Oil drop experiment

In Millikan's experiment is an experiment with it the American physicists Robert Andrews Millikan and Harvey Fletcher in 1910 succeeded, the size of the elementary charge to determine much more accurately than was previously possible. For this measurement, Robert Millikan was awarded the 1923 Nobel Prize in Physics.

At the suggestion of Robert Millikan Harvey Fletcher grabbed contribution during his doctoral thesis on previously by Harold Albert Wilson, Joseph John Thomson and other researchers conducted tests back, which he improved significantly. His most important improvement was to replace the substances water or alcohol previously used by low-volatile liquids such as oil and mercury. To determine the elementary charge, the rate of descent of electrically charged oil droplets present in the electric field was measured in comparison with the case of no electric field. The determined value of the elementary charge was:

Robert Millikan insisted occur in the publication of this result in the journal Science, as a single author. In return, Harvey Fletcher was named as the sole author of a paper in Physical Review on the confirmation of Brownian motion and was able to use for his dissertation. At the Nobel Prize Harvey Fletcher was not involved and was also mentioned not adequately addressed by Robert Millikan. Harvey Fletcher made ​​the deal with Robert Millikan in a text public, which was not printed until after his death in 1982 posthumously in the journal Physics Today.

• 2.1 The flotation method
• 2.2 The direct field method
• 2.3 Cunningham correction

Experimental setup and basic procedure

Electrically charged droplets in a plate capacitor field

With an atomizer first minute oil droplets are produced, which are so small ( about 0.5 microns ) that they can not be observed directly with a conventional microscope. In order to track them yet, use is made of dark field method, in which you lit the oil droplets at an angle of about 150 ° to the observer, ie, from almost the opposite direction and the resulting diffraction disk followed in the microscope ( bearing in mind that the microscope reversed up and down, you enter an Airy disk falling oil droplets sees move upwards and vice versa). At least a portion of the oil droplets has to be electrically charged, what has been achieved in Millikan's experimental set-up by an X-ray tube, the ionizing radiation boosted the oil droplets electrostatically. As a rule, but even the friction of the oil droplets is enough to each other during sputtering or in the air to make them sufficiently charge.

The droplets then pass between the plates of a parallel plate capacitor. The oil droplets are so small that the air like a viscous fluid acts for them. They float for a long time as an aerosol in the air. However, the electric field of the capacitor exerts a force on charged droplets of oil in excess of the force of gravity far. The Coulomb force attracts the positively charged droplets to the negatively charged plate of the capacitor. The resulting motion can be observed as a movement of detectable with the microscope diffraction pattern.

The unreachable levitation case

Mounted to the plates of the capacitor horizontally one above the other, you can practice by applying a suitable voltage to the plates, an electric force on the droplet, which compensates for the sum of the first two forces by acting downward force of gravity, therefore, the scale with the sum of the electric force and the buoyancy force and keeps the oil droplets in question so that hovers in principle.

By solving the equation, the charge on the oil droplets could now therefore in principle be determined - but in practice it fails the fact that the Airy disk in the microscope not allow any conclusions on the radius of the oil droplets, the right side of the equation thus remains undetermined. In addition, the state of uncertainty can be seen only with difficulty precisely because of the Brownian motion.

Indirect determination of the droplet radius on the Stokes friction

To determine the radius of the droplet still, one can use the fact that adjusts not only by the electric field in the capacitor, but also by the influence of the speed-dependent Stokes friction force, a force equilibrium, but now is not in the form of a floating state of the respective oil droplets but a constant speed of their falling or rising.

In practice, there are to two different processes: In the " single-field " method to measure after an approximately reached limbo of a selected oil droplet its rate of fall solely on the basis of gravity, in the " two-field method ", however, allowed to the oil droplets initially from the capacitor box down and then pull (after reversing the polarity of the field) back to the top, where you logged in each case the rate of descent and rate of climb of the droplet.

Derivation of the relationships

There are two variants of the experiment, the levitating (or single-field ) and the constant field method (or two-field method). When the floating method, a speed is selected to be zero and the second speed and the voltage needed for the deadlock measured. In the two- field method, the amount of voltage is fixed and the two velocities measured at reversing the polarity of the electric field. The two- field method is the more common.

During the movement of the oil droplet following forces arise, which are illustrated graphically in the images:

Occurring in the sizes are defined as follows:

• = Kreiszahl
• = Density of the oil
• = Density of air
• = acceleration due to gravity
• = Voltage at the plate capacitor
• = Distance between the plates of the plate capacitor
• = Viscosity of air
• = Amount of the settling velocity of the oil droplet
• = Amount of rise velocity of the oil droplet

The flotation method

A desired oil droplet is brought nearly to a standstill ( float ) by variation of the capacitor voltage, and then measured while the electric field its falling speed. Once it has set a balance between friction, buoyancy and weight when falling of the oil droplet, the following applies:

Inserting the known relationships gives:

Changing after results:

Thus, the radius of the oil droplets alone from the measurable rate of fall is determined. To get to the charge, the balance condition is now considered. This applies analogously to the above formula, the equation:

Because now the electric force is in equilibrium with weight and buoyancy force. Inserting the relations for the forces yields:

Which can be converted according to the charge:

Inserting the equation for the equation yields an equation for the load, which depends only on the voltage measurable quantities and rate of fall:

Thus it can be calculated from the measured quantities directly the charge and the radius.

The DC field method

For a given capacitor voltage its climb rate is for a selected initially moving down oil droplets its rate of descent, then, by reversing the polarity of the electric field in terms of amount beibehaltener capacitor voltage is determined. In the case of the sinking of the following applies:

In the case of climbing holds:

Subtracting the two equations for supplies from each other, inserting the known relationships and resolving:

Substituting this equation into equations of the two power supplies, an equation for the charge

Inserting the equation for the equation provides the radius

Now both radius and charge are determined solely by measurable quantities.

Cunningham correction

Since the size of the oil droplets is in the range of the mean free path of air, the Cunningham correction should be taken into account for the Stokes friction yet. The friction force is extended by a term which can be neglected in the normal case with large bodies:

Wherein the mean free path of air and the droplet radius. The equations must now be re- released and are a bit more complex, but also significantly more accurate.

Determination of the elementary charge

Because each oil droplet is comprised of a large number of atoms and not only one, but also can carry a plurality of charges each calculated load of an oil droplet is an integer multiple of the elementary charge. If one draws the charge distribution of many attempts in a graph a, there is no continuous distribution. It turns out that only multiples of the elementary charge may occur.

A single elementary charge on a particle can be observed when the voltage is high enough to just keep visible oil droplets with an elementary charge, at least in limbo only. This is not the case in most experimental setups.

Since 1910, considerably more accurate methods for determining the elementary charge have been developed. The elementary charge can be determined very accurately from the quantum Hall effect. Determined in this way is recommended by CODATA value.