Apparatus Controls
Squeeze the atomizer to spray drops, then work the plates and the ionization source. The focus and the stopwatch are beside the eyepiece once you look into it.
Apparatus View
3D cutaway of Millikan's oil drop apparatus
A model of Millikan's apparatus with a quarter of the iron chamber cut away. Inside, near the bottom, two brass plates 14.92 mm apart are separated by a glass ring; the top plate has a pinhole at its centre. An atomizer on a pillar at the left sprays oil through a port near the top of the chamber, and the drops drift down to the top plate and through the pinhole into the gap. The viewing scope, on its stand at the front left, looks into the gap through a window port and has its eyepiece turned up at 45 degrees; the arc lamp lights the gap through a port on the right; the alpha source sits in the front port. Leads from the right of the chamber run to the plate voltage supply on the bench, which has a voltmeter, a counter showing the voltage, Raise and Lower buttons, a knob and a knife switch. A magnified view of the gap in the top right corner shows the drops, the field arrows when the plates are charged, and the alpha tracks when the source is exposed. The bulb, the knife switch, Raise and Lower, the source lever and the eyepiece can be clicked to work them. The clock, the number of drops in view and the tracked drop's position are in the caption below the view.
Scope Focus
Up to 1 mm nearer to you or farther away than the centre of the gap; drops in the focal plane are sharp points, the rest are blurred
Stopwatch and Recording
0.00 s
With this on, the page notes the moment the tracked drop crosses each long reticle line and records a measurement each time it has moved the Distance timed chosen above. A freshly sprayed drop is left alone until the puff of air that carried it in has died away.
In the cutaway you can work the apparatus directly: click the atomizer bulb to spray, the knife switch on the supply to turn the field on or off, Raise and Lower beside the voltmeter to change the voltage (hold to keep going), the lever on the α source to expose or shield it, and the eyepiece to look into it. Drag to turn the model, or focus it and use the arrow keys; hold Ctrl and scroll (or pinch) to zoom, or press + and −; Whole Apparatus and Chamber jump between views; Cutaway puts the missing quarter of the chamber back. The magnified view at the top right shows the gap between the plates. The controls above do the same from the keyboard. In either view, click a drop to track it, or use the Previous Drop and Next Drop buttons; the tracked drop is ringed in both views. The scope shows an upright image: drops that fall move down.
Key to the apparatus model
- Orange dot: oil drop, hundreds of times life size in the magnified view
- Pale rubber bulb: atomizer, click to spray
- Thick blue ring: tracked drop
- Fading violet ring: charge just changed
- Brass discs: plates, + top and − bottom, 14.92 mm apart
- Blue arrows E: electric field, when on
- Dashed circle: 3 mm field of view
- Pale streaks: alpha particles, source on
- Red lead: + to the top plate; dark lead: − to the bottom plate
- Reticle: lines 0.5 mm apart, ticks 0.1 mm
Measurements
Every field-on row needs a field-off fall for the same drop before its charge can be worked out. To work through the calculation yourself, put a drop's numbers into the Charge Calculation panel below.
| Drop | Field | Motion | Distance (mm) | Time (s) | Speed ± scatter (mm/s) | |q| ± scatter (10−19 C) | How | Remove |
|---|
No measurements yet. Look into the eyepiece, track a drop, and let it cross the reticle lines.
The ± is one standard deviation of the scatter that Brownian motion puts into a timing over that distance; a longer Distance timed shrinks it, and so does averaging several falls of the same drop.
Drop Properties
From each drop's timed falls: the fall speed sets its radius through Stokes' law, and the radius and the oil's density give its mass. The ± is the Brownian scatter of the mean fall speed, smaller the more falls are averaged.
| Drop | Falls timed | Fall speed ± scatter (mm/s) | Radius (µm) | Mass (10−15 kg) | Charges |
|---|
No drop has been timed falling yet.
Charge Calculation
Type the numbers from one drop's rows in the Measurements table: a fall with the plates shorted and a run with the field on. Then work through the steps below. Each gives its formula and a worksheet line to put your numbers into, and checks your result against those measurements, down to the drop's charge in coulombs.
- Fall speed
- Radius, from Stokes' law with the slip correction
- Mass, from the oil's density
- Velocity with the field on
- Electric field between the plates
- Charge, from the force balance
Charge Analysis
If charge comes in a smallest unit, every drop's charge is a whole number of units. Slide the trial unit until the charges line up with its multiples, or let the page search.
0.80 to 4.00 × 10⁻¹⁹ C. The dashed lines on the chart sit at its multiples
On, a drop timed more than once with the field on, with no exposure to the source in between, counts as one charge: the mean of those runs, with the scatter of the mean
- Filled blue dot: one measured charge (stacked when two coincide)
- Bar through a dot: one standard deviation each way, the scatter expected from Brownian motion
- Dashed lines: multiples of the trial unit, numbered
- Hollow orange ring: the true charge of that drop (instructor check)
Show the Charges as a Table
| Drop | |q| (10−19 C) | ± scatter (10−19 C) | Sign | Multiple n | |q| ÷ n (10−19 C) | Off by (units) | True n |
|---|
About the Model
The experiment
Robert Millikan (1909 to 1913) sprayed oil into the gap between two horizontal metal plates, watched single drops through a scope, and timed them. With the plates shorted a drop falls at a steady speed set by its weight and by the air's drag; with a voltage across the plates a charged drop is pushed up (or down) as well, and moves at a different steady speed. From the two speeds the drop's radius, mass and charge follow. Charging the drops again with ionizing radiation, Millikan found the charge always changed by a whole number of one unit.
Working the apparatus
- Spray Oil Drops, or click the atomizer bulb in the cutaway. The bulb blows a mist from the nozzle into the space above the top plate, and the puff of air carries the drops through the hole in the plate into the gap; the rest land on the plate. Look into the eyepiece and pick one that falls slowly (a small drop) and is sharp at the current focus.
- Track it by clicking it, or with the Previous Drop and Next Drop buttons. Keep the source off while timing.
- Time its fall with the plates shorted, across a known number of long reticle lines (0.5 mm apart). The Drop Properties panel then shows its radius and mass.
- Switch the plate voltage on. The top plate is positive and the bottom plate negative, so a negatively charged drop (most of them) rises; time its rise. A positively charged drop falls faster instead, and its charge follows just the same. Time a fall and a rise more than once if you can.
- Change its charge. Expose the ionization source for a few seconds, then time the rise again. A violet ring spreads from a drop at the moment it captures an ion; with the field on you then see it rise or fall at a new speed, and with the field off nothing else changes until the field goes on, because a drop's fall does not depend on its charge. Repeat for several charges on the same drop, and for several drops.
- Search for Unit of Charge. All the charges should be whole-number multiples of one value.
Reset Experiment clears the drops, the clock and every measurement and puts the controls back to their starting values, leaving the view as it is; it asks first when there are measurements to lose.
The calculation
A drop of radius r and effective density ρ (oil less air) falling at speed vf has its weight balanced by Stokes drag, corrected for the fact that such small drops slip between the air molecules:
(4⁄3) π r³ ρ g = 6 π η r vf ÷ (1 + b ⁄ (p r))
which gives the radius from the fall speed, and the mass as m = (4⁄3) π r³ ρ. With the field E = V ⁄ d on and the drop moving at velocity v (up positive), the electric force makes up the difference, so that the charge is
|q| = m g (1 + v ⁄ vf) d ⁄ V
For a drop that rises at speed vr this is the familiar form (vf + vr) ⁄ vf; a drop that still falls with the field on, only more slowly, gives a charge the same way with v negative. Because the field always points down, a drop that falls faster with the field on than off is positively charged, and the table says so.
Constants used: g = 9.80 m/s², ρ = 886 − 1.2 kg/m³, d = 14.92 mm (the gap in Millikan's 1913 condenser), b = 8.20 × 10⁻³ Pa·m, p = 1.013 × 10⁵ Pa, and the viscosity of air at the chamber's 22.0 °C, η = 1.82 × 10⁻⁵ Pa·s. The Charge Calculation panel works through these steps with numbers you type in from the Measurements table, so the same arithmetic the page does for every row can be followed by hand.
Finding the unit
The page works out |q| for every timed run with the field on, using the mean fall speed of the same drop. Search for Unit of Charge scans trial values from 4 × 10⁻¹⁹ C downward and takes the largest one whose multiples fit the charges about as well as any unit does (a local minimum of the root-mean-square deviation, within 2.5 times the best), then refines it by least squares and slides the trial unit to it. With only one or two charges almost anything fits: the search needs several drops, or one drop at several charges, and small charges (a few units) are far more useful than large ones, whose errors swamp the steps. With the instructor check on, the search uses the true charges of the measured drops instead of the measured values, which shows what the method gives with perfect timings. The accepted value is e = 1.602 × 10⁻¹⁹ C.
What the simulation does
- Each drop has a radius between about 0.35 and 1.3 µm, a charge of a few elementary units (three quarters of them negative), and moves at its terminal velocity, recomputed every frame. A fresh drop rides the puff of air from the bulb: swept toward the 0.8 mm hole in the top plate, through it, and a few millimetres down into the gap before the stream dies away.
- Drops jitter with Brownian motion of the right size for their radius and the air temperature, which is why repeated timings of the same drop differ slightly, and why very small drops are hard to time.
- With the source on, each drop captures an air ion about every two seconds, changing its charge by one unit (sometimes two) of either sign. With the source off, a drop's charge never changes.
- A slow convection current drifts the drops sideways; drops that reach a plate or drift out of the chamber are lost.
- The scope has a shallow depth of field: only drops near the focal plane are sharp. It shows an upright image; some real scopes invert it.
- The cutaway is a 3D model of Millikan's apparatus, after the original at Caltech, with a quarter of the chamber cut away. The chamber, scope, lamp and atomizer are at about their true size, and the plates are 14.92 mm apart, as in Millikan's 1913 condenser. At that scale a drop is far too small to see, so the magnified view of the gap draws the drops hundreds of times larger than life. The eyepiece shows the drops at their true relative positions, each as the point of light a real drop scatters.
- The clock, the stopwatch and the automatic timer all run on simulated time, so the Speed setting changes nothing but your waiting.
- The automatic timer works while you look through the eyepiece. It notes the moment the tracked drop crosses each long reticle line and records a measurement each time the drop has covered the Distance timed set beside the stopwatch, in one direction under one field setting; a shorter stretch, cut off by a change of field, a change of direction or the drop leaving the view, is not recorded, and timing pauses while the source is on.
Keyboard
Tab moves between controls; arrow keys move the sliders. Previous Drop and Next Drop track drops without the mouse, and every reading is in the Now list and the tables. Escape closes the chart's tooltip. Alt + Shift + P (Option + Shift + P on a Mac) switches presentation mode on and off, and Escape leaves it.