In a Millikan oil-drop experiment, the charges on several different oil drops were as follows: - 5.92; - 4.44; - 2.96; - 8.88. The units are arbitrary. What is the likely value of the electronic charge in these arbitrary units? For more background on the Millikan oil-drop experiment, refer to section 2.4 in your textbook.

In this hypothetical experiment we found that the fundamental electronic charge is - 1.48

Explanation:

Millikan's experiment aims to find the charges of different drops of oil, and to check in all the charges their entire multiples of a minimum elementary charge.

Q = n q

With Q the charge of the drop, n an integer (1, 2.3 ...), q the minimum elementary charge

We can try this hypothesis is easily dividing all the charges go the smallest

-4.44 = n (-2.96) ⇒ n = 1.5

This value is not an integer, so the equation is not fulfilled, which implies that the elementary charge must be smaller than the minimum measured value, suppose then the minimum measured value is a multiple of the elementary charge, let's test with the smallest n = 2; in this case we have

-296 = 2 q ⇒ q = - 296 / 2 = 1.48

To believe this, let's check that all charges have an integer multiple of this value

(-4.44) = n (-1.48)

n = 3

We create a table with all the charges to test this possible elementary charge

Q n

-8.88 6

-5.92 4

-4.44 3

-2.96 2

In this hypothetical experiment we found that the fundamental electronic charge is - 1.48

In the Millikan's actual experiment, the elementary charge found was 1.6, it differs by less than 8% from that found in this hypothetical experiment.