# Millikan Oil Drop Experiment Question

• Kennedy111
In summary, a 1.50 x 10^-14 kg oil drop with a downward acceleration of 1.80 m/s^2 between two horizontal plates with a potential difference of 980 V has a magnitude of charge of approximately -1.15 x 10^-17 C, which corresponds to approximately 72 electrons. This value may not be exact due to experimental uncertainty.
Kennedy111

## Homework Statement

A 1.50 x 10^-14 kg oil drop accelerates downward at a rate of 1.80 m/s^2 when placed between two horizontal plates that are 9.40 ch apart. The potential difference between the two plates is 980 V. Determine the magnitude of the charge on the oil drop.

m = 1.50 x 10^-14 kg
a = 1.80 m/s^2 (down)
d = 9.40 cm = 9.40 x 10^-2 m
V = 980 V

Fnet = Fg + Fe
Fnet = ma
Fe = Eq
Fg = mg
E = V/d

## The Attempt at a Solution

Fnet = Fg + Fe
Fe = Fnet - Fg
= ma - mg
= ((1.50 x 10^-14 kg)*1.80 m/s^2)) - ((1.50 x 10^-14 kg)(9.81 m/s^2))
= -1.2015 x 10^-13 N

E = V/d
= (980 V) / (9.40 x 10^-2 m)
= 10425.53191 V/m

Fe = Eq
q = Fe / E
= (-1.2015 x 10^-13 N) / (10425.53191 V/m)
= -1.1524592 x 10^-17 C

The charge on the oil drop is approx. -1.15 x 10^-17 C ?

Looks ok to me. Does the charge correspond to an integer number of electrons on the drop?

{Accurate analysis of the Millikan Oil Drop Experiment would take into account the viscosity of the air and the buoyant force acting on the drop, and involves measuring terminal velocities rather than accelerations. See http://en.wikipedia.org/wiki/Oil_drop_experiment . But what you did looks correct based on the information given.}

If I divide that charge by 1.60 x 10^-19 C I get 72.0207 electrons. Does it have to be a whole number?

Kennedy111 said:
Does it have to be a whole number?

Yes! At least if the data is good! That's one reason the experiment is considered a classic. Millikan found the net charge of the drops to be "quantized" as integer multiples of a fundamental amount of charge e. 72.02 is close to an integer. The discrepancy can be chalked up as "experimental uncertainty in the data".

[EDIT: Millikan reported net charges on the drops ranging from 1*e to 136*e. See http://www.aip.org/history/gap/PDF/millikan.pdf ]

Last edited:
Okay, I understand! Thank you for your help!

## 1. What is the Millikan Oil Drop Experiment?

The Millikan Oil Drop Experiment is an experiment conducted by Robert Millikan in 1909 to determine the charge of an electron. It involved observing the motion of oil droplets in an electric field and using mathematical calculations to determine the charge on each droplet.

## 2. How does the Millikan Oil Drop Experiment work?

The experiment involved suspending oil droplets in a chamber and observing their motion under the influence of an electric field. By adjusting the strength of the electric field, the droplets could be made to either rise or fall. By measuring the rate of motion and the strength of the electric field, the charge on each droplet could be calculated.

## 3. What was the significance of the Millikan Oil Drop Experiment?

The Millikan Oil Drop Experiment provided the first direct measurement of the charge of an electron, which was previously only known through theoretical calculations. It also helped to confirm the quantization of electric charge, providing important evidence for the development of quantum mechanics.

## 4. What were the challenges faced during the Millikan Oil Drop Experiment?

The experiment required precise measurements and control of the electric field, as well as careful observation of the motion of the oil droplets. The oil droplets also tended to evaporate or collect impurities, which could affect the results. Additionally, the calculations involved were complex and time-consuming.

## 5. How did the results of the Millikan Oil Drop Experiment contribute to our understanding of electrons?

The experiment provided the first accurate measurement of the charge of an electron, which helped to refine our understanding of the structure of atoms and the behavior of electrons. It also provided evidence for the quantization of charge and paved the way for further research on the nature of subatomic particles.

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