The quantum nature of charge

INTRODUCTION
In this experiment you will experimentally determine the quantum nature of charge.
Robert Millikan was awarded the Nobel Prize in physics in 1923 for the oil drop
experiment. A simplistic schematic of his apparatus is shown below
A spherical drop of oil, falling through a viscous medium like air, will quickly reach a
constant velocity. When it reaches this equilibrium position, the viscous force is balanced by
other forces acting on the drop, such as gravity, buoyant forces from the air, electrical
forces, etc. In this experiment an electrical force of varying magnitude is introduced to
change the motion of the falling drop by an ionization source. By measuring the velocity
of the oil drop under different conditions the amount of charge on the drop may be
determined. If the charge on the drop is an integer multiple of the fundamental unit of
charge (the electron), then one will be able to confirm the quantization of charge.[1]
WHAT IS MIILIKAN OIL DROP EXPERIMENT
Oil-drop experiment was the first direct and compelling measurement of the electric charge of a single electron. It was performed originally in 1909 by the American physicist Robert A. Millikan. Using a perfume atomizer, he sprayed tiny drops of oil into a transparent chamber. At the top and bottom were metal plates hooked to a battery, making one positive (red in animation) and the other negative (blue in animation). Since each droplet picked up a slight charge of static electricity as it traveled through the air, the speed of its motion could be controlled by altering the voltage on the plates. When the space between the metal plates is ionized by radiation (e.g., X rays), electrons from the air attach themselves to oil droplets, causing them to acquire a negative charge. Millikan observed one drop after another, varying the voltage and noting the effect. After many repetitions he concluded that charge could only assume certain fixed values. The smallest of these portions was none other than the charge of a single electron.[3]

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OUTLINE OF EXPERIMENT
Very small oil drops are produced by spraying air over oil (or premade latex spheres are used) into a “drift chamber”. The oil drops fall but reach terminal velocity very quickly because of their large area to mass ratio. The terminal velocity is measured using a microscope with a graduated scale and a stopwatch. If the drop is charged it can then be moved upward (or forced down) using the electric field produced by metal plates above and below the experimental chamber. The upward and downward terminal velocities are also measured.
APPARATUS
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 invacuum apparatus and was chosen because it had an extremely lowvapour 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 anX-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.[2]
Principal
The method is based upon the observation of the rate of motion of a small oil drop. Under free fall due to gravity and under the application of suitable electric field. By adjusting the electric field suitably, a given oil drop can be made to move up or down or even kept balanced in the field of view for sufficiently long time and a series of observation can be made.
Construction
Robert Millikan apparatus in corporate a parallel pair of horizontal metal plates. By applying a potential difference across the pates a uniform electric was created in space between them a ring of insulating material was used to hold the plate apart four holes were cut into the ring, three for illumination by a bright light and another to allow viewing through a microscope.
Method
Initially the oil drops are allowed to fall between the plates with the electric field turned off. Millikan’s basic idea was to measure the rate of fall of a single drop acted on by gravity and drag forces, apply stokes law to determine the drop radius and mass, then to measure its upward velocity in an opposing electric field and hence determine the total charge on an individual drop. The field is then turned on and if it is large enough some of the drops will starts to rise. Oil droplets charged by an atomizer are allowed two pass to small hole in the upper plate of parallel plate capacitor. If these droplets are illuminated from the side. They appear as brilliant stars against a dark background and the rate of fall of individual drops may be determined.
If an electrostatic field of several thousand volts per meter is applied to the capacitor plates the drop may moves slowly upwards typically at rates of hundreds of a centimeter per second. Because the rate of fall is comparable a single droplets with constant mass and radius may be followed for hours alternately rising and falling by simply turning the electric field on and off. The atomicity of charge is shown directly by observation that after a long series of measurements of constant upward velocities one observe discontinuous charge or jump to a different upward velocity. This discontinuous charge is caused by the attraction of an ion to the charged droplet and consequent charge in droplet charge. Such charge become more frequent when a source of ionizing radiation is placed between the plates.
The quantitative analysis of the Millikan experiments starts with Newtons second law applied to the oil drop . ?y-= may because the drag force is large a constant velocity of fall is quickly achieved and all measurement are made for the case ay = 0 or ?fy=0. If we assume that magnitude of the drag force is proportional to the speeds Cv.
Cv-mg=0(field off)
q1E -mg- Cv’1=0 (field on)
Eliminate c from this expression gives
q1 = mg/E (v+v’1/v)
when the droplet undergoes a discontinuous change in its upward speed from v’1 to v’2 its new charge q2 is given by
q2 = mg/E (v+v’2/v)
Dividing q1 by q2
q1/q2 = v+ v’1/v+v’2
Electric Charge
Electric charge is an intrinsic characteristics of the fundamental particles making up those objects that is it is a property that comes automatically with those particles wherever they exist.
The vast amount of charge in an everyday object is usually hidden because the object contains equal amounts of the two kinds of charge positive and negative charge. With such an equality or balance of charge. The object is said to be electrically neutral that is it contains no net charge. If the two type of charge are not in balance then there is a net charge.
Charge object interact by exerting forces on one another charges with the same electrical sign repel each other and charges with opposite electrical attract each other.
Stokes law
When a solid body moves through a fluid, the fluid is contact with the solid is dragged with it relative velocities are stabilized between the layers of the fluid near the solid so that viscous force start operating. The fluid exerts viscous force on the solid oppose the motion the of the solid. The magnitude of the viscous force depends on the shape and size of the solid body. Its speed and the coefficient of the viscosity of the fluid.
Suppose a spherical body of radius r moves at a speed v through fluid of viscosity ?. The viscous force f acting on the body depends on r, v and ?. Assuming that the force is proportional to the viscous powers of these quantities, we can obtain the dependence through dimensional analysis.
F= kra vb ?c
Where k is the dimensional constant. Dimensional constant k = 6 p, so that the equation becomes
F = 6 p ? r v
Viscosity
When a layer of a fluid slips or tends to slip on another layer in contact. The two layer exert tangential force on each other. The direction such that relative motion between the layer is opposed. This property of a fluid to oppose relative motion between its layer is called viscosity.
The force between the layers opposing relative motion between them are known as the forces of viscosity. Thus, viscosity may be through of as the internal friction of a fluid in motion.
If a solids surface is kept in contact with a fluid and is moved, force of viscosity appear between the solid surface and the fluid layer in contact. The flid in contact is dragged with solid and there is no relative slipping. When a boat moves slowly on the water calm river. The water in contact wwitth the boat is dragged with it, whereas the water in contact with the bed of the river remains at the rest. Velocities of the different layer are coefficient. Let v be th velocity of the layer at a distance from the bed and v+dv be the velocity at a distance z+dz.
Thus the velocity differs by dv in going through a distance dz perpendicular to it. The quantity dv/dz is called the velocity gradient.
The force of viscosity between two layers of a fluid is proportional to the velocity gradient in the direction perpendicular to the layers. Also the force is proportion to the area of the layer.
Thus if F is the force exerted by a layer of area a on a layer in contact.
F a A and F a dv/dz
F = – ? A dv/dz
The negative slide is included as the forceis fractional in the nature and opposes relative motion. The constant of proportionality ? is called the coefficient of viscosity.
The S.I unit of viscosity is N-s/m2 and CGS unit is dyne sec/cm2+ is in common use and is called a poise.
IMPORTANCE OF MILLIKAN METHOD

It is a direct and a prices method for determination of electronic charge, yielding fairly accurate results.
It proves that an electron carries a definite amount of charge and that the charge on an ion , positive or negative, is numerically equal to that on electron. It establishes that electricity is atomic in nature.
Avogadro’s number- The knowledge of the charge on an electron helps to determine Avogadro’s number which is the number of molecules contained in 1 gram molecule of an element. Gram atom and gram molecule of an element is its weight in gram numerically equal to its atomic weight or molecular weight respectively.

CONCLUSION
REFERENCE

http://facultyfiles.deanza.edu/gems/lunaeduardo/MillikanOilDropExperiment.pdf
http://en.wikipedia.org/wiki/Oil-drop_experiment#Apparatus
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=357.0