Millikan Oil Drop PDF
Millikan Oil Drop PDF
Millikan Oil Drop PDF
Millikan’s Experiment
Introduction
The charge of the electron is one of the most important fundamental constants in nature.
The ratio of the mass to charge of the electron may be readily determined via the
observation of the path of a pre-accelerated electron through a magnetic field. However,
the determination of the charge alone is a little more difficult. The first attempt was
performed by Thomson in 1896, using a cloud chamber, and resulted in a value close to
1.1×10-19 Coulombs, but with a large error. The more precise measurements of Millikan
were performed in 1911 in his now famous oil drop experiment.
In Millikan’s experiment the terminal velocities are achieved rapidly, and only the
motion of the oil drops with terminal velocity is observed. If the oil drops are observed
to move a distance L in times Tf (fall) and Tr (rise), then it is possible to solve the
equations (3) and (5) for q.
mg
q=
Ev f
(v f + vr ) (6)
This is however expressed in terms of the effective mass of the oil drop moving through
the air, where
4
m = πa 3 ( ρ oil − ρ air ) (7)
3
This can be used in conjunction with equation 3 to calculate an expression for a
9 ηv f
a= (8)
2 ( ρ oil − ρ air ) g
and thus m can be calculated and thus the corresponding charge
1 2η 3v f
q = 9π (v f + vr ) (9)
E ( ρ oil − ρ air ) g
Noting that the electric field can be expressed in terms of the voltage between the two
plates and their distance, then
d 2η 3v f
q = 9π(v f + vr ) (10)
V ( ρoil − ρ air ) g
The two equations (8) and (10) are required for the rise and fall method for determining
q.
There is a second technique for determining q, which is the float technique. For these
measurements the appropriate equations are;
3
9 ηv f d 2η 3v f
a= and q = 9π (11)
2 ( ρ oil − ρ air ) g V ( ρ oil − ρ air ) g
You might attempt deriving the latter two equations (11) yourself.
Apparatus
The equipment to be used in the measurement is shown in Fig. 2. The Millikan
equipment should be connected to the voltage control system and timer as shown Fig. 3.
Fig. 3. The connections and switch functions for the voltage control system and
timer.
Procedure
Setting up the equipment
- Turn the lens holder of the micrometer eyepiece until you can clearly see the
micrometer scale.
- If necessary, turn the eyepiece to orient the micrometer scale vertically. For this purpose
you should slightly loosen the fastening screw. Since falling droplets are observed on the
micrometer scale as rising droplets due to the reversion of the image in the microscope,
the scale start (0) should point upward and the scale end should point downward (10).
- Use the knurled knob to push the measuring microscope close to the plastic cover. The
illuminated capacitor plates can be seen at the top and bottom in the circular-viewing
field. The beginning and end of the micrometer scale are at a small distance to the
capacitor plates.
To eliminate disturbing light reflections or to correct the observation region, if you are
not satisfied with the illumination:
- Loosen the fastening screw of the capacitor and move the capacitor.
- You can also adjust the lamp with the help of the adjusting screw (recessed head screw).
Objective magnification
Due to the objective magnification M, a fall or rise distance s of the oil droplet between
the capacitor plates is represented on the scale section
x = Ms
If the image of an oil droplet moves in the time ∆t on the scale over a distance ∆x, the
velocity of the oil droplet is
∆x
v=
M∆t
The objective magnification is M = 2 quite accurately. For more exact measurements, you
should determine the magnification:
Timer/Counter Operation
o Set mode to “tE,F”.
o Press start until corresponding LED is lit
o Cable from clock1 on Millikan control box should be connected to E.
o Cable from clock2 on Millikan control box should be connected to F.
o Zero timer: press “→0←”.
o Times can be read out using button tE,F – when E LED is lit, first time is given i.e.
time between start of clock and event E. When F LED is list this gives the time
between events E and F.
Fall/rise method
The fall velocity vf and the rise velocity vr are determined from the fall time tf and rise
time tr for a pre-selected distance s. The following equations can then be used for the
radius a and the charge q of the droplet (see the introduction).
9 ηv f d 2η 3v f
a= q = 9π (v f + vr )
2 ( ρ oil − ρ air ) g V ( ρoil − ρ air ) g
Float Method
The float potential U and the fall speed v are determined from the fall time t for a pre-
selected distance s. The following applies for the radius a and the charge q of the droplet:
3
9 ηv f d 2η 3v f
a= and q = 9π
2 ( ρ oil − ρ air ) g V ( ρ oil − ρ air ) g
Analysis
Use both methods to deduce the charge and radius of the oil drops. The viscosity of air,
η, is 1.824×10-5 Nsm-2, and you will need to calculate the density of the air. A plot of the
charge against radius should resemble that shown in Fig. 4.
Fig 4. Measurements of
the charge and radius of
oil drops.
Cunningham found that there was a small deviation from Stoke’s equation for the friction
for small oil drops with a radius a (this is the deviation shown for small diameters in Fig.
4) . This results is a modification of the equation for the charge such that
q
q' =
3
A
1 +
a
where the constant A takes the value 0.07776×10-6 m at standard pressure and at 25oC.
Reanalyse your results using this correction.
t
References
Adapted from Leybold instruction sheets 559 421, 575 451 and 559 411.