Oil-drop experiment

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Millikan's setup for the oil drop experiment.

The oil-drop experiment was an experiment performed by Robert Millikan and Harvey Fletcher in 1909 to measure the elementary electric charge (the charge of the electron).

The experiment entailed balancing the downward gravitational force with the upward buoyant and electric forces on tiny charged droplets of oil suspended between two metal electrodes. Since the density of the oil was known, the droplets' masses, and therefore their gravitational and buoyant forces, could be determined from their observed radii. Using a known electric field, Millikan and Fletcher could determine the charge on oil droplets in mechanical equilibrium. By repeating the experiment for many droplets, they confirmed that the charges were all multiples of some fundamental value, and calculated it to be 1.5924(17)×10⁻¹⁹ C, within one percent of the currently accepted value of 1.602176487(40)×10⁻¹⁹ C. They proposed that this was the charge of a single electron.

Contents

[h1 Background

• 2 Experimental procedure
  • 2.1 Apparatus
  • 2.2 Method
• 3 Millikan's experiment and cargo cult science
• 4 Notes
• 5 Further reading
• 6 External links

[e

Robert A. Millikan in 1891

Starting in 1900, while a professor at the University of Chicago, Millikan, with the significant input of Fletcher, worked on the oil-drop experiment in which he measured the charge on a single electron. After a publication on his first results^[1] in 1910, contradictory observations by Felix Ehrenhaft^[2] started a controversy between the two physicists. After improving his setup he published his seminal study in 1913.^[3]

His experiment measured the force on tiny charged droplets of oil suspended against gravity between two metal electrodes. Knowing the electric field, the charge on the droplet was determined. Repeating the experiment for many droplets, Millikan showed that the results could be explained as integer multiples of a common value (1.592×10⁻¹⁹ C), the charge on a single electron.

At the time of Millikan and Fletcher's oil drop experiments, the existence of subatomic particles was not universally accepted. Experimenting with cathode rays in 1897, J. J. Thomson had discovered negatively charged "corpuscles", as he called them, with a mass about 1000 times smaller than that of a hydrogen atom. Similar results had been found by George FitzGerald and Walter Kaufmann. Most of what was then known about electricity and magnetism, however, could be explained on the basis that charge is a continuous variable; in much the same way that many of the properties of light can be explained by treating it as a continuous wave rather than as a stream of photons.

The so-called elementary charge e is one of the fundamental physical constants and its accurate value is of great importance. In 1923, Millikan won the Nobel Prize in physics in part because of this experiment.

Aside from the measurement, the beauty of the oil drop experiment is that is a simple, elegant hands-on demonstration that charge is actually quantized. Thomas Edison, who had previously thought of charge as a continuous variable, became convinced after working with Millikan and Fletcher's apparatus.

There is some controversy over the use of selectivity in Millikan's results of his second experiment measuring the electron charge raised by the historian Gerald Holton. Holton (1978) pointed out that Millikan disregarded a large set of the oil-drops gained in his experiments without apparent reason. Allan Franklin, a former high energy experimentalist and current philosopher of science at the University of Colorado has tried to rebut this point by Holton^[4]. Franklin contends that Millikan's exclusions of data did not affect the final value of e that Millikan obtained but concedes that there was substantial "cosmetic surgery" that Millikan performed which had the effect of reducing the statistical error on e. This enabled Millikan to quote the figure that he had calculated e to better than one half of one percent; in fact, if Millikan had included all of the data he threw out, it would have been to within 2%. While this would still have resulted in Millikan having measured e better than anyone else at the time, the slightly larger uncertainty might have allowed more disagreement with his results within the physics community.

This experiment has since been repeated by generations of physics students, although it is rather expensive and difficult to do properly.

[edit] Experimental procedure

[edit] Apparatus

Simplified scheme of Millikan’s oil-drop experiment.

Robert Millikan’s apparatus incorporated a parallel pair of horizontal metal plates. By applying a potential difference across the plates, a uniform electric field was created in the space between them. A ring of insulating material was used to hold the plates apart. Four holes were cut into the ring, three for illumination by a bright light, and another to allow viewing through a microscope.

A fine mist of oil droplets was sprayed into a chamber above the plates. The oil was of a type usually used in vacuum apparatus and was chosen because it had an extremely low vapour pressure. Ordinary oil would evaporate away under the heat of the light source causing the mass of the oil drop to change over the course of the experiment. Some oil drops became electrically charged through friction with the nozzle as they were sprayed. Alternatively, charging could be brought about by including an ionising radiation source (such as an X-ray tube). The droplets entered the space between the plates and, because they were charged, could be made to rise and fall by changing the voltage across the plates.

[edit] Method

Initially the oil drops are allowed to fall between the plates with the electric field turned off. They very quickly reach a terminal velocity because of friction with the air in the chamber. The field is then turned on and, if it is large enough, some of the drops (the charged ones) will start to rise. (This is because the upwards electric force F_E is greater for them than the downwards gravitational force W, in the same way bits of paper can be picked up by a charged rubber rod). A likely looking drop is selected and kept in the middle of the field of view by alternately switching off the voltage until all the other drops have fallen. The experiment is then continued with this one drop.

The drop is allowed to fall and its terminal velocity v₁ in the absence of an electric field is calculated. The drag force acting on the drop can then be worked out using Stokes' law:

where v₁ is the terminal velocity (i.e. velocity in the absence of an electric field) of the falling drop, η is the viscosity of the air, and r is the radius of the drop.

The weight W is the volume V multiplied by the density ρ and the acceleration due to gravity g. However, what is needed is the apparent weight. The apparent weight in air is the true weight minus the upthrust (which equals the weight of air displaced by the oil drop). For a perfectly spherical droplet the apparent weight can be written as:

Now at terminal velocity the oil drop is not accelerating. So the total force acting on it must be zero. So the two forces F and W must cancel one another out (that is, F = W). This implies

Once r is calculated, W can easily be worked out.

Now the field is turned back on, and the electric force on the drop is

where q is the charge on the oil drop and E is the electric field between the plates. For parallel plates

where V is the potential difference and d is the distance between the plates.

One conceivable way to work out q would be to adjust V until the oil drop remained steady. Then we could equate F_E with W. But in practice this is extremely difficult to do precisely. Also, determining F_E proves difficult because the mass of the oil drop is difficult to determine without reverting back to the use of Stoke's Law. A more practical approach is to turn V up slightly so that the oil drop rises with a new terminal velocity v₂. Then

From Wikipedia, the free encyclopedia

Jump to: navigation, search

Millikan's setup for the oil drop experiment.

The oil-drop experiment was an experiment performed by Robert Millikan and Harvey Fletcher in 1909 to measure the elementary electric charge (the charge of the electron).

The experiment entailed balancing the downward gravitational force with the upward buoyant and electric forces on tiny charged droplets of oil suspended between two metal electrodes. Since the density of the oil was known, the droplets' masses, and therefore their gravitational and buoyant forces, could be determined from their observed radii. Using a known electric field, Millikan and Fletcher could determine the charge on oil droplets in mechanical equilibrium. By repeating the experiment for many droplets, they confirmed that the charges were all multiples of some fundamental value, and calculated it to be 1.5924(17)×10⁻¹⁹ C, within one percent of the currently accepted value of 1.602176487(40)×10⁻¹⁹ C. They proposed that this was the charge of a single electron.

Contents

[h1 Background

• 2 Experimental procedure
  • 2.1 Apparatus
  • 2.2 Method
• 3 Millikan's experiment and cargo cult science
• 4 Notes
• 5 Further reading
• 6 External links

[e

Robert A. Millikan in 1891

Starting in 1900, while a professor at the University of Chicago, Millikan, with the significant input of Fletcher, worked on the oil-drop experiment in which he measured the charge on a single electron. After a publication on his first results^[1] in 1910, contradictory observations by Felix Ehrenhaft^[2] started a controversy between the two physicists. After improving his setup he published his seminal study in 1913.^[3]

His experiment measured the force on tiny charged droplets of oil suspended against gravity between two metal electrodes. Knowing the electric field, the charge on the droplet was determined. Repeating the experiment for many droplets, Millikan showed that the results could be explained as integer multiples of a common value (1.592×10⁻¹⁹ C), the charge on a single electron.

At the time of Millikan and Fletcher's oil drop experiments, the existence of subatomic particles was not universally accepted. Experimenting with cathode rays in 1897, J. J. Thomson had discovered negatively charged "corpuscles", as he called them, with a mass about 1000 times smaller than that of a hydrogen atom. Similar results had been found by George FitzGerald and Walter Kaufmann. Most of what was then known about electricity and magnetism, however, could be explained on the basis that charge is a continuous variable; in much the same way that many of the properties of light can be explained by treating it as a continuous wave rather than as a stream of photons.

The so-called elementary charge e is one of the fundamental physical constants and its accurate value is of great importance. In 1923, Millikan won the Nobel Prize in physics in part because of this experiment.

Aside from the measurement, the beauty of the oil drop experiment is that is a simple, elegant hands-on demonstration that charge is actually quantized. Thomas Edison, who had previously thought of charge as a continuous variable, became convinced after working with Millikan and Fletcher's apparatus.

There is some controversy over the use of selectivity in Millikan's results of his second experiment measuring the electron charge raised by the historian Gerald Holton. Holton (1978) pointed out that Millikan disregarded a large set of the oil-drops gained in his experiments without apparent reason. Allan Franklin, a former high energy experimentalist and current philosopher of science at the University of Colorado has tried to rebut this point by Holton^[4]. Franklin contends that Millikan's exclusions of data did not affect the final value of e that Millikan obtained but concedes that there was substantial "cosmetic surgery" that Millikan performed which had the effect of reducing the statistical error on e. This enabled Millikan to quote the figure that he had calculated e to better than one half of one percent; in fact, if Millikan had included all of the data he threw out, it would have been to within 2%. While this would still have resulted in Millikan having measured e better than anyone else at the time, the slightly larger uncertainty might have allowed more disagreement with his results within the physics community.

This experiment has since been repeated by generations of physics students, although it is rather expensive and difficult to do properly.

[edit] Experimental procedure

[edit] Apparatus

Simplified scheme of Millikan’s oil-drop experiment.

Robert Millikan’s apparatus incorporated a parallel pair of horizontal metal plates. By applying a potential difference across the plates, a uniform electric field was created in the space between them. A ring of insulating material was used to hold the plates apart. Four holes were cut into the ring, three for illumination by a bright light, and another to allow viewing through a microscope.

A fine mist of oil droplets was sprayed into a chamber above the plates. The oil was of a type usually used in vacuum apparatus and was chosen because it had an extremely low vapour pressure. Ordinary oil would evaporate away under the heat of the light source causing the mass of the oil drop to change over the course of the experiment. Some oil drops became electrically charged through friction with the nozzle as they were sprayed. Alternatively, charging could be brought about by including an ionising radiation source (such as an X-ray tube). The droplets entered the space between the plates and, because they were charged, could be made to rise and fall by changing the voltage across the plates.

[edit] Method

Initially the oil drops are allowed to fall between the plates with the electric field turned off. They very quickly reach a terminal velocity because of friction with the air in the chamber. The field is then turned on and, if it is large enough, some of the drops (the charged ones) will start to rise. (This is because the upwards electric force F_E is greater for them than the downwards gravitational force W, in the same way bits of paper can be picked up by a charged rubber rod). A likely looking drop is selected and kept in the middle of the field of view by alternately switching off the voltage until all the other drops have fallen. The experiment is then continued with this one drop.

The drop is allowed to fall and its terminal velocity v₁ in the absence of an electric field is calculated. The drag force acting on the drop can then be worked out using Stokes' law:

where v₁ is the terminal velocity (i.e. velocity in the absence of an electric field) of the falling drop, η is the viscosity of the air, and r is the radius of the drop.

The weight W is the volume V multiplied by the density ρ and the acceleration due to gravity g. However, what is needed is the apparent weight. The apparent weight in air is the true weight minus the upthrust (which equals the weight of air displaced by the oil drop). For a perfectly spherical droplet the apparent weight can be written as:

Now at terminal velocity the oil drop is not accelerating. So the total force acting on it must be zero. So the two forces F and W must cancel one another out (that is, F = W). This implies

Once r is calculated, W can easily be worked out.

Now the field is turned back on, and the electric force on the drop is

where q is the charge on the oil drop and E is the electric field between the plates. For parallel plates

where V is the potential difference and d is the distance between the plates.

One conceivable way to work out q would be to adjust V until the oil drop remained steady. Then we could equate F_E with W. But in practice this is extremely difficult to do precisely. Also, determining F_E proves difficult because the mass of the oil drop is difficult to determine without reverting back to the use of Stoke's Law. A more practical approach is to turn V up slightly so that the oil drop rises with a new terminal velocity v₂. Then