Zeeman's Effect

The more refrangible components are the ones whose period is shorter than that of the original radiation.

Cornu[93] and by C. G. W. König[94] found that their circular vibration was the same as the current in the electromagnet.

Thgis means that the vibration is due to a resinously-charged electron.

Let the magnetizing current and the electron be supposed to circulate round the axis of z in the direction in which a right-handed screw must turn in order to progress along the positive direction of the axis of z; then the magnetic force is directed positively along the axis of z, and, in order that the force on the electron may be directed inward to the axis of z (so as to shorten the period), the charge on the electron must be negative.

The value of e/m for this negative electron may be determined by measurement of the separation between the components of the triplet in a magnetic field of known strength; for, as we have seen, the difference of the frequencies of the outer components is eK/m. The values of e/m thus determined agree well with the estimations[95] of e/m for the corpuscles of cathode rays.

The phenomenon discovered by Zeeman is closely related to the magnetic rotation of the plane of polarization of light.[96]

Both effects may be explained by supposing that the molecules of material bodies contain electric systems which possess natural periods of vibration, the simplest example of such a system being an electron which is attracted to a fixed centre with a force proportional to the distance.

Zeeman’s effect represents the influence of al external magnetic field on the free oscillations of these electric systems, while Faraday’s effect represents the influence of the external magnetic field on the forced oscillations which the systems perform under the stimulus of incident light. The latter phenomenon may be analysed without difficulty on these principles, the equation of motion of one of the electrons being taken in the form

where m denotes the mass and e the charge of the electron, r its distance from the centre of force, κ2r the restitutive force, E and H the electric and magnetic forces. When the electron performs forced oscillations under the influence of light of frequency n, this equation becomes

The influence of the magnetic force on the motion of the electron is small compared with the influence of the electric force, i.e. the second term on the right is small compared with the first term; so in the second term we may replace r by its value as found from the first term, namely, eE/(κ2 – mn2). The equation thus becomes

If P denote the electric moment per unit volume, we have:

P = er × the number of such systems in unit volume of the medium;

so P must be of the form

where ε evidently represents the dielectric constant of the medium, and σ is the coefficient which measures the magnetic rotatory power. In the magneto-optic term we may replace H by K, the external magnetic force, since this is large compared with the magnetic force of the luminous vibrations. Thus if D denote the electric induction, we have

Combining this with the usual electromagnetic equations,

we have

When a plane wave of light is propagated through the medium in the direction of the lines of magnetic force, and the axis of x is taken parallel to this direction, the equation gives

and these equations, as we have seen,[98] are competent to explain the rotation of the plane of polarization.

From the occurrence of the factor (κ2 – mn2) in the denomi. nator of the expression for the magneto-optic constant σ, it may be inferred that the magnetic rotation will be very large for light whose period is nearly the same as a free period of vibration of the electrons. A large rotation is in fact observed[99] when plane-polarized light, whose frequency differs but little from the frequencies of the D-lines, is passed through sodium vapour in a direction parallel to the lines of magnetic force.

The optical properties of metals may be explained, according to the theory of electrons, by a slight extension of the analysis which applies to the propagation of light in transparent substances, It is, in fact, only necessary to suppose that some of the electrons in metals are free instead of being bound to the molecules: a supposition which may be embodied in the equations by assuming that an electric force E gives rise to a polarization P, where

the term in α represents the effect of the inertia of the electrons; the term in β represents their ohmic drift; and the term in γ represents the effect of the restitutive forces where these exist. This equation is to be combined with the customary electromagnetic equations

In discussing the propagation of light through the metal, we may for convenience suppose that the beam is plane-polarized ​and propagated parallel to the axis of z, the electric vector being parallel to the axis of x. Thus the equations of motion reduce to

For Ex, and Px we may substitute exponential functions of

where n denotes the frequency of the light, and μ the quasi-index of refraction of the metal: the equations then give at once

Writing

for μ, so that ν is inversely proportional to the velocity of light in the medium, and κ denotes the coefficient of absorption, and equating separately the real and imaginary parts of the equation, we obtain

When the wave-length of the light is very large, the inertia represented by the constant α has but little influence, and the equations reduce to those of Maxwell’s original theory[100] of the propagation of light in metals. The formulae were experimentally confirmed for this case by the researches of E. Hagen and H, Rubens[101] with infra-red light; a relation being thus established between the ohmic conductivity of a metal and its optical properties with respect to light of great wavelength.

When, however, the luminous vibrations are performed more rapidly, the effect of the inertia becomes predominant; and ​if the constants of the metal are such that, for a certain range of values of n, ν2κ is small, while ν2(1 - κ2) is negative, it is evident that, for this range of values of n, ν will be small and κ large, i.e., the properties of the metal will approach those of ideal silver.[102] Finally, for indefinitely great values of n, ν2κ is small and ν2(1 - κ2) is nearly unity, so that ν tends to unity and κ to zero: an approximation to these conditions is realized in the X-rays.[103]

In the last years of the 19th century, attempts were made to form more definite conceptions regarding the behaviour of electrons within metals.

The original theory of electrons had been proposed by Weber[104] for the purpose of explaining the phenomena of electric currents in metallic wires. Weber, however, made but little progress towards an electric theory of metals; for being concerned chiefly with magneto-electric induction and electromagnetic ponderomotive force, be scarcely brought the metal into the discussion at all, except in the assumption that electrons of opposite signs travel with equal and opposite velocities relative to its substance.

The more comprehensive scheme of his successors half a century afterwards aimed at connecting in a unified theory all the known electrical properties of metals, such as the conduction of currents according to Ohm’s law, the thermo-electric effects of Seebeck, Peltier, and W. Thomson, the galvano-magnetic effect of Hall, and other phenomena which will be mentioned subsequently.

The later investigators ranged beyond the group of purely electrical properties, and sought by aid of the theory of electrons to explain the conduction of heat.

The principal ground on which this extension was justified was an experimental result obtained in 1853 by G. Wiedemann and R. Franz,[105] who found that at any temperature the ratio of the thermal conductivity of a body to its ohmic conductivity is approximately the same for all metals, and that the value of this ratio is proportional to the absolute temperature.

In fact, the conductivity of a pure metal for heat is almost independent of the temperature; while the electric conductivity varies in inverse proportion to the absolute temperature, so that a pure metal as it approaches the absolute zero of temperature tends to assume the character of a perfect conductor.

The 2 conductivities are closely related was shown to be highly probable by the experiments of Tait, in which pieces of the same metal were found to exhibit variations in ohmic conductivity exactly parallel to variations in their thermal conductivity.

The attempt to explain the electrical and thermal properties of metals by aid of the theory of electrons rests on the assumption that conduction in metals is more or less similar to conduction in electrolytes; at any rate, that positive and negative charges drift in opposite directions through the substance of the conductor under the influence of an electric field.

It was remarked in 1888 by J. J. Thomson,[106] who must be regarded as the founder of the modern theory, that the differences which are perceived between metallic and electrolytic conduction may be referred to special features in the two cases, which do not affect their general resemblance. electrolytes the carriers are provided only by the salt, which is dispersed throughout a large inert mass of solvent; whereas in metals it may be supposed that every molecule is capable of furnishing carriers.

Thomson, therefore, proposed to regard the current in metals as a series of intermittent discharges, caused by the rearrangement of the constituents of molecular systems—a conception similar to that by which Grothuss[107] had pictured conduction in electrolytes. This view would, as he showed, lead to a general explanation of the connexion between thermal and electrical conductivities,

Most of the later writers on metallic conduction have preferred to take the hypothesis of Arrhenius[108] rather than that of Grothuss as a pattern; and have therefore supposed the interstices between the molecules of the metal to be at all times swarming with electric charges in rapid motion.

11: 1898 E. Riecke[109] effected an important advance by examining the consequences of the assumption that the average velocity of this random motion of the charges is nearly proportional to the square root of the absolute temperature T. P. Drude in 1900 replaced this by the more definite assumption that the kinetic energy of each moving charge is equal to the average kinetic energy of a molecule of a perfect gas at the same temperature, and may therefore be expressed in the form qT, where q denotes a universal constant.

In the same year J. J. Thomson remarked that it would accord with the conclusions drawn from the study of ionization in gases to suppose that the vitreous and resinous charges play different parts in the process of conduction.

The resinous charges may be conceived of as carried by simple negative corpuscles or electrons, such as constitute the cathode rays: they may be supposed to move about freely in the interstices between the atoms of the metal. The vitreous charges, on the other hand, may be regarded as more or less fixed in attachment to the metallic atoms.

According to this view the transport of electricity is due almost entirely to the motion of the negative charges.

An experiment which was performed at this time by Riecke[112] lent some support to Thomson’s hypothesis.

A cylinder of aluminium was inserted between two cylinders of copper in a circuit, and a current was passed for such a time that the amount of copper deposited in an electrolytic arrangement would have amounted to over a kilogramme. The weight of each of the three cylinders, however, showed no measurable change; from which it appeared unlikely that metallic conduction is accompanied by the transport of metallic ions.