 

MaxweU-Boltzmann distribution. At high electric fields, E > 10 kV/cm, no longer increases with electric field and approaches a limiting saturation speed, determined primarily by optical phonon emission. Eigure 3 shows the variation of drift speed with electric field for electrons and holes in various semiconductors. 

When an electric field was applied across the chamber some positrons annihilated prematurely, following field-induced drift to one of the electrodes. In this case the free-positron component of the lifetime spectrum was field dependent the maximum drift time, rmd, was given by the end-point of the lifetime spectrum and was due to thermalized positrons which had traversed the entire drift length l. The drift speed was then v+ = 1/rmd and the mobility could be found from... 

The elementary condition for obtaining conductivity in solutions is obviously the dissolution of electrolyte and considerable charge separation. The most common and important conduction mechanism relates to the motion of separated ions in the liquid medium, retarded by friction (solvent-solute and ion-ion interactions). The ions thus reach a constant drift speed (S) under the electric field ... 

Diffusing particles experience a viscous drag that opposes Fp When Fj and the viscous drag are balanced, diffusing particles reach a steady drift speed, s, (i.e., a steady rate of mass transfer). Hence, Fj is proportional to Sp Now consider M, particles that pass through area, A, normal to the direction of transport during time increment At. The flux, Jp of these particles is defined as... 

This equation shows that the electric field increases the drift velocity, whereas the drag coefficient reduces it. We define the proportionality constant between the drift speed (the magnitude of the drift velocity) and the field to be the mobility, /t, of the ion (a positive number), giving the following relation ... 

P19.29 The isoelectric point is the pH at which the protein has no charge. At that point, then, its drift speed under electrophoresis, s, vanishes. Plot the drift speed against pH and extrapolate the line to s = 0. The plot is shown in Fig. 19.9. 

D21.7 Because the drift speed governs the rate at which charge is transported, we might expect the conductivity to decrea.se with increasing solution viscasity and ion size. Experiments confirm these predictions for bulky ions, but not for small ions. For example, the molar conductivities of the alkali metal ions increase... 

When the particle has reached its drift speed, the accelerating and viscous retarding forces are equal, so we can write... 

At this point we can compare this expression for the drift speed with eqn 8.22 and hence find the expression for mobility given in eqn 8.23. 

An important application of the preceding material is to the determination of the molar mass of biological macromolecules. Electrophoresis is the motion of a charged species, such as DNA and ionic forms of amino acids, in response to an electric field. Electrophoretic mobihty is a result of a constant drift speed, so the mobility of a macromolecule in an electric field depends on its net charge, size (and hence molar mass), and shape. 

Electrophoresis is a very valuable tool for the separation of biopolymers from complex mixtures, such as those resulting from fractionation of biological cells. We shall consider several strategies controlling the drift speeds of biomolecules in order to achieve separation of a mixture into its components. 

Find the drift speed of a particle of radius 20 m and density 1750 kg m that is settling from suspension in water (density =... 

Find the mean speed of electrons at 293 K using this formula, b. If a current per unit area of 1.00 x lO A m 2 is flowing in a sample of gold at 293 K, find the mean drift speed. Find the ratio of the mean drift speed to the root-mean-square speed of electrons at this temperature. 

The drift speed times the density of mobile electrons equals the number of electrons passing per second. 

To satisfy Ohm s law, this collision time must be independent of the field. If we assume that these collisions are between the electrons traveling over some mean free path A that is associated with the lattice, the average speed of the electrons would have to be much larger than the drift speed produced by the applied electric field. This would be the case if the electrons behaved as an ideal gas in thermal equilibrium with the lattice. 

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