THE DISCOVERY OF THE ELECTRON

  1. FARADAY'S LAW OF ELECTROLYSIS.
    Within months of the announcement in 1800 by the Italian professor at the University of Pavia, Allessandro Volta, of his discovery of the Voltaic cell, a battery, to produce an electric current, the English chemist, Humphery Davy, using a Voltaic cell of very great power, passed an electric current through water. He found that the water was broken down into its elements, hydrogen and oxygen, the hydrogen gas bubbling up at the negative electrode and oxygen gas at the other, the positive electrode. This process became known as "electrolysis." Davy found that other materials could be broken down by an electric current. He passed electric current through what was known then as "muriatic" acid, and he found that hydrogen gas bubbled up at the negative electrode and a new element that he called "chlorine" at the other, the positive electrode. As a result of this experiment, muriatic acid was called "hydrochloric" acid. In 1807 Davy decomposed other chemical substances, soda and potash, by electrolysis, and discovered sodium and potassium. In 1833 Michael Faraday repeated and extended the experiments of Davy and others. He took great care to measure the precise amounts of hydrogen and oxygen evolved to the quantity of current flowing. He found that for each unit of electricity flowing, precisely two volumes of hydrogen and one volume of oxygen was evolved. Faraday's experiment made clear that matter was composed of atoms and that electricity was involved in the structure of chemical compounds. That is, the mass of an element liberated from the liquid, either in the form of gas bubbles (as for hydrogen, oxygen and chlorine) or as metal deposited at or near the electrode (as for copper), is proportional both to the molecular weight of the material freed and to quantity of electric charge transferred, but inversely proportional to the valence of the material liberated. For example, the electric charge passing through a molten quantity of common salt caused the sodium metal to collect at the negative electrode or cathode and liberated chlorine gas bubbles at the positive electrode or anode. The mass of metallic sodium that was deposited for each coulomb of charge transferred between the electrodes was 2.38 × 10-4 grams and 3.68 × 10-4 grams of chlorine gas was liberated. That is, for 1 gm-at.wt. (gram atomic weight) of sodium (that is, 23.0 gm, which is the atomic weight of sodium in grams) to be deposited on the cathode, there must be transferred a quantity of charge equal to
    23.0 gm / (2.38 × 10-4 gm/coul), or 96,500 coulombs.
    At the same time, 1 gm-at.wt. of chlorine gas (that is, 35.5 gm) is liberated at the anode by the transfer of a quantity of charge equal to
    35.5 / (3.68 × 10-4) = 96,500 coulombs.
    And when 96,500 coulombs is passed through water, to which a small amount of acid is added, there will be released 1 gm-at.wt. of hydrogen (1.008 gm) at the cathode, but only 1/2 gm-at.wt. of oxygen, that is, 1/2 of 16.000 grams or 8.000 grams at the anode. Hydrogen is a monovalent element (that is, it has a valence of one), as is the case for sodium and potassium, but oxygen is divalent (that is, it has a valence of two). This means that the passage of 96,500 coulombs through a solution, the quantity of charge capable of releasing 1 gm-at.wt. of a monovalent element, will release only 1/2 gm-at.wt. of a divalent element. Experiments bear out the conjecture that only 1/3 gm-at.wt. of a trivalent element will be released. This data allowed Faraday to formulate his law of electrolysis, which can be summarized in modern terms in the following equation:
    mass of material liberated at one electrode [gm] =
    {(charge passed [coul]) / (96400 coul)}{(no. of grams per gm-at.wt. of elemet) / (valence of element)}. (1)
    Faraday's law is sometimes as stated as two laws. The first law states that the mass of any given substance liberated or deposited by an electric current is directly proportional to the total quantity of electric charge passed. And the second law states the mass of an element liberated or deposited by a given quantity of electricity is proportional to the atomic weight of the element divided by it valence. Algebraic, the mass liberated is given by
    M = (It / 96500)[(Atomic weight in grams) / Valence], (2)
    where I is the current in amperes and t is the time in seconds. The quantity 96,500 coulombs of electric charge is a constant and is called appropriately one faraday of electric charge. The term electrolyte designates the conducting solution, electrode for the terminal at which the chemical element is liberated, and electrolysis for the process of passing an electric charge through a chemical solution. So Faraday's law of electrolysis says simply that in electrolysis one faraday releases 1 gm-at.wt. of any monovalent element, 1/2 gm-at.wt. of any divalent element, etc.

    The conduction of electric charge through a solution is carried by charged atoms, or ions (from Greek word for to wander, to go). For example, the breakdown of molten salt (sodium chloride) is composed of charged atoms (ions) of each element which are free to move about. These ions are symbolized by Na+ for sodium ion, and Cl- for chlorine ion. Similarly, water separates into hydrogen ions (H+) and oxygen ions (O--) when a small amount of acid is added to it. According to modern theory the size of charge on each ion is equal to the valence of that element, and is equivalent to the number of electrons carried by the ion. When the ion reaches the electrode it gives up its electrons if a negative ion or takes on electrons if a positive ion. The positive and negative ions in the solution migrate in opposite directions, the positive ions to the negative electrode (the cathode) and the negative ions to the positive electrode (the anode). Thus for each pair of Na+ and Cl- ions which reach their respective electrode, one electron moves through the circuit attached to the electrodes (that is, through the battery or generator).

    The logical implication of Faraday's laws of electrolysis is that, if elementary substances are composed of atoms, then electricity is divided into elementary quantity that behave like atoms of electricity. The idea had occurred to Faraday, but he was not convinced of the existence of atoms to regard the idea as justified. If there are charged atoms (ions) in the electrolyte, there must be some smallest quantity of charge that can be carried by any ion, the same for all ions of the same valence, since the fixed quantity of charge, 96,500 coulombs, deposits 1 gm-at.wt. of any univalent element. If we call the magnitude of this atom of charge e, then
    N0e = 96,500 coul., (3)
    where N0 is Avogadro's number, the number of atoms in 1 gram-atomic weight of an element, and is equal 6.02 × 1023 atoms, which has been determined by independent and entirely different experiments. If each atom carries one electron, then the charge transferred by 1 gm-at.wt. is
    (96,500 coulombs) / N0. Thus we get
    (96,500 coulombs) / (6.02 × 1023) = 1.60 × 10-19 coulombs.
    This is the charge on an electron.

    Conversely, this relation can be used to determine the value of Avagadro's number, if the charge of an electron e can be independently determined.

    But despite the clear implications of Faraday's discovery, the idea of discontinuity, or "atomicity" electricity, like the atoms of matter, was not generally accepted until near the end of the 19th century.

  2. GASEOUS DISCHARGE TUBES.
    A gas discharge tube is a glass tube into which a pair of metal plate electrodes have been sealed, called cathode (Greek, "the way down") and anode (Greek, "the way up"), the cathode being connected to the negative terminal and the anode to the positive terminal of the electric power source. When a potential difference is applied across the electrodes of the tube which contains air or another gas at a reduced pressure, the interior of the tube is filled a steady glow. The invention of these gaseous discharge tubes became possible with the invention of the air pump. Further improvement in vacuum pump design was achieved by a skilled German glass blower, Heinrich Geissler, in Bonn, Germany. In 1855 he devised a new vacuum pump, the mercurial air-pump. Certain elaborate tubes of glowing gas are still called "Geissler tubes." With the improvements of vacuum techniques, it became possible to make a systematic study of the behavior of discharge tubes at low pressures. The color of the discharge depends up the nature of gas present in the tube as well as pressure. As the pressure of the gas is lowered the internal luminosity of the gas is diminished, and a green fluorescent glow in the walls of the tube appear at very low pressures. The glow appears to be produced by something emanating from the negative electrode, the cathode. Although these rays were invisible, they cause light emission or fluorescence when they strike glass or other objects inside the tube. William Crookes in 1878 called these discharges from the cathode cathode rays. In 1869, J. W. Hittorf at Bonn observed that these rays could produce sharp shadows, indicating that they travel in straight lines. But Bonn professors Plucker and Hittorf observed the fluorescent cathode ray glow was shifted by a magnet, indicating that they could be deflected by a magnetic field. Later it was shown that the cathode rays could be deflected by an electric field.

    There were two hypotheses that were proposed to explain the nature of these strange "cathode rays". The German physicists proposed and defended the hypothesis that they were electromagnetic waves, similar to light. Heinrich Hertz (1857-1894), who had brilliantly verified Maxwell's electromagnetic theory of light, maintained that the cathode rays were longitudinal ether waves. He had failed to detect a magnetic field which should accompany the cathode rays, if they were an electric current, and also he was unable to detect the deflectability by an electric field. Hertz was probably unable to detect the effects that he sought because of the poor vacuum techniques. The English physicists defended the hypothesis proposed by Cromwell Fleetwood Varley (1828-1883) in 1871 that cathode rays are tiny corpuscles, "attenuated particles of matter, projected from the negative pole by electricity", that is, shot off in straight lines from the cathode. In 1878 Sir William Crookes (1832-1919) called the corpuscles "radiant matter", a name suggested by Faraday in 1816. G. Johnstone Stoney (1826-1911) of Dublin in 1894 proposed that these particles be designated by name electron.

  3. THE DISCOVERY OF THE ELECTRON.
    In 1897, J.J. Thomson (1856-1940) at Cambridge University settle the problem by a series of experiments. He showed that the particles had mass, although it was extremely small compared to the mass of hydrogen atom. Also he measured the ratio of the amount of charge to the amount of mass with considerable precision, finding that this ratio is constant regardless of the material of the cathode that acted as their source. He made what would be considered today a very primitive cathode ray tube. The anode had a hole through which a narrow beam of rays may pass into the main body of the evacuated container. The beam could be deflected by two additional electrode plates built into the tube. The difference of electric potential across the plates, with positive charge on upper plate and negative on the lower plate, would deflect the beam upward consistent with the assumption that of the negative charge on the particles of the beam. The cathode ray particles enter the region between the plates at the point O (origin of the coordinate system) with a velocity v; the particles will continue with this velocity as the horizontal component of the velocity of the rays. The x-coordinate and y-coordiante of particle are given by
    x = vt, y = ½ at2. (4)
    Eliminating the time t between these equations (4), we obtain the equation of the path,
    y = ½ a(x / v)2 = (a / 2v2)x2, (5)
    which is an equation of a parabola, verifying that the path of cathode ray particles follow a parabolic trajectory. We can obtain the deflection angle as the particles leaves the electric field by taking the derivative dy/dx of this equation (5), that is,
    tan φ = dy/dx = (a / 2v2)2x = ax / v2, (6)
    and evaluating it at x = s and φ = α,
    tan α = as / v2. (7)
    The acceleration a of a particle can be calculated from the equation of motion of an electric charge in an electric field:
    ma = Eq, or a = (e/m)E, (8)
    thus the acceleration of a particle depends upon the ratio of e/m, the ratio of charge to mass of the particle.
    Substituting in the previous equation (7) for the tangent of the angle of deflection α, we get
    tan α = eEs / mv2. (9)
    Also substitute the acceleration in equation (7) into the equation (5) of the path, and we get
    y = ax2 / 2v2 = (eE / m)(x2 / 2v2). (10)
    In this equation let h1 be the value of y when x = s, so that we get
    h1 = (eE / m)(s2 / 2v2) = (eEs2 / 2mv2). (11)
    The total deflection d of the beam of particles when it reaches the screen at the end of the tube is
    d = h1 + h2,
    where d is the distance from the center of the screen to the point where the deflected beam strikes the screen. Now let L designate the distance from end of the electric field between the plate electrodes to the screen at the end of the tube. Since the tangent of the angle of deflection α is equal to h2 / L, then h2 is L tan α; and using the equation (9) above, we get
    h2 = L tan α = L(eEs / mv2) = (eEsL / mv2). (12)
    Then using equations (11) and (12), the total deflection is
    d = h1 + h2 = (eEs2 / 2mv2) + (eEsL / mv2) = (eEs / mv2)[(s / 2) + L],
    d = (e/m)(Es / v2)[(s + 2L) / 2]. (13)
    Solving for e/m, we get
    e/m = (v2d / Es)[2 / (s + 2L)]. (14)
    This ratio of e to m can be determined if the velocity v of the rays can be determined. This is where the electromagnet and the magnetic field come in. An electromagnet could be slipped over the tube to produce a magnetic field at right angles to the electric field between the plate electrodes, deflecting the beam downward by the magnetic field. The magnetic field B exerts a force on a moving charge e perpendicular to the velocity v, directed at right angles to the plane of B and v. The magnitude of the force Fm is equal to Bev. An magnetic force can be applied to the cathode rays as they pass between the plates when an electric force is also simultaneously applied by electric field between the plates, and in a direction opposite to that applied by the magnet. By adjusting the magnitude of this potential difference, the beam can be returned to its original undeflected position on the screen. If we denote by E the applied electric field intensity, which is the electric force per unit charge, then the total electrical force is
    Fe = Ee,
    which is just balanced by the magnetic force
    Fm = Bev.
    That is, Thomson adjusted E until the electric force balanced the magnetic force. Hence,
    Bev = Ee, (15)
    or solving for v, he got
    v = E / B, (16)
    a ratio that can be measured. By substituting this value of v into the equation (14) above, he got
    e/m = (E2 / B2)(d / Es)[2 / (s + 2L)] = (Ed / B2s)[2 / (s + 2L)], (17)
    and since E, B, d, s, and L are known, Thomson was able to get a numerical value for the ratio e/m. The accepted numerical value of e/m for electrons today is about 1.76 × 108 coul/gm. This quantity is about 1840 times larger than the value of 96,500 coul/gm found for the charged hydrogen atoms (ions) in electrolysis. Since hydrogen has the lightest atoms known, electrons must be vastly smaller in mass to any atom of any element. And if the electron and the hydrogen ion are assumed to have the same quantity of charge on them, the mass of the electron must be only 1/1840 of the mass of the hydrogen ion. The success of Thomson's experimental measurement of charge to mass, e/m, is often said to be the "discovery" of the electron, although the existence of this subatomic particle had previously been inferred.

  4. DETERMINATION OF THE ELECTRONIC CHARGE.
    Thomson's experiment only determined the ratio of e to m, but no direct determination of the electronic charge e and that it had a unique value. Thomson outlined the basic method for the determination of the electronic charge, but the experiment was difficult to perform practically, and self-consistent, reproducible results were not obtained for some years. The American physicist Robert A. Millikan (1868-1953), who undertook work on the problem in 1906, was the first to achieve success. In 1911 he finally succeeded in measuring the charge as
    1.602 × 10-19 coulombs
    and in demonstrating that this value was precise within 0.1%. The experiment is beautiful in conception and simple to understand. It shows how indirectly quantities can be measured in the submicroscopic realm. In summary the method is as follows. Minute droplets of oil will reach a terminal velocity of only a few millimeters per second when allowed to fall freely in air. When they are confined inside a draft-free chamber and illuminated, such droplets can be observed with a microscope or short focus telescope and their velocities may be easily measured. The mass of a given oil droplet can be calculated from its observed terminal velocity. Now, if this same droplet acquires a charge, it can be accelerated by means of an applied electric field until it achieves its terminal velocity in the upward direction. From the terminal velocities, the amount of charge on the drop can be determined.

    Millikan's apparatus consists of an enclosed cylindrical chamber into which a cloud of fine droplets of oil is blown into its upper part by an atomizer. These droplets settle, a few of them passing through a pinhole at the center of a plate P near the bottom of the chamber. At the bottom of the chamber is another plate P'; these two plates are made of brass, and may be charged to a potential difference (voltage) by a battery or other electrical source. An electric force field is thus produced between the two plates that is uniform and may be regulated by varying the voltage between the plates. The direction of the field can be also reversed by an appropriate switch which can reverse the voltage. A small glass window on the side of the chamber between the two plates allows a bright beam of light to enter this lower chamber and out through another glass window on the opposite side. A third window at 120 degrees from the first window allows, as Millikan said, "for observing, with the aid of a short focus telescope placed about two feet distant, the illuminated oil droplet as it floats in the air between the plates. The appearance of this drop is that of a brilliant star on a black background." The droplets appear like specks of dust dancing in a beam of sunlight. The observing telescope contains a system of cross hairs, accurately calibrated, so that, as the droplet moves either downward, under the force of gravity, or upward because of electric field of force, the distances traveled in a given period of time may be measured precisely and accurately. When the droplets are sprayed into the upper chamber, a few of them become charged by friction. An external radiation source may have to be used to give the required charge to the oil droplets. With a little practice the observer can single out a droplet and measure its terminal velocity of free fall by means of the scale in the eyepiece of microscope or telescope. Before the droplet falls out of the field of view, the electric field is turned on. A careful experimenter can use the same droplet for an hour or more, making repeated measurements of the terminal velocities during free fall and with the electric field turned on. If the droplet fails to respond to the electric field, it is still uncharged. In that case, another droplet that has acquired a charge can be used.

    If a particular droplet carries a negative charge, an upward force will be exerted on this charge by the electric field as it falls into the lower chamber. This upward force will be
    F = Eq, (18)
    where the E is the electric field strength and q is the charge carried by the droplet. Now it is possible to adjust this field strength in such a way that the upward force on the droplet is just sufficient to balance the downward force of gravity. Under these conditions,
    Eq = mg, (19)
    where m is the apparent mass of the droplet, that is, the true mass reduced by the effect of the buoyancy of the air; solving for q, we get
    q = mg / E. (20)
    Now the charge q on the droplet can now be determined if the mass m of the droplet can be measured. The mass of the spherical droplet of oil can be given by the following equation
    m = (4/3) π r3 (ρO - ρA), (21)
    where ρO is the density of the oil and ρA is the density of the air. Now the radius r and thus the mass m of these extremely small droplets can be determined by a method based upon a law known as Stokes' law. This law was discovered about 50 years earlier by George Gabriel Stokes (1819-1903), who was working on the problem, first mentioned by Galileo, of how objects fall when they are in a resisting medium instead of in a vacuum. For spherical objects falling in a resisting medium, it is found that they reach a terminal velocity. For very small spheres, less than 1/100 inch in diameter, this terminal velocity is proportional to the square of the radius. For very small objects the laws of acceleration do not apply, but resistant must be taken into account. Stokes worked out the formula for the resistance on a spherical drop, and had shown how it is related to the constant "terminal" or drift velocity with which the sphere falls in still air. Consider the following.

    The net downward force F acting on the droplet during free fall (no electric field) is given by
    F = mg - f - Kv, (22)
    where mg is the weight of the droplet, f is the buoyant force due to the air, Kv is the friction force, which is proportional to the speed v of the droplet. According to Stokes' law, the proportional coefficient K of the velocity in the frictional force is given by
    K = 6 π η r, (23)
    for a small sphere of radius r moving through a homogeneous fluid of viscosity .

    Since the buoyant force f is simply the weight of the air displaced by the volume of the droplet, then
    mg - f = (4/3) π r3 (ρO - ρA) g, (24)
    where ρO is the density of the oil and ρA is the density of the air.

    During free fall the terminal velocity vt is reached when F = 0.
    Then, from equation (22), we get
    mg - f = Kvt, (25)
    or, using equations (24) and (23), we get
    (4/3) π r3 (ρO - ρA) g = 6 π η rvt. (26)
    Solving equation (26) for r, we get
    r = 3 √[ηvt / 2g(ρO - ρA)]. (27)
    By means of this formula the radius r can be calculated, if the terminal velocity vt of its fall is known. For each droplet this terminal velocity can be found by timing its rate of fall when there is no electric field between the plates. Then using the radius r, the mass m of the droplet can be computed by equation (21) from known properties of the material of which the spherical droplet is composed. Finally, the charge on the oil drop can be calculated, using equation (20).

    Note that it is not assumed that q is equal to e, or even that there is any smallest amount of charge on any drop. The smallest charge measured in this way is
    1.60 × 10-19 coulombs,
    and all other charges were found to be integral multiples of this amount. Millikan listed the 5 lowest values of q that he obtained as 1.60 × 10-19 coul,
    3.20 × 10-19 coul,
    4.80 × 10-19 coul,
    6.40 × 10-19 coul, and
    8.00 × 10-19 coul; these are
    1, 2, 3, 4, and 5 times 1.60 × 10-19 coul. No smaller quantity of charge, either positive or negative, has ever been observed. Millikan's experiment proved the existence of elementary indivisible charges, although it did not directly identify these charges with e, the charge on Thomson's electron. But other indirect evidence, as well as additional direct evidence, confirms the identity of Millikan's elementary charges with Thomson's electron, and Millikan's experiment is commonly referred to as the measurement of the electronic charge.

    Once an accurate measurement of the charge on an electron was made, then many other important physical constants could also be accurately determined.

    First, the mass of the electron followed immediately from the value of the ratio of e/m determined by Thomson's experiment. Using presently accepted value of
    e = 1.602 × 10-19 coul, and of
    e/m = 1.7589 × 108 coul/gm or
    1.7589 × 1011 coul/kg,
    then the value of the mass of the electron is
    me = e/(e/m) = (1.602 × 10-19 coul) / (1.7589 × 108 coul/gm)
    me = 9.108 × 10-28 gm = 9.108 × 10-31 kg.
    Today, this value is known to a precision better than 0.01%.
    This mass of electron is called the rest-mass of the electron.

    Second, Avogadro's number N0, that is, the number of atoms in a gram-atomic weight of an element, can be determined with great accuracy using Millikan's results and Faraday's laws of electrolysis. According to Faraday's laws of electrolysis the passage of 96,500 coulombs through an electrolyte releases 1 gm-at.wt. of a monovalent element at either electrode. Now 1 gm-at.wt. contains one Avogadro's number of atoms. If each atom of a monovalent element transfers one electron, then the charge transferred by 1 gm-at.wt. is the product of Avogadro's number N0 times the charge on the electron e, that is,
    N0e = 96,500 coulombs.
    Solving for Avogadro's number, we get
    N0 = (96,500 coulombs) / e = (96,500 coulombs) / (1.60 × 10-19 coulombs) = 6.02 × 1023.
    This result assumes that the valence of an element is due to an excess of electrons (negative valence) or deficiency of electrons (positive valence) in an atom of the element.

    And thirdly, with an accurate knowledge of Avogadro's number we can determine the mass of any atom. For example, since 16 grams of oxygen (1 gm-at.wt.) contains
    6.02 × 1023 atoms,
    the mass of 1 atom of oxygen is 16 divided by 6.02 × 1023
    or 2.66 × 10-23 grams or 2.66 × 10-26 kilograms.

    The following are some of the theoretical importance of Millikan's experiment in determining the charge on the electron:
    (a) there exists a particle smaller than the atom, even of lightest atom of hydrogen, which is 1840 times more massive than the electron;
    (b) the electron is a constituent of all atoms of matter;
    (c) the atom has parts and a structure; and
    (d) all matter has electricity in it.
    In 1901, Lord Kelvin said, "electric fluid consists of minute, equal and similar bodies called electrons, much smaller than the atoms of ponderable matter, atoms of electricity."