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

[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

 

[ehild]

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

ehild

 

[technician]

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

 

[bobsmith76]

Good, now I got it. Thanks for your help.

 

[asteriatic]

, 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.