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Lab Manual
General Physics Lab (International Campus)
Department of PHYSICS
YONSEI University
Millikan Oil Drop Experiment
Ver.20160901
[International Campus Lab]
Millikan Oil Drop Experiment
Objective
Determine the charge of an electron by observing the effect of an electric field on a cloud of charged oil droplets.
Theory
-----------------------------
Reference
--------------------------
Young & Freedman, University Physics (14th ed.), Pearson, 2016
23. Electric Potential – Problem 23.81 (p.807)
-----------------------------------------------------------------------------
The droplets can be observed through a viewing scope with
illumination by the bright light of a lamp. The scope has reticle
marks spaced to 0.1mm, so the velocity of the falling or rising
drop can be calculated.
In 1909, Robert Millikan conducted the oil drop experiment
to determine the charge of an electron. He suspended tiny
charged droplets of oil between two metal electrodes by balancing downward gravitational force with upward electric
force. The density of the oil was known, so he could determine the droplets’ masses from their observed radii. Using
the known electric field and the value of gravity and mass, he
determined the charge on oil droplets in mechanical equilibrium. By repeating the experiment, he confirmed that the
charges were all multiples of some fundamental value. He
proposed that this value was the charge of a single electron.
The figure 1 shows a simplified scheme of Millikan’s oil drop
experiment. A fine mist of oil droplets is sprayed into the
chamber and some droplets enter the space between the
plates. The droplets become electrically charged by an ionizing radiation source such as an X-ray or electrical discharges.
By applying a potential difference across a parallel pair of
horizontal metal plates, a uniform electric field is created in
the space between them. The electric field can be controlled
Fig 1
(a) Simplified scheme of the Millikan oil drop experiment.
(b) Forces on a falling drop. (plates not charged)
(c) Forces on a rising drop. (plates charged)
by changing the voltage across the plates.
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Lab Manual
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Department of PHYSICS
YONSEI University
Millikan Oil Drop Experiment
Ver.20160901
Figure 1(b) shows the forces acting on a droplet when it is
The velocities
and
of the equation (5) can be meas-
falling in air. The velocity of drop has reached its terminal
ured experimentally and only the radius
velocity
remains unknown.
in a few milliseconds for the droplets used in this
experiment. The frictional force
velocity of the drop, where
of the oil droplet
is proportional to the
is the coefficient of friction be-
tween the air and the drop. Since the gravitational force
and the frictional force
are equal and opposite,
The frictional force
in figure 1 actually results from
the viscosity between the oil and the air. The viscous force on
a small sphere moving through a viscous fluid is given by
6
(1)
(6)
Figure 1(c) shows the forces acting on the drop when it is
Equation (6), known as Stokes’ law, is the frictional force
rising under the influence of an electric field. The electric in-
acting on the interface between a fluid and a particle, where
⁄ , where
tensity is given by
is the potential differ-
ence across the parallel plates separated by a distance
the charge on the droplet is
is the viscosity,
. If
is the flow velocity relative to the object. (Millikan suggest-
then there is an additional
ed the corrected form of Stokes’ law with effective viscosity
⁄
1
on it. If the sign and magnitude of the
electric force
is the radius of the spherical object, and
, where
is a constant and
is the
field are such to make the droplet rise, it will quickly acquire a
atmospheric pressure. We will neglect this correction factor
terminal velocity
here, however, it is desirable to consider it for more accurate
and the frictional force
acts on
it. Adding the forces vectorially yields
analysis.) Now Equation (6) can be substituted for
in equation (1). Substituting equations (4), (6) into equation (1)
(2)
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
10
yields
4
3
6
or
9
2
(7)
of that of oil, this force may be neglected.
Substituting equation (7) into equation (5) and rearranging
Eliminating
from equations (1) and (2) and solving for
the terms yields
yields
1
To eliminate
(3)
18
2
1
(8)
from equation (3), we use the expression for
: Charge carried by the droplet (C)
the volume of a sphere
: Potential difference across the plates (V)
: Separation of the plates of the capacitor (m)
4
3
(4)
: Density of oil (kg⁄m )
: Acceleration of gravity (m⁄s )
where
is the radius of the droplet, and
is the density of
: Viscosity of air (Pa ∙ s
N ∙ s⁄m ) (See appendix.)
: Velocity of fall without E-field (m⁄s)
the oil. Substituting equation (4) into equation (3) yields
: Velocity of rise without E-field (m⁄s)
4
3
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Lab Manual
General Physics Lab (International Campus)
Department of PHYSICS
YONSEI University
Millikan Oil Drop Experiment
Ver.20160901
Equipment
1. List
Items
Millikan Apparatus
Qty.
1
Description
Measures the elementary electric charge using a classical method of Millikan.
Supplies voltage for the capacitor plates.
Power Supply
(Power cord included)
Power Adapter
1
range 0 to 500 volts.
1
(for LED lamp)
Patch Cords (High Voltage)
(with safety shrouded banana plugs)
Patch Cords
(with banana plugs)
Produces regulated DC power up to 50mA in a voltage
2
2
Supplies voltage for the LED lamp.
Connect the power supply to the capacitor plates of the
Millikan apparatus.
Connect the multimeter to the thermistor of the Millikan
apparatus.
886 kg⁄m
Atomizer
1
Sprays oil droplets of density
Multimeter
1
Measures voltage, current, and resistance.
A-shaped Base
1
Support Rod 600mm
2
Vernier Caliper
1
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Provide stable support for experiment set-ups.
Measures external or internal diameter of an object with
a precision to 0.05mm.
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Lab Manual
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Department of PHYSICS
YONSEI University
Millikan Oil Drop Experiment
Ver.20160901
2. Details
(1) Millikan Apparatus
(2) Power Supply
The power supply provides regulated DC power up to
50mA in a voltage range 0 to 500 volts.
(4) Vernier Caliper
The Vernier caliper measures external, internal diameter or
depth of an object with a precision to 0.05mm.
(3) Multimeter
The multimeter measures voltage, current, and resistance.
① 22mm is to the immediate left of the zero on the vernier
scale. Hence, the main scale reading is 22mm.
② Look closely for and alignment of the scale lines of the
th
main scale and vernier scale. In the figure, the aligned (13 )
line corresponds to 0.65mm
0.05
13 .
③ The final measurement is given by the sum of the two
readings. This gives 22.65mm
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0.65 .
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Lab Manual
General Physics Lab (International Campus)
Department of PHYSICS
YONSEI University
Millikan Oil Drop Experiment
Ver.20160901
Setup
Setup 1. Equipment Setup
(3) Reassemble the chamber.
(1) Adjust the height of the platform.
Mount the apparatus on two support rods on the A-shaped
base with the viewing scope at a height which permits the
experimenter to sit erect while observing the drops.
(2) Measure the plate separation distance.
Disassemble the chamber by lifting the Housing straight up
and then removing the upper capacitor plate and spacer
plate. Measure the thickness of the spacer (which is equal to
the plate separation distance) with vernier calipers. Be sure
that you are not including the raised rim of the spacer in your
measurement.
The flat cut (with black painted hole) of the spacer ring must
face the viewing scope.
_______________ m
Make sure fit the electric discharge terminal into the groove
on the underside of the spacer, and leave no gap between
Caution
the spacer and capacitor plates.
To prevent electric shock, do not touch the plates inside
the chamber while the power supply is turned on. Prior to
Caution
disassembling the chamber, you should be sure to turn
off the power supply and rotate the plate charging knob
to the Plate Grounded (middle) position.
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Be careful not to lose any parts of the chamber, especially the droplet hole cover.
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(4) Turn on the LED lamp.
Millikan Oil Drop Experiment
Ver.20160901
Adjust the position of the lamp by using two lamp position
knobs.
Connect the 12V DC adaptor to the lamp power jack.
The light is best focused when the right edge of the wire is
brightest (in highest contrast compared to the center of the
(5) Focus the scope and adjust the position of the lamp.
wire).
Remove the droplet hole cover. Unscrew the focusing wire
from its storage place on the platform and carefully insert it
into the hole in the center of the top capacitor plate.
Return the focusing wire to its storage location on the platform.
Bring the reticle into focus by turning the reticle focus ring.
Complete the reassembly of the chamber by placing the
View the focusing wire through the viewing scope and bring
droplet hole cover on the upper plate and the lid on the hous-
the wire into sharp focus by turning the droplet focusing ring.
ing. (If you do not cover the droplet hole of the plate, the hole
could be clogged with oil.)
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(6) Realign the optical system while observing the droplets.
Millikan Oil Drop Experiment
Ver.20160901
(8) Connect the power supply to the plate voltage connectors.
Move the air vent lever to the OPEN positon. Place the nozzle of the atomizer into the hole on the lid of the chamber and
squeeze the atomizer bulb with quick squeeze. While viewing
a shower of drops through viewing scope, realign the optical
system.
Caution
To prevent electric shock, use ONLY safety patch cords
with shrouded banana plug.
Do not apply voltage to the thermistor connectors.
(7) Determine the temperature of the chamber and calculate
(9) Set the output voltage of the power supply.
the viscosity of the air.
Prior to turning on the power supply, set the plate charging
knob to Plate Grounded (middle) position and rotate voltage
adjustment knob fully counterclockwise
0V .
Turn on the power and increase SLOWLY the output voltage to 300V.
Connect the multimeter to the thermistor connectors and
measure the resistance of the thermistor. Refer to the Sutherland’s Formula and the Thermistor Resistance Table (see
appendix) to find the viscosity of air.
_______________ Pa ∙ s
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Setup 2. Stopwatch Software
(1) Run Watchy software.
Millikan Oil Drop Experiment
Ver.20160901
(2) How to use the Watchy.
[Start] or [F5] : Start the clock.
[Stop] or [F6] : Stop the clock.
[Reset] or [F7] : Reset the stopwatch to zero. Clear the log.
[Lap] or [F10] : Add a lap time without stopping the clock.
[Split] or [F11] : Add a split time without stopping the clock.
[Split] records overall time at any given point, whereas [Lap]
records elapsed time between splits.
Procedure
(2) Rotate the plate charging knob of the power supply to the
Note
Plate Grounded (middle) position.
It is recommended you do not use any air conditioner or
fan while performing your experiment. The airflow outside
the chamber could affect the motion of oil droplets. The
high velocity stream of air creates a region of lower pres-
The plate charging knob changes the direction of the electric
field between the plates. We will introduce the droplets into
the chamber with no electric field by setting the knob to the
Plate Grounded position.
sure above the chamber lid, compared with standard
atmospheric pressure inside the chamber. This pressure
difference results in a net force pushing droplets up.
Step 1. Setting the Plates Voltage
(1) Set the potential difference across the parallel plates.
Set the output voltage of the power supply to 300V or any
desired value. (Do not exceed 400V.)
_______________ V
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Lab Manual
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Step 2. Introducing Droplets into the Chamber
(1) Move the air vent lever to OPEN position.
Millikan Oil Drop Experiment
Ver.20160901
Step 3. Charging the Droplets
The apparatus uses the piezo igniter to charge droplets. An
applied mechanical stress on piezoelectric ceramic in the
Move the air vent lever to the OPEN position to allow air to
igniter generates a high voltage. The voltage produces an
escape from the chamber during the introduction of droplets
electric field in the gap between the end of the connected
into the chamber.
wire and the lower plate in the chamber.
Free electrons in the gap are accelerated by the electric field.
(2) Introduce the droplets into the chamber.
As they collide with air molecules, they create additional ions
and newly-freed electrons. The exponentially increasing electrons and ions cause regions of the air in the gap to become
electrically conductive in a process called dielectric break-
Note
down and finally an electrical discharge or an electric spark
The object is to get a small number of drops, not a
occurs.
large, bright cloud from which a single drop can be choThe ions or electrons produced during this process adhere
sen.
to the surface of oil droplets in differing numbers.
① To make oil droplets, squeeze the atomizer bulb with
one quick squeeze.
(1) Charge the droplets by pressing the piezo igniter.
② Then squeeze it slowly to force the droplets through
the hole in the droplet hole cover, through the droplet
hole in the top capacitor plate, and into the space between the two capacitor plates.
Excessive use of the atomizer can cause too many
drops to be forced into the viewing area and prevent ob-
The droplets are charged with unknown charge. Some could
servation of drops. Besides, repeated squirts of the atom-
have many electrons (or positive ions), some a few, and
izer can cause the plate hole to be clogged and fail to
some could have no charge. If you find too few droplets have
produce any drops in the viewing area. In such cases,
net charges, press the piezo igniter again.
turn off the power supply, disassemble the chamber, and
then clean them with a soft tissue.
(3) When you see a shower of drops, move the air vent lever
to the CLOSE position.
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Lab Manual
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Department of PHYSICS
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Millikan Oil Drop Experiment
Ver.20160901
Step 4. Selection of the Drop
Step 5. Collecting Data on the Rise and Fall of the Droplet
Measure the rise (plates charged) and fall (plates not
(1) Select an appropriate droplet for your measurement.
charged) velocities of the selected droplet about 5-10 times.
As in the table below (which is calculated according to the
300V ,
The greatest accuracy of measurement is achieved if you
0.0074m ,
time from the instant that the droplet passes the reticle line A
25
; the
to the instant that the droplet passes the reticle line B (or C).
values could be completely different on your experimental
The distance between the reticle lines is 0.1 mm, so A and B
conditions), a droplet that requires about 10 seconds to fall
are 0.5 mm apart, and A and C are 1.0mm apart.
Eq. (8) on the conditions of
886 kg⁄m , and
1.862
10 Pa ∙ s
0.5mm will rise the same distance in the 16.8 seconds if it
has 3 excess electrons.
Fall time s
10
12
14
16
18
20
Rise time s
Charge
1
207
63.0
39.6
2
155
30.1
18.3
13.9
11.5
9.94
3
16.8
10.9
8.51
7.17
6.30
5.69
4
8.85
6.67
5.54
4.84
4.35
3.98
5
6.01
4.80
4.11
3.65
3.32
3.06
6
4.56
3.75
3.26
2.93
2.68
2.49
7
3.67
3.08
2.71
2.44
2.25
2.10
(1) With the plates not charged, start the stopwatch at the
The fall velocity of a droplet (with no electric field) depends
moment the falling drop passes the line A.
on the size of the droplet. The rise velocity of a droplet (with
an electric field) depends on both the size and the charge of
(2) At the moment that the droplet reaches the line B or C,
the droplet.
record the lap time by clicking the [Lap] button of the stopwatch, and apply electric fields at the same time.
Select a droplet that both falls slowly (about 10-20 seconds
to fall 0.5mm) when the plate charging switch is in the plates
(3) At the moment that the rising drop reaches the line A, rec-
grounded position (plates not charged) and rises slowly
ord the lap time again and stop applying electric fields at the
(about 4-60 seconds to rise 0.5mm) when the plates charged.
same time.
If too many droplets are in view, you can clear out many of
them by connecting power to the capacitor plates for several
seconds. If you find that too few droplets have net charges to
permit the selection of an appropriately sized and charged
drop, press the piezo igniter again.
When you find an appropriately sized and charged oil droplet, fine tune the focus of the viewing scope. (The oil droplet
is in best focus for accurate data collection when it appears
as a pinpoint of bright light.)
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Lab Manual
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Department of PHYSICS
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Millikan Oil Drop Experiment
Ver.20160901
Step 6. Changing the Charge of the Droplet
(4) Repeat step (2)~(3) 5~10 times.
distance m
Fall time s
Rise time s
It is desirable to observe as many different charges on a
1
single drop as possible. If the droplet is still in view, attempt to
2
change the charge on the droplet and measure the new rising
3
velocity many times, if possible.
4
5
(1) Bring the droplet to the bottom of the field of view using
…
the plate voltage switch.
average
(2) Rotate the plate charging switch to the charging position
to the droplet to rise.
(5) Calculate the average fall and rise velocities of the selected droplet.
(3) Change the charge on the droplet by pressing the piezo
igniter as described previously.
_______________ m/s
_______________ m/s
If the rising velocity of the droplet changes, make as many
measurements of the new rising velocity as you can.
(4) Repeat Step 5.
(6) Calculate the charge on the droplet.
18
2
1
(8)
(5) If the droplet is still in view, repeat Step 6 as many times
as you can.
: Charge carried by the droplet (C)
: Potential difference across the plates (V)
: Separation of the plates of the capacitor (m)
Step 7. Additional Measurement
: Density of oil (886 kg⁄m )
: Acceleration of gravity (m⁄s )
: Viscosity of air (Pa ∙ s
Repeat step 1 to 6 with other droplets.
N ∙ s⁄m ) (See appendix.)
: Velocity of fall without E-field (m⁄s)
: Velocity of rise without E-field (m⁄s)
If the result of this first determination for the charge on the
Repeat the experiment with at least 20 different charge
drop is too great, you should use slower moving droplets in
through the steps 5~7. It is desirable to get as many data as
subsequent determinations.
you can.
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Lab Manual
General Physics Lab (International Campus)
Department of PHYSICS
YONSEI University
Millikan Oil Drop Experiment
Ver.20160901
Step 8. Analysis
H
G
1.629
1
1.629
I
H
3.189
2
1.595
J
I
4.962
3
1.654
The following tables show an example of alternative method
_. ___
Average
for calculating the charge of an electron.
* Sample Table of Results
Droplet
A
B
C
D
E
10
6.287
8.051
1.523
1.608
11.268
Droplet
F
G
H
I
J
10
17.613
3.072
4.701
7.890
12.852
* Sample Table of Final Analysis
Droplet
A
B
C
D
E
Number of
4
5
1
1
7
Droplet
F
Number of
11
G
H
2
3
I
J
5
8
* Sample Table of Final Analysis
Differences between charges
B
A
1.764
C
B
6.528
D
C
E
D
F
G
1
4
0.085
9.660
6
E
6.345
4
F
14.541
10
1.764
1.632
0
Note that the most precise value of the charge of an electron
available at present is
1.610
1.586
9
1.602176487 40
10
C.
1.616
Appendix
1. Viscosity
2. Thermistor
Sutherland’s formula can be used to derive the viscosity
of an ideal gas as a function of a temperature
A thermistor is a specialized resistor, intentionally designed
to be thermally sensitive and its primary characteristic is its
ability to alter its electrical resistance in response to changes
in case temperature. The resistance of a 10kΩ thermistor at
follows the table below.
: Surtherland’s constant
kΩ
kΩ
: input temperature (K)
kΩ
0
27.616
26
9.6306
36
6.6859
5
22.266
27
9.2768
37
6.4535
10
18.066
28
8.9879
38
6.2304
15
14.748
29
8.6132
39
6.0162
20
12.110
30
8.3020
40
5.8104
21
11.650
31
8.0037
45
4.8965
22
11.210
32
7.7177
50
4.1454
291.15K
23
10.789
33
7.4435
60
3.0106
1.827
24
10.386
34
7.1805
80
1.6669
25
10.000
35
6.9281
100
0.97771
: reference temperature (K)
: reference viscosity (Pa ∙ s) at reference temperature
Surtherland’s constant and reference values for dry air are
120
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Lab Manual
Millikan Oil Drop Experiment
Ver.20160901
Result & Discussion
Your TA will inform you of the guidelines for writing the laboratory report during the lecture.
End of Lab Checklist
Please put your equipment in order as shown below.
□ Delete your data files and empty the trash can from the lab computer.
□ Turn off the computer.
□ With the voltage adjustment knob set at zero, turn off the power supply and unplug the power cable.
□ Unplug the dc adapter of the LED lamp.
□ Assemble the chamber. (Be careful not to lose any parts of it.)
□ Screw the focusing wire to its storage location on the platform.
□ Place the atomizer into the holder on the platform. (Handle the atomizer with care. It is very fragile.)
□ Do not unplug the high voltage patch cords.
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