Measuring the smallest unit of charge
Robert A Millikan
It is strange how one thing leads to another. Today, the electron is an accepted fact of life. Even though nobody can vouch that he has seen an electron, scientists have not only found out all its behavioural properties, they have rallied around beams of electrons in CRTs and TV sets and harnessed their behaviour to the benefit of mankind in gadget after gadget.
However, before succumbing to the tyranny of human technology, the electron teased the scientific intellect for more than 200 years and lured scientists to come out of the Daltonian dogma of indivisibility of an atom.
The electrons – the free electrons, freed from the bondage of the nucleus, first made their presence felt in studies of passage of electricity through air. As far back as 1705, it had been noticed that sparks from an electrical machine would jump further in rarefied air than in air at normal pressures. As early as 1748, it was observed that an aurora borealis-like arch flew in a 32 inches long glass tube of rarefied air.
These were spectacular sights. But nobody knew what caused the spectacle. It was like a genie in the bottle.
In 1838, Michael Faraday sent a current from an electrostatic machine through a glass tube containing air at low pressure and observed a purple glow extending from the positive electrode (anode) at one end almost to the cathode at the other end. The cathode was covered with a glow and there was dark space between the glow and the purple column. The dark space has since been called Faraday Dark Space. Some speculated on the existence of electroplasm – the stuff that ghosts are supposed to be made of.
The studies of electrical discharge through gases continued in Germany with improved vacuum technology. It was concluded that the luminescent glow on the tube was caused by “rays” originating at the cathode. Nobody understood what these “rays” were, but they were deflected by a magnet and were able to cast the shadow of an obstacle placed in their path. So they travelled in straight lines, just like light. Goldstein called these mysterious rays ‘cathode rays’.
Between 1879 and 1888, the English scientist William Crookes made a series of comprehensive investigations on these rays and concluded that ‘cathode rays’ actually consisted of a stream of negatively charged particles, which were expelled from the cathode with extremely high velocities.
J.J Thompson, a young Cavendish professor at the Cavendish Lab in Cambridge, jumped into the fray. He succeeded in showing that these cathode rays were deflected by electric field as well as magnetic field. Thompson concluded, “I can see no escape from the conclusion that cathode rays are charges of negative electricity carried by particles of matter. But what are these particles? Are they atoms or molecules or matter in a still finer state of sub division?”
Dalton still held sway in the minds of scientists. With some trepidation Thompson suggested a ‘finer state of sub division’. There was good reason for scientists to have faith in Dalton. Matter as we see around us, is electrically neutral. So the smallest particle of matter too has to be neutral. If electrically neutral matter discharges a stream of negatively charged particles, how is the balancing of charge done in the matter?
J.J Thompson came up with the preposterous plum pudding model of an atom. But that is another story. What Thompson did calculate conclusively was the charge to mass ratio of the cathode rays, by balancing out the pulls of the electric field and the magnetic field on the stream of negatively charged particles. The charge to mass ratio or e/m worked out to be 1.75888×1011 Coulombs/Kg, a
value thousand times higher than e/m of a hydrogen atom. It did not matter what kind of gas was in the glass tube or what cathodes were used. The ratio remained unchanged. The rays were all made of the same stuff. Thompson’s instinct told him that he had discovered something almost unthinkable – a subatomic particle.
Thompson’s e/m experiment is now so standardized that every undergraduate student studying physics performs this experiment and gets the above result.
However, the result does not tell us anything about the minuteness of the particles or the quantum of charge on each particle.
It was left to Robert Millikan, a scientist working in the University of Chicago, to glean the charge on each tiny particle. The year was 1906. Ten years ago, he had been mesmerized by Wilhelm Rontgen’s X ray pictures of bones inside a hand. He was determined to do something path-breaking.
Millikan and his assistant Fletcher purchased a perfume atomizer and watch oil from a local drug store. They began assembling the equipment – two round brass plates, the top one with a hole drilled at the centre, mounted on a lab stand and illuminated from the side by a bright light. They sprayed a mist of oil above the apparatus and watched through a telescope. The field was full of little starlets having all the colours of a rainbow. The larger drops soon fell to the bottom, but the smaller ones seemed to hang in the air for nearly a minute. They executed the most fascinating dance.
By the next morning Fletcher and Millikan had wheeled in a large bank of batteries capable of producing one thousand volts and connected them to the plates. Turning on the current, they watched with fascination as some of the drops were pushed slowly up and the others were pulled down. Friction at the tiny nozzle of the atomizer had given some droplets positive charge and some others negative charge.
Millikan and Fletcher refined the setup and spent nearly every afternoon for the next six months taking data. In order to charge the oil droplets he used the radioactive element radium. Later he wrote in his diary:
“I’d pick out one that was falling straight and slow and switch on the plate voltage. If it suddenly began moving upward, I knew that it carried a charge. Flipping the knife switch up and down and adjusting the voltage, I’d time the drops as they rose and fell between the hairlines in the eyepiece – 4.2 seconds down, 2.6 seconds up…..6.8 down, 4.0 up….7.1 and 2.2…..8.1 and 3.3. I was starting to get the hang of it. But to do this right I needed to grab on to a single drop long enough to watch for the sudden variations in rise time, which would signal that it had lost or gained an electron. When I had collected the data for a dozen drops and estimated their masses with an equation called Stokes’ Law, I could calculate the fundamental unit of charge.”
The mathematics behind the experiment is quite simple.
With the battery disconnected, the droplet falls slowly under the influence of gravity. The drag force acting upon the drop is calculated from Stokes’s law and is given as Fv = 6πηrV1
The apparent weight (true weight minus up thrust) for a perfectly spherical body is given by FG = 4/3 πr3g (ρ – ρair).
At terminal velocity the oil drop is not accelerating, so the total force acting on it must be zero FV-FG=0, i.e., v1 = 2r2g (ρ – ρair)/9η ……(1)
The high voltage battery was then switched on, thus producing the electric field, the direction being such as to make the charged droplet move upward, against the force of gravity. The strength of the electric field E, is given by the voltage of the battery divided by the distance between the plates. The upward force acting on the droplet is Een, where en is the charge carried by the droplet. Since this is opposed by the gravitational force mg, the net upward force is Een – mg. For a drop moving up with constant velocity, the net upward force is nullified by the viscous drag. So one may write 6πηrv2 = Een – mg = Een – 4/3
πr3g (ρ – ρair) = Een – 6πηrV1
Thus en = 6πηr (v1 + v2)/E ….(2)
Since the quantities v1, v2, g are available, it is possible to calculate the charge en carried by the oil drop if the radius of the drop r is known. ‘r’ may be determined from equation (1) above. Inserting the value of ‘r’ into equation (2), together with the measured velocity, v1 and v2, the magnitude of the charge en carried by the oil droplet can now be determined.
As a result of a large number of measurements, Millikan found that the charge en was always an integral, i.e., a whole number, multiple of a definite elementary charge, which was presumably the electronic charge. After applying numerous corrections to the foregoing equations, Millikan concluded that the most reliable value of the unit charge was 1.5924 x 10-19 Coulomb, which is very close to the modern value 1.60217653 x 10-19 Coulomb.
Even though the calculation is fairly simple, doing the experiment is not. Sometimes a drop is so heavy that it sinks like a stone; or it carries so much charge that when the voltage is turned on, it would rocket out of sight. Millikan’s touch was so deft that he could snag an oil drop in his gun sights, go home for dinner and return later that evening to find that it had barely moved.
“He who has seen that experiment ….has in effect SEEN the electron”, Millikan later wrote. In 1913 he published his definitive value for the basic unit of electric charge. Ten years later he was awarded the Nobel Prize.
Today, the charge of an electron is accepted as one of the fundamental constants of the universe.
References
http://www.vigyanprasar.gov.in/dream/may2001/electron.htm.
George Johnson, The Ten Most Beautiful Experiments, The Bodley Head, London.
