®
Instruction Manual
Chamber Cover
Platform
Plate Charging
Switch
LED Light Source
Viewing Scope
Droplet Viewing
Chamber
012-13093B
012-13093B
Millikan Oil Drop Apparatus
AP-8210A
®
The cover page shows the PASCO AP-8210A Millikan Oil Drop Apparatus with a light-emitting diode (LED)
light source. A power supply for the light source, a bottle of non-volatile oil, and a spray atomizer are included
(but not shown).
ii
®
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Equipment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Aligning the Optical System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Functions of Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Adjusting and Measuring the Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Determining the Temperature of the Droplet Viewing Chamber . . . . . . . . . . . . . . . . . . . 9
Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Computations of the Charge of an Electron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Using a Projection Microscope with the Millikan Oil Drop Apparatus . . . . . . . . . . . . . . 12
Historical Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Maintenance Notes
Cleaning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
Adjusting the Vertical Reticle and Viewing Scope Alignments. . . . . . . . . . . . . . . . . . . . 17
Adjusting the Horizontal Reticle Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Touching Up the Black Painted Surface on the Plastic Spacer . . . . . . . . . . . . . . . . . . . 18
Appendix
A. Viscosity of Dry Air as a Function of Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . 19
B. Thermistor Resistance at Various Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Teacher’s Guide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Technical Support, Warranty, and Copyright . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
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Millikan Oil Drop Apparatus
iv 012-13093B
Millikan Oil Drop Apparatus
®
2.895x 1014e.s.u./gm equivalent weight
4.803x 10
10–
e.s.u.
----------------------------------------------------------------------------------------------
kv
f
mg
Figure 1
mg kvf ( 1 )=
AP-8210A
-Introduction
The PASCO Millikan Oil Drop Apparatus is designed to conduct the Millikan Oil Drop Experiment where the
electric charge carried by a particle may be calculated by measuring the force experienced by the particle in an
electric field of known strength. Although it is relatively easy to produce a known electric field, the force exerted
by such a field on a particle carrying only one or several excess electrons is very small. For example, a field of
1000 volts per centimeter would exert a force of only 1.6 10
one excess electron. This is a force comparable to the gravitational force on a particle with a mass of 10
million millionth) gram.
-9
dyne (1 dyne = 10-5 newtons) on a particle bearing
-l2
(one
The success of the Millikan Oil Drop experiment depends on the ability to measure forces this small. The behavior
of small charged droplets of oil, having masses of only 10
-12
gram or less, is observed in a gravitational and an
electric field. Measuring the velocity of fall of the drop in air enables, with the use of Stokes’ Law, the calculation
of the mass of the drop. The observation of the velocity of the drop rising in an electric field then permits a calculation of the force on, and hence, the charge carried by the oil drop.
Although this experiment will allow one to measure the total charge on a drop, it is only through an analysis of the
data obtained and a certain degree of experimental skill that the charge of a single electron can be determined. By
selecting droplets which rise and fall slowly, one can be certain that the drop has a small number of excess electrons. A number of such drops should be observed and their respective charges calculated. If the charges on these
drops are integral multiples of a certain smallest charge, then this is a good indication of the atomic nature of electricity. However, since a different droplet has been used for measuring each charge, there remains the question as
to the effect of the drop itself on the charge. This uncertainty can be eliminated by changing the charge on a single
drop while the drop is under observation. An ionization source placed near the drop will accomplish this. In fact, it
is possible to change the charge on the same drop several times. If the results of measurements on the same drop
then yield charges which are integral multiples of some smallest charge, then this is proof of the atomic nature of
electricity.
The measurement of the charge of the electron also permits the calculation of Avogadro’s number. The amount of
current required to electrodeposit one gram equivalent of an element on an electrode (the faraday) is equal to the
charge of the electron multiplied by the number of molecules in a mole. Through electrolysis experiments, the faraday has been found to be 2.895 x 10
expressed in the m-k-s system as 9.625 x 10
14
electrostatic units (e.s.u.) per gram equivalent weight (more commonly
7
coulombs per kilogram equivalent weight). Dividing the faraday by
the charge of the electron,
yields 6.025 x 10
23
molecules per gram equivalent weight, or Avogadro’s Number.
Equation for Calculating the Charge on a Drop
An analysis of the forces acting on an oil droplet will yield the equation for the determination
of the charge carried by the droplet. Figure 1 shows the forces acting on the drop when it is
falling in air and has reached its terminal velocity. (Terminal velocity is reached in a few milliseconds for the droplets used in this experiment.) In Figure 1, v
coefficient of friction between the air and the drop, m is the mass of the drop, and g is the
acceleration of gravity. Since the forces are equal and opposite:
is the velocity of fall, k is the
f
1
Millikan Oil Drop Apparatus -Introduction
®
Figure 2
kv
r
mg
Eq
Eq mg kvr ( 2 )+=
q
mg v
fvr
+
Ev
f
----------------------------
( 3 )=
m
4
3
---
a3 ( 4 )=
a
9v
f
2g
----------- ( 5 )
*
=
eff
1
1
b
pa
------
+
---------------
( 6 )
**
=
a
b
2p
------
2
9v
f
2g
--------------
+
b
2p
------
( 7 )–=
q
6
E
------
9
3
2g 1
b
pa
------
+
3
---------------------------------- vfvr+vf ( 8 )=
E
V
d
---
( 9 )=
Figure 2 shows the forces acting on the drop when it is rising under the influence of an electric field. In Figure 2, E is the electric intensity, q is the charge carried by the drop, and v
r
is
the velocity of rise. Adding the forces vectorially yields:
In both cases there is also a small buoyant force exerted by the air on the droplet. Since the
density of air is only about one-thousandth that of oil, this force may be neglected.
Eliminating k from equations ( 1 ) and ( 2 ) and solving for q yields:
To eliminate m from equation ( 3 ), one uses the expression for the volume of a sphere:
where a is the radius of the droplet, and is the density of the oil.
To calculate a, one employs Stokes’ Law, relating the radius of a spherical body to its velocity of fall in a viscous
medium (with t
he coefficient of viscosity, ).
Stokes’ Law, however, becomes incorrect when the velocity of fall of the droplets is less than 0.1 cm/s. (Droplets
having this and smaller velocities have radii, on the order of 2 microns, comparable to the mean free path of air
molecules, a condition which violates one of the assumptions made in deriving Stokes’ Law.) Since the velocities
of the droplets used in this experiment will be in the range of 0.01 to 0.001 cm/s, the viscosity must be multiplied
by a correction factor. The resulting effective viscosity is:
where b is a constant, p is the atmospheric pressure, and a is the radius of the drop as calculated by the uncorrected
form of Stokes’ Law, equation ( 5 ).
Substituting
in equation (6) into equation (5), and then solving for the radius a gives:
eff
Substituting equations (4), (5), and (6) into equation (3) yields:
The electric intensity is given by:
Where V is the potential difference across the parallel plates separated by the distance d.
2
012-13093B
®
Model No. AP-8210A -Introduction
q
4d
3
----------
1
g
------
9
2
------
3
1
2
---
1
1
b
pa
------
+
---------------
1
2
---
v
fvrvf
+
V
------------------------
( 10 )=
Substituting equations ( 7 ) and ( 8 ) into equation ( 6 ) and rearranging yields:
The terms in the first set of brackets need only be determined once for any particular apparatus. The second term is
determined for each droplet, while the term in the third set of brackets is calculated for each change of charge that
the drop experiences.
The definitions of the symbols used, together with their proper units for use in equation ( 10 ) are:
q – charge carried by the droplet
d – separation of the plates in the droplet viewing chamber
– density of oil
g – acceleration of gravity
– viscosity of air
b – constant, equal to 8.13 × 10
-8
N/m
p – barometric pressure
a – radius of the drop in cm as calculated by equation ( 5 )
v
– velocity of fall
f
v
– velocity of rise
r
V – potential difference across the plates in
Note: The accepted value for e is 1.60 x 10
-19
coulombs
--------------------------------------------------
*For additional information about Stoke’s Law, please refer to Introduction to Theoretical Physics
(New York, Van Nostrand), Chapter 6.
**A derivation can be found in The Electron
by R.A. Millikan (Chicago, The University of Chicago Press), Chap-
ter 5.
, by L. Page
012-13093B 3
Millikan Oil Drop Apparatus Equipment
®
AC adapter
mineral oil
atomizer
Figure 3: Included equipment
Equipment
The AP-8210A Millikan Oil Drop Apparatus includes the following:
Included Equipment Part Number
Millikan Oil Drop Apparatus AP-8210A
AC Adapter, 100 - 240 VAC to 12 VDC, 1.0 A 540-092
Atomizer 699-093
Non-volatile mineral oil*, 120 mL (~4 ounces)
Required Equipment Part Number
Power Supply, high voltage, well-regulated, 500 VDC, 10 mA (minimum) SF-9585
Digital Multimeter to measure voltage and resistance SB-9599A
Banana plug patch cords (4) SE-9750 or SE-9751
Digital Stopwatch ME-1234
Recommended Equipment Part Number
Large Rod Stand ME-8735
Steel Rod, 45 cm (2) ME-8736
Micrometer (0 to 25 mm with 0.1 mm resolution) SE-7337
Ken-A-Vision VideoFlex Microscope (optional) SE-7227
3
*The Squibb #5597 Mineral Oil has a measured density of 886 kg/m
.
However, the density of different lots of mineral oils may vary
slightly. Therefore, for greatest precision, you should determine the
density of the mineral oil you are using.
It is recommended that you store the equipment in the original packing
material. After unpacking, remove the foam insert from inside the
droplet viewing chamber. Store the plate charging switch on the
hook-and-loop tabs located on the top of the platform.
4
012-13093B
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