Download 64-311 Laboratory

64-311 Laboratory
Experiment 2
MILLIKAN’s OIL DROP EXPERIMENT
The Objective
The aim of the experiment is to measure the electrical charge on small drops of
oil and to see if these charges are integral multiples of a fundamental amount.
Historically, Robert Millikan (and his student Harvey Fletcher) determined the
magnitude of the quantum of charge using this technique (1909-1913). Millikan
received the Nobel Prize for his work determining e and h in 1923.
Apparatus
Oil drops are injected from an "atomiser" into a draught-free region between two horizontal plates. A
reversible and variable potential difference can be applied between these plates. A microscope is used to
view the oil drops which are illuminated via a light pipe.
Theoretical Background
A spherical drop of radius r and density ρ falling through a fluid of density σ and viscosity η will
reach a terminal velocity u. This will occur when the gravitational force is balanced by the viscous drag,
given by Stokes' law, resulting in the following expression:
4 3
πr ( ρ − σ ) g = 6πrηu
3
(1)
where (ρ - σ) = 935 kgm-3, η ≈ 1.836 x10-5 Nsm-2. Since the oil drops in this experiment are tiny, the
terminal velocity is attained in a very short distance. If u is measured, given that ρ, σ, η and g are known
then the radius of the drop is given by:
r=
9ηu
2( ρ − σ ) g
(2)
A charged drop can be brought to rest in an electric field E when the gravitational force is balanced
by the electrostatic force:
4 3
πr ( ρ − σ ) g = qE
3
(3)
where q is the charge of the oil drop. Combining equations (1) and (3), so that the drop size r is eliminated,
enables q to be determined in terms of the measurable and known quantities:
6π
q=
E
⎛ 9η 3 u 3 ⎞
⎜
⎟
⎜ 2( ρ − σ ) g ⎟
⎝
⎠
1/ 2
(4)
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The electric field is simply given by E = V/d where V is the potential difference between the two plates,
which are separated by d.
Unfortunately, the very small oil drops have sizes that are comparable with the density fluctuations in
the air. This causes Stokes' law, on which equation (1) is based, to fail. However, Millikan found the
following empirical correction made his results more self consistent:
q corr =
q
b ⎞
⎛
⎜1 + ⎟
⎝ rP ⎠
(5)
3/ 2
where b = 6.18 x 10-8 m2, P is the air pressure, in metres of mercury, and r - the radius of the oil drop - is
obtained from equation (2).
Experimental Method
1)
The apparatus contains one high voltage power supply unit (PSU) and a low voltage supply for the
light. Connect wires from the control switch system (CSS) to the plates and to the voltmeter before
connecting to the PSU.
WARNING HIGH VOLTAGE: Before dismantling the cell, ensure that the
three-way switch of the CSS is in the CENTRE (OFF) position.
2)
Take off the plastic lid and the top plate. Remove any oil from the plates with a tissue and use a wire
to clean the injection hole. Ensure that the plates are horizontal with a spirit level.
3)
Calibrate the microscope graticule by focusing the microscope on a millimetre scale in the centre of
the cell; use the lamp to provide the necessary light. Ensure that the graticule in the eyepiece is arranged so
that you observe the scale with a ‘relaxed’ eye. (If you are not sure how to achieve this, speak with your
TA). Reassemble the cell and focus on a fine wire pushed through the injection hole. Replace the plastic lid
and arrange the apparatus to face the wall, so that you are not distracted by stray light.
4) Record the air pressure for Windsor from http://www.theweathernetwork.com. Calculate the viscosity of
air for the day’s room temperature using: http://www.lmnoeng.com/Flow/GasViscosity.htm. Repeat both
measurements at the end of the day, and find the average pressure and viscosity for the duration of the
experiment.
5)
With the voltage reversing switch still in the central (off) position, inject some oil drops into the cell
by sharply squeezing the atomiser. The image through the microscope is inverted, therefore look for drops
falling upwards under gravity†. Operate the controls of the CSS and bring to rest a suitable oil drop. Whilst
still viewing the drop and without adjusting the voltage, turn the three-way switch to its central (off)
position. Allow a short time for the droplet to reach terminal velocity. Use a stopwatch to time the drop's
traversal of a number of graticule spacings under gravity. Record the potential difference between the
plates, noting the sign of the voltage. (Choose drops that are not moving too fast, nor too slow! Voltage =
100-200V, Time = 30-40 seconds for two graticule spacings is optimal†.) First: Repeat this procedure for
the same drop. This will (or should) help give a more accurate result for that particular drop – assuming
that it (a) does not evaporate (i.e. the mass and radius are constant, which is reasonable given the vapour
pressure of silicone oils) and (b) does not change its charge. This latter effect can sometimes occur and the
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drop is seem to accelerate/decelerate suddenly for no apparent reason. If this occurs while taking a
measurement it will obviously invalidate the result. Secondly, Repeat this procedure many times for many
different drops endeavouring to get a range of stopping potentials and times. A correctly adjusted eyepiece,
blackout conditions, patience and concentration are vital! If necessary, re-clean the plates and unblock the
injection hole ensuring that the three-way switch is in the "off" position.
Analysis
Forget anything you may know about the size of the charge on an electron! The aim of the
experiment is to discover (a) that charge is discrete, rather than continuous, and (b) determine the discrete
magnitude or quantum for charge.
Using Excel (or another software package) create a worksheet for the data. Determine the (a) radius,
(b) velocity, and (c) charge for each drop using equations (2) and (4). See the effect of equation (5) on your
values of q. Assuming the charge is quantised, the droplet’s charge can only be in units of nq0, where n is
an integer and q0 is the quantum of charge. Assuming the smallest difference between two different qcoor
values is 1q0, see if the differences between all your charge values can be shown to be in integer
multiples of 1q0. If this proves inconsistent, perhaps the smallest difference between two different qcoor
values is actually 2q0, (or some other integer multiple). Re-analyze your results until they are self
consistent – within experimental uncertainty.
Using propagation of errors formulae, or better fractional error analysis for products and
quotients, find the experimental uncertainty q0 for each droplet. Show them graphically.
Combine your results to determine the best value of fundamental unit of charge and its uncertainty.
How does this compare with the accepted value of 1.6022x10-19C? Discuss any differences and comment
on any possible sources of error.
†
Choosing suitable drops: Using the atomiser provided, droplets are sprayed into the settlement
chamber the top of which can be rotated off to give access. The droplets drift down, through the hole
on the top plate, into the space between the plates.
WARNING: direct only a very short burst from the atomiser into the settlement chamber. If you
produce too many they will swamp the field of view and make it difficult to pick out one to observe. In
the spray of droplets produced by the atomiser are a few which are charged by a friction process and
which respond when the voltage is switched on. You will find that there are few of these in the first
droplets which come into view, indeed most of the initial burst are so large that they fall far too quickly
to measure. Wait for these to clear. Obviously charged droplets are more numerous amongst the small
droplets which arrive later so be patient, you could wait several minutes before finding charged drops.
The short burst from the atomizer will produce a continuous stream of falling droplets which lasts for a
couple of hours.
Warning: The falling droplets are particularly sensitive to vibrations conducted via the optical
bench. Make sure that you do not knock or even tap the optical bench or components on it. If you do
so the drops will be dispersed and lost from view.
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