chemistry question:?

Question

In a hypothetical universe, an oil-drop experiment gave the following measurements of charges on oil drops: -3.48×10-19 C, -4.64×10-19 C, -8.12×10-19 C, and -9.28×10-19 C. Assume that the smallest difference in charge equals the unit of negative charge in this universe. What is the value of this unit of charge?

Answer 1

You're finding the unit of charge, which may be determined as the smallest difference between your 4 numbers.

Step 1.) Eyeball the numbers and cull numbers with a difference of less than 2 * 10^-19.
The only two sets of numbers that meet the criteria are:

-3.48×10-19 C, -4.64×10-19 C
-8.12×10-19 C, -9.28×10-19 C

Step 2: Find the differences in the sets above.
1.) -1.16 * 10^-19
2.) -1.16 * 10^-19

They are the same, therefore they are the smallest difference, and they are the unit of negative charge.

Check:
Since one cannot have a change in charge that is not a multiple of this unit, compare the difference between 2 other values:

Let's pick:
4.64×10-19 C - -8.12×10-19 C = 3.48 * 10^-19
3.48 * 10^-19 / 1.16 * 10^-19 = 3 (check!)