Download Measuring Fundamental charge by Millikan`s Oil Drop Apparatus

 an experiment of the Electron topic
Measuring Fundamental charge by Millikan’s
Oil Drop Apparatus
Instructor: 梁生
Office: 7-318
Email: [email protected]
Introduction
Measuring the Fundamental charge is a milestone of investigating on Electron.
Millikan’s experiment is effective and with artful ideas, which is an illumination for
design and development of instrumentation.
Purposes
There are two purposes in this experiment as follow:
1. To master measuring fundamental charge by Millikan’s oil drop apparatus;
2. To measure the fundamental charge and validate the discontinuity of electric
charge.
Experimental instruments
Millikan oil drop apparatus.
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Principle
The tiny oil droplet is sprayed between the two parallel plates with a distance of d,
then, the droplet obtains an electric charge of q due to the friction. When a voltage of
V between the two parallel plates are operated, an electric field E is generated,
therefore, the oil droplet is affected by both of the electric force and gravity. By tuning
the value of the voltage V, balancing the gravity and the electric force on the oil
droplet can be realized. And the oil droplet can be suspended between two parallel
plates. Then, we have:
mg = qE = q
V
d
(1)
where, V and d are physical constants easy to measure, by further measurement of the
mass of the oil droplet m, the electric charge of the droplet can be obtained. It can be
found that, the charge of the oil droplet is always an integer multiples of the smallest
charge observed, namely, q=ne, n=±1, ±2 ……, which validates the discontinuity of
the electric charge, and the smallest unit of electrical charge, is defined as the value
of the fundamental charge e.
By supposing the density of the oil droplet is ρ, the mass of oil droplet m can be
expressed as:
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m = π r3ρ
3
(2)
To measure the radius of oil droplet r, remove the voltage between the two parallel
plates to make oil droplet fall by the gravity, at the same time, resistance is generated
by the air viscosity. Viscous force is proportional with the fall velocity, and it obeys
Stokes’ law:
f r = 6π rη v
(3)
where η is the viscosity of the air, r is the radius of the droplet, and v is the droplet
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velocity, respectively. Furthermore, the oil droplet gravity is m = π r 3 ρ g .
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When the oil droplet falls some distance in the air, the viscous resistance increases,
two forces reach balance, then, the oil droplet fall with a constant velocity. In this case,
it can be found that:
4 3
π r ρ g = 6π rη v
3
(4)
To solve the radius of the droplet from (4), it is can be expressed as:
r=
9η v
2ρ g
(5)
Because oil droplet’s radius is less than 10-6 m, the air medium cannot be
considered evenly continuous, so we need to rewrite the η to η ′ =
η
b
1+
pr
, where b is
a correction factor and b=8.22×10-3 mPa, p is the atmosphere pressure, so we can get
r=
9η v
1
⋅
2ρ g 1 + b
pr
(6)
and
⎛
4 ⎜ 9η v
1
⋅
m= π⎜
3 ⎜ 2ρ g 1 + b
⎜
pr
⎝
3
⎞ 2
⎟
⎟ ⋅ρ
⎟
⎟
⎠
(7)
Above expression still contains radius r, but it is only in the correction item, it doesn’t
need quite accurate.
Considering the velocity of the oil droplet equal with the ratio of fall distance l to the
time t, V=l/t, we can get:
3
⎛
4 ⎜ 9η l
1
m= π⎜
⋅
3 ⎜ 2 ρ gt 1 + b
⎜
pr
⎝
3
⎞ 2
⎟
⎟ ⋅ρ
⎟
⎟
⎠
(8)
Substitute above formula into (1):
⎛
18π ⎜ η
⎜
q = ne =
2ρ g ⎜ 1 + b
⎜
pr
⎝
3
⎞ 2
⎟ ⎛ l ⎞32 d
⎟ ⎜ ⎟
⎟ ⎝t ⎠ V
⎟
⎠
(9)
Formulas (5) and (9) are the basic formulas in this experiment.
Procedures
1. Apparatus regulation
Put the work voltage select switch on “fall” block, at this moment the upper and lower
plates are short circuit without electric, and the oil droplets are easy to be sprayed in.
Remove the drop chamber, check the insulation ring and the plates. Install the drop
chamber back, and keep spray aperture towards the front right side, open it for droplet
spraying.
Make the apparatus steady, adjust the two level screws to make the level bubble
indicate level.
Turn on the power switch, tune the focus for CCD to make clear vision in the monitor.
2. Observation and controlling of droplet
Spray oil droplets into the drop chamber (only a little) by the atomizer, tune the
focus hand wheel of microscope to make the oil droplets clear in the monitor, then the
oil droplets in the sight field seems to be like just stars in the night sky. If the scale is
not brilliant enough, or the luminosity of up and down visual field is not uniform, it is
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necessary to adjust the direction of the light emitting diode (LED) to make the visual
field and the oil droplets clear. Keep the work voltage switch on “fall” for safety while
removing drop chamber.
Put working voltage switch to “Balance” to put 250 V working voltage to the two
parallel plates, to observe the motion of the oil droplets; choose a clear oil droplet (not
too large), adjust the voltage, observe the velocity changes of the oil droplet till it
stops keeping balance; put the work voltage switch to the “rise”, let the oil drop in the
top of visual field. Then put the switch to the “fall”, the oil droplets begin to fall,
measure the time for falling through this distance. Repeat above operation to be
skilled in controlling the oil droplet.
3. Measurement
From formula (9), it is found that we just need to measure two parameters, one is the
balance voltage V, the other is the time t for falling through the distance l. To measure
the balance voltage we need adjust carefully. Put the oil droplets near the cross hair on
the scale for judging whether it is balanced.
Choose the right size droplet is the key point to this experiment. For large, bright oil
droplet, due to its large quality and charge, the time of falling a distance is shorter,
which increases the measurement and data processing errors. However, the little oil
droplets is difficult to observe due to Brownian motion. It is better to choose the oil
droplet which takes about 20 s to fall 2 mm at the balance voltage from 200 V to 300
V. For guaranteeing the oil droplet fall uniform, we should measure time after the oil
droplet fall a distance. The selected measurement distance should be in the middle of
the two parallel plates. If the distance is too near to the up plate, it will influence the
result for the airflow near the hole and the electric field is not uniform yet. It will
influence repeat measurement for easily missing of the oil droplet because of the
distance is too near the down plates. After the oil droplet is balanced, put the oil drop
on a proper place through adjusting “rise” voltage. Let oil droplet fall a distance then
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start timing and measure the time t while the oil droplet falling distance l. Then
increase the balance voltage again, otherwise the droplets will soon disappear.
4. Data processing
The known data in this experiment are as follow:
density of the oil ρ=981 kg/m3
viscosity of air η=1.83×10-5 kg/(ms)
acceleration of gravity g=9.80 m/s2
fixed constant b=6.17×10-6 m cmHg
air pressure p=76.0 cmHg
distance between two parallel plates is d=5.00×10-3 m.
Put above data into formula, we can get the charge of the oil droplet:
q=
1.6 ×10−10 × l 3 2
⎡ ⎛
⎞⎤
−4 t
⎢t ⎜ 1 + 8.76 ×10
⎟⎥
l ⎠ ⎥⎦
⎢⎣ ⎝
32
⋅
1
V
(10)
Obviously, as the density of the oil droplet, the viscosity of air η is the function of
temperature, gravity and air viscosity force will change during in experiment.
However, in general condition, this calculation just brings 1% relative error.
Repeat the measurement operation 6~10 times for one oil droplet, adjust the balance
voltage for each measurement, and record it. Achieve measuring 6 to 8 different oil
droplets.
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Table 1. Data Record
Droplet 1
Droplet
V(V)
Time
Droplet 2
t(s)
V(V)
Droplet 3
t(s)
V(V)
t(s)
Droplet 4
V(V)
t(s)
Droplet 5
V(V)
t(s)
Droplet 6
V(V)
t(s)
1
2
3
4
5
6
Ave.
Table 2. Data Processing
Droplet 1
Electric
charge
Ratio
Approximate
Integer
Measured e
Relative
Error
Droplet 2
Droplet 3
Droplet 4
Droplet 5
Droplet 6
q (C)
q/e
n
e′
e − e′
e
Attentions
1. The experimental report need to be achieved in English.
2. Do not lose droplets after timing, keep the droplet static before the eyes leave the
microscope. Keep watching CCD monitor during droplets moving.
3. After choosing oil droplet, close the electrode into hole in time until beginning to
measure.
4. For the accuracy of the measurement balance voltage, it should be appropriate to
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extend the observation time of balance state of droplet.
5. Tune and record the balance voltage continuously in every measurement. If the
voltage changes obviously, this oil droplet should be considered as a new one.
6. Due to that oil droplet is very difficult to control and measure, therefore, to get
better results, it is necessary to have rigorous scientific attitude, experimental
operation and data processing.
Basic requirements
1. Observe and control the movement of the charged oil droplets in electric field.
2.
According to the formula (10) for calculating charges more than 6 different oil
droplets. Note: the selected droplet’s balance voltage and the falling velocity should
be different, otherwise all the droplets are with the same charge, which can not
validate discontinuity of the electric charge.
3. Measure the fundamental charge, and verify the discontinuity of the charge.
4. In order to verify the charge is always an integer multiple of the charge of the
electron and get the value of fundamental charge e, we should seek the common
denominator to every measured q. and the common denominator is the fundamental
charge. For data processing, you can use “reverse validation” approach. Use the
recognized fundamental charge e=1.602×10-19 C to divide the measured charge q, get
a data close to an integer (if has a large difference to an integer, delete it), take the
integer, and this integer is the basic charged number n of droplet. Then, the measured
charge q is divided by n, the fundamental charge e can be obtained, find and compare
it with the recognized value.
5. Tables for data record and processing should be designed by yourself. Tables
should be clearly to illustrate the measured data and calculated results. Here Table 1
and 2 are presented for references.
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Discussions
1. What are the causes of that droplets fall too fast or too slow without work voltage?
What are the influences on the experimental results?
2. If the oil droplet’s balance voltage is too high or too low, what does that mean?
3. We find a significant change in balance voltage during the measurement, what is
the matter? If the balance voltage decreases in a small range, what does that mean?
4. The droplet’s image is found to be dark during observation. What is the problem?
How to deal with it?
5. According to your experimental results, calculate the radius and mass of two
droplets that the fall time is maximum and minimum for the same distance,
respectively. What is the cause for the differences of time.
6. Use the experimental data of one of the oil droplets to calculate the buoyancy that
effects on the droplet. Compare the calculated buoyancy with the gravity, viscous
force and electric force.
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Appendix: MOD-5 Millikan’s Oil Drop Apparatus
MOD-5 oil drop apparatus is shown in Fig. 1. It mainly consists of oil drop chamber,
illumination system, leveling system, measuring microscope, timer, power supply,
atomizer and CCD image monitor.
Fig. 1. MOD-5 Millikan Drop Apparatus.
1. Oil droplets chamber
As shown in Fig. 1, oil droplets chamber consist of two fine grinding parallel plates
(upper, lower electrodes, respectively) with insulation ring composition among
cushion, the distance between the parallel plates is 5 mm. There are apertures for LED
and microscope on insulation ring. Oil drops chamber is located in the organic glass
wind covering. There is a hole with diameter of 0.4 mm in the middle of upper plate.
The oil droplets from the chamber fall between the upper and lower electrodes
through this hole and lighted by LED. You can use level screws to adjust the level of
the oil droplets chamber, and check with level bubble. There is a microscope in the
front of oil droplets chamber wind covering, you can observe oil drops between the
parallel plates through the observation hole on the insulation ring. There is a reticle in
the ocular, the total vertical length is equivalent to 0.300 cm (each division is 0.050
cm), which is used to measure the distance l of the oil droplets falling. The falling
time of oil droplets can be measured by the digital timer. By the regulation of
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microscope, reticle and oil droplets can be seen clearly. Put CCD camera close to the
ocular of microscope, rotate and move CCD lens appropriately, and then you can see
the reticle and the oil droplets clearly on the monitor. Sometimes you can also omit
the CCD imaging lens and the ocular of microscope, make the view directly imaged
in the CCD sensitive surface through a microscope objective lens. Sensitive surface of
CCD transforms imagine signal in every sensitive unit into a video signal and transmit
it to the monitor, which shows the original image on the screen.
2. Power supply
There are four different voltages supplied by the power supply system.
(1) A 500 V DC working voltage is added to parallel plates to produce electric field
between the two plates. The voltage can be continuously tuned. Voltage value can be
read on the digital voltage meter, and controlled by work voltage switch. Switch has 3
states: “BALANCE” provides balance voltage; “FALL” removes balance voltage,
makes oil droplets fall; “RISE” provides balance voltage plus a rise voltage of about
200 V to make the oil rise to repeat the measurement of the same oil droplet.
(2) 200 V RISE voltage.
(3) 5 V voltage as the power supply for digital voltage meter, digital timer and LED.
(4) 12 V voltage as power supply for CCD.
3. Microscope and monitor
The amplified imagine of oil droplet can be realized by the microscope and shown on
the monitor. It is easy to observe, control and measure the oil droplet by the monitor.
There is a reticle on the screen. Every small grid is 0.050 cm and total 4 grids are
0.200 cm, which is employed to measure the fall distance and calculate the fall
velocity of the oil droplet.
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