Millikan’s Oil Drop Experiment

(The text below is transcript of video without images or equations)

In 1887 J.J. Thomson discovery of the electron was a significant step that led to a much deeper understanding of the microscopic properties of Nature.  In this entry, I will discuss the famous Millikan Oil drop experiment which was done in 1909.

The significance of Thomson’s work was recognized in 1906 when he was awarded the Nobel Prize in Physics

“in recognition of the great merits of his theoretical and experimental investigations on the conduction of electricity by gases”.

But recall that in his characterization of the properties of the electron he could only determine the charge to mass ratio, given by -1.76 times ten to the 11^th Coulombs per kilogram.  Was this ratio a result of two big values or two small values?

Robert Millikan was able to separate the ratio in order to show that the ratio was that of two small numbers and in this way he was able to extract the elementary charge and the electron mass.  Comparing the electron mass to that of the lightest element, Hydrogen, it is found that the mass of an electron is 1800 times smaller.  Indeed at that time this was the smallest particle known.

Millikan devised an ingenious experiment to separate the two by placing oil drops in a chamber and then ionizing the air with X-rays.  The electrons so produced attached in varying numbers to the oil drops.  Applying an electric field would counteract the pull of gravity, to suspend the drops.  He studied these suspended drops.  Let’s have a look.

Millikan’s famous oil drop experiment allowed the charge on an electron to be measured independently from its mass.  The basic idea is to charge oil drops with electrons and then apply an electric field to stop them from falling.  From the balance of gravity and applied electric field, the charge on the electron was determined.

Here is seen (please see video above) a representation of Millikan’s apparatus.  The oil is atomized by spraying it into the upper chamber.

Gravity causes the mist of tiny oil drops to fall and pass through a hole into the lower part of the chamber.

X-rays are applied to the chamber thereby ionizing the air.  The free electrons so produced adhere to the surface of the oil drops in differing numbers.

A magnified view of the oil drops shows them falling under the action of gravity.

By positively charging the upper portion of the lower chamber and negatively charging the lower portion, the oil drop can be made to move up and down.  The electric field strength can be chosen to just stop the drop.

Using the same formula as gave the charge to mass ratio in the cathode ray tube experiment, Millikan was able to deduce the charge on the oil drops.  In this case, the acceleration is due to gravity on an oil drop of mass m.  The field E is adjusted to stop an oil drop seen through the microscope.

The oil drop is charged with n electrons of unknown charge.  Some oil drops have many electrons and others have a few.  Differently charged oil drops require different field strengths to bring them to rest.

By choosing many different oil drops, recording their diameter, to calculate their mass, and applying different stopping electric fields, Millikan could plot the charges on oil drops as a function of the electric field required to stop them.  By extrapolating the values he arrived at the smallest charge requiring the smallest stopping field.  From this the charge of a single electron was obtained.

Here we have one oil drop suspended in the chamber by the application of just the right magnitude of the electric field to stop the drop falling under the action of gravity.

The applied electric field E so adjusted is different for every drop because the drop sizes vary and the charge on the drops vary.  The applied electric field E so adjusted is different for every drop because the drop sizes vary and the charge on the drops vary.  This gives the basic formula in terms on known quantities. That is we know the value of the Stopping Potential E, we know the acceleration due to gravity, so if we know the mass, then the charge on the oil drop can be measured. So what is the mass?

The mass is easily obtained because the density of oil is known.  Density is the ratio of the mass to volume. Recall oil floats on water, so it has a density less than water.  The density of water is 1 gram per ml, (a liter of water has a mass of 1 kilogram), and the density of oil is about 0.8 g per ml.  Millikan knew the density of his oil, and he could calculate the mass by measuring the oil drops radius through his calibrated microscope.

Then, using the formula for the volume of a sphere and the known value of the radius, the mass of each oil drop can be obtained. But the mass of the oil is not the same as the mass in the oil drop formula because the oil is floating in air. So there is an upward force due to the buoyancy of air, which is due to the mass of air displaced by the oil.  Hence the downward force due to the mass of the oil only is balanced not only by the electrostatic potential, but also by the buoyancy of air.

Now everything is known in the experiment except the charge on the oil drop. Each oil drop varies in size and varies in the number of electrons that attach to the oil drop.  By using different intensities of X-rays, a greater number or a lesser number of electrons attached to the drops, and in each case, Millikan measured the charge on the oil drop. The experiment was performed many times and each time a different number of electrons attached to the drop.  It is from this data he found that the oil drop charge was always an integral number times a small charge.  That is, he extrapolated his data down to the case of one electron attached to an oil drop. In this way the charge to mass ratio was resolved.  Here is Millikan’s first published value which is within 1 percent of today’s accurate value.  With the charge, it is then possible to extract the mass of the electron.

In fact the magnitude of the charge on the electron is called the fundamental charge.  It is the smallest charge found to date on stable particles (that is particles that have a long lifetime).  The electron has –e, the proton had +e, the alpha particle has +2 e, etc.  The charge e is a fundamental constant.  It has this value which cannot be broken down into more fundamental parts.

Find similar topics and their explanations, along with  interactive multimedia animations, in the Physical Chemistry e-book by Laidler, Meiser, Sanctuary

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