Millikan's Oil Drop Experiment
Payton Price - Southern Methodist University Physics 3305 - Fondren Science 151 November 29, 2016 Outline
I. Who Robert A. Millikan was
II. How the Oil Drop Experiment was setup
III. The measurements taken during the experiment
IV. Millikan's results
V. Modern manifestations of the Oil Drop Experiment
Payton Price – Phys3305 11/29/16 1 Robert A. Millikan • Bachelor's in Classical Studies from Oberlin College (1891)
• Doctorate in Physics from University of Columbia (1895)
• Received the Nobel Prize in Physics 1923 • What motivated this experiment?
Payton Price – Phys3305 11/29/16 2 The Apparatus
Payton Price – Phys3305 11/29/16 3 An Abstract 1. Atomizer sprays oil droplets
2. An oil droplet falls through charged plate reaching terminal velocity
3. The oil droplet becomes ionized
4. Forces equalize and give a result
Payton Price – Phys3305 11/29/16 4 (+)
2
1
(-)
Forces on the oil drop: Initial downward motion 1. Gravitational Force 2. Drag force of the oil drop in the air
Payton Price – Phys3305 11/29/16 5 (+) 3
2 1
(-)
Forces on the oil drop: Rising Motion 1. Gravitational Force 2. Drag force of the oil drop in the air 3. Electric Force on oil drops with charge q
Payton Price – Phys3305 11/29/16 6 • Equation of motion: • m(dv/dt) = mg – bv Balancing Forces- Downward Motion • Solve Equation for Terminal Velocity (1) Gravitational Force: mg • Why? m – Mass of Droplet g - gravity
• = (2) Drag Force: bv (Stokes Law: b = 6πµr) • - Terminal velocity for downward motion µ - Viscosity Coefficient r - Radius of the drop
Payton Price – Phys3305 11/29/16 7 • Equation of Motion: • m(dv/dt) = qE – mg – bv Balancing Forces - Rising Motion • Solve Equation for Terminal Velocity • = E (1) Gravitation Force: mg • - Terminal velocity for rising motion (2) Drag Force: bv
(3) Electric Force: qE q – Charge of droplet • Now we're able to begin solving for q E – The applied electric field
Payton Price – Phys3305 11/29/16 8 • Substituting Vf into the Vr Equation and solving for q,
• q = Solving For q • As vf and vr are constant velocities, we can use L = vT • . • L – The measured distance, where the droplet is moving at a constant vf or vr • T – Time taken for the rise or fall of a distance L
• . • Thus, • vf = (1/Tf) and vr = (1/Tr)
• Substituting into the equation for q,
• q =
Payton Price – Phys3305 11/29/16 9 • Through ionization from x-ray, additional charge is acquired changing the rising terminal velocity, v'r • The charge becomes q', giving a new equation:
Solving For q - • . Ionization • Subtracting q from q' gives an equation for the change in charge: • . • q' - q = • Define q = ne ~ n – number of charges • Substituting in q' = n'e and rearranging we get, ~ e – The Fundamental charge
• Rearranging we get; • Now we're able to manually solve for n and n', we only need Time Payton Price – Phys3305 11/29/16 10 Measuring For Time
Stop rise time measurement Begin fall time measurement
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L – The fall / rise distance
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Stop fall time measurement Begin rise time measurement Payton Price – Phys3305 11/29/16 11 Finding the Fundamental Charge e
• Knowing the mass m, rise and fall time, and number of charges we are now able to solve for e
• Millikan's value of e: 1.591 * 10^-19 C
• Today's accepted value of e: 1.60217733 * 10^-19 C
• Why the discrepancy?
• Implications for particle physics
Payton Price – Phys3305 11/29/16 12 Sources "Stokes' Law." Wikipedia. Wikimedia Foundation, n.d. Web. 5 Nov. 2016. https://en.wikipedia.org/wiki/Stokes'_law
"Robert A. Millikan." Robert A. Millikan - Engineering and Technology History Wiki. N.p., 24 Feb. 2016. Web. 31 Oct. 2016. http://ethw.org/Robert_A._Millikan
"The electron and the light-quant from the experimental point of view." Nobel Prize Lecture, Nobel Prize. Web. 31 Oct. 2016. http://www.nobelprize.org/nobel_prizes/physics/laureates/1923/millikan-lecture.pdf
"Millikan's Oil-Drop Experiment." WFU Physics. Wake Forest University. Web. 6 Nov. 2016. http://physics.wfu.edu/lectures/phy215/CourseMaterials/MillikanOilDropExperiment.pdf
Payton Price – Phys3305 11/29/16 13