# Finding the voltage of an oil droplet, Millikan's experiment

• bobsmith76
In summary, the conversation discusses the calculation of the potential difference applied across horizontal plates in the Millikan experiment, using the density and radius of the oil droplets. The steps involve finding the mass of the droplet, determining the charge, and plugging the numbers into the equation V = mgd/q to arrive at the correct answer. The conversation also clarifies the calculation of the volume of a droplet from its radius.
bobsmith76

## Homework Statement

The density of the oil used to form droplets in the Millikan experiment is 9.20 × 102 kg/m3 and the radius of a typical oil droplet is 2.00 μm. When the horizontal plates are placed 18.0 mm apart, an oil drop, later determined to have an excess of three electrons, is held in equilibrium. What potential difference must have been applied across the plates?

## Homework Equations

V = (4/3)(3.14)r^3

q = (mgd)/V

where q = charge
V = voltage

## The Attempt at a Solution

step 1. find the mass of the droplet.

4/3(3.14)(2*10^-6)

step 2
then multiply that by the viscosity which is 92 kg/m^3 which is .007

step 3
get V by itself

V = mgd/q

step 4
find the charge (q)

1.6 * 10^-19 * 3 = 4.8*10^-19

step 5
plug the numbers into the above equation

.007(9.8)(.018)/(4.8*10^-19)

the correct answer is 1.3 * 10^4, my answer is way off

How do you calculate the volume of a droplet from the radius?

ehild

you have forgotten r^3
Sorry ehild... did not see your post in time

Last edited:
Good, now I got it. Thanks for your help.

, what did I do wrong?

I appreciate your attempt at finding the voltage in Millikan's experiment. However, there are a few errors in your calculations that may have resulted in your answer being significantly different from the correct answer.

Firstly, in step 2, you multiplied the mass of the droplet by the density of the oil, but it should have been divided instead. This is because the equation for charge (q) involves dividing the mass by the volume of the droplet, not multiplying.

Secondly, in step 4, you calculated the charge (q) by multiplying the elementary charge (1.6 * 10^-19) by 3, which is incorrect. The number of excess electrons in the droplet should have been divided by the elementary charge, not multiplied.

Lastly, in step 5, you used the incorrect value for the distance between the plates. The correct value is 18 mm, which should be converted to meters (0.018 m) before being used in the equation.

By correcting these errors and following the correct equations, you should be able to arrive at the correct answer of 1.3 * 10^4 V.

## 1. How did Millikan's experiment determine the voltage of an oil droplet?

Millikan's experiment involved suspending an oil droplet in an electric field and adjusting the voltage until the droplet was stationary. By measuring the voltage needed to balance the gravitational force on the droplet, the charge of the droplet could be calculated using the known mass of the droplet.

## 2. What materials were used in Millikan's experiment?

Millikan's experiment used a glass chamber filled with air, a microscope to observe the oil droplets, and an atomizer to create the droplets from oil. The electric field was created using charged plates and the voltage was measured using a sensitive electrometer.

## 3. Why was Millikan's experiment significant?

Millikan's experiment was significant because it provided the first accurate measurement of the charge of a single electron. This helped to confirm the existence of subatomic particles and contributed to the development of quantum mechanics.

## 4. What were the limitations of Millikan's experiment?

One limitation of Millikan's experiment was that it required the oil droplets to have a specific charge, which limited the range of droplets that could be used. Additionally, the experiment was difficult to replicate and required careful calibration of equipment.

## 5. How did Millikan's experiment impact the field of science?

Millikan's experiment had a significant impact on the field of science by providing evidence for the existence of subatomic particles and laying the foundation for the development of quantum mechanics. It also helped to establish the concept of quantization of charge, which has important implications for understanding the behavior of matter at a microscopic level.

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