In an alternate universe, the smallest negative charged particle, analogous to our electron, is called a blorvek. To determine the charge on a single blorvek, an experiment like Millikan's with a charge oil droplets was carried out and the following results were recorded:

Droplet Number Charge (C)

1 7.74 * 10^-16

2 4.42 * 10^-16

3 2.21 * 10 ^-16

4 4.98 * 10 ^-16

5 6.64 * 10^-16

a) Based on these observations, what is the largest possible value for the charge on a blorvek?

b) Further experiment found a droplet with a charge of 5.81 * 10^-16 C does this new result charge our part answer to part (a) ? If so, what is the new largest value for the blorvek's charge?

The charge of a blorvek has to be a number that divides exactly all the charges found, and the largest possible charge on a blorvek is the largest number that divides the five charges found for the drops. When you divide 4.42, and 2.21 you get whole numbers (2 and 1). But 2.21 does not divide exactly 7.74 and 4.98. You can find that 0.5525 is the largest number that divides the five numbers: 7.74 / 0.5525 = 14, 4.42 / 0.5525 = 8, 2.21 / 0.5525 = 4, 4.98 / 0.5525 = 12. So, the answer is 0.5525 * 10 ^ - 16 C or 5.525 * 10^ - 17 C. For the part b) you find that 5.81 / 0.5525 = 10.5, so this charge means that the charge value in the first part is not valid anymore. If you divide 0.5525 by 2 you will find the new largest value: 0.5525 / 2 = 0.27625. You can check that 5.81 / 0.27625 = 21. And the new largest value is 2.7625 * 10^ - 17 C.