Suppose a scientist repeats the Millikan oil-drop experiment but reports the charges on the drops using an unusual (and imaginary) unit called the warmomb (wa). The scientist obtains the following data for four of the drops: Droplet Calculated Charge (wa) A 3.84⨉10⁻⁸ B 4.80⨉10⁻⁸ C 2.88⨉10⁻⁸ D 8.64⨉10⁻⁸ (b) From these data, what is the best choice for the charge of the electron in warmombs?

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Welcome back everyone. A scientist in a parallel universe performs the Millikan oil drop experiment. The unit charge in that universe is Gaelic G. A. He obtained the following data for the four oil droplets A through D. Based on these observations, determine the charge on a single electron in or Gaelic units. So we're going to begin by recognizing that the charge for oil drop A is our smallest in magnitude. And so because we have this at the smallest charge, we can compare oil drop A. Two or in a ratio with oil drops B through D. And so we can go ahead and take first the ratio between oil drop B two A. So we're going to divide by we're going to divide the unit charge of oil drop B 2.75 times 10 to the negative 11th Gaelic. And we're going to divide by two point oh six times 10 to the negative 11th Gaelic. For the charge of oil drop A. This is going to yield a ratio equal to 1.33. Now moving on to oil drop C. Which has a unit charge of 4.13 times 10 to the negative 11 power Gaelic, looking at it in a ratio with oil drop A. We will divide by two point oh six times to the negative 11 power Gaelic. The charge for oil drop A. And we get a ratio equal to a value of two point oh And then moving on to oil drop D. We have a unit charge of 5.50 times 10 to the negative 11th power Gaelic. Now dividing this out by the unit charge of oil drop a. We have two point oh six times 10 to the negative 11 power Gaelic which yields a ratio of value being 2.67. And then dividing the charge of will drop a by itself two point oh six times 10 to the negative 11th Gaelic. We get of course the value one. So recognize that these ratios at least three of them are decimals and we need them to be whole numbers. So recognize that we compared the smallest charge for oil drop a two or three other oil drops. And so we can go ahead and multiply each of these ratios by a factor of three, meaning we would still need to multiply the ratio for world drop A by three. So that gives us a total of 34 oil drop A which would represent the three electrons that make up this unit charge of oil drop a. Moving on to will drop be we would get a total or a value equal to four, which would represent four electrons that make up the unit charge of oil drop B. Then for oil dropsy, we, when we multiply by three, we get a total of six electrons which make up the unit charge of oil drop C. And lastly for oil drop D. When we multiply the ratio by three, we get a whole number equal to eight which represents eight electrons that make up the unit charge of oil dropsy. And so recognize that. We can say that based on these whole numbers which determined the number of electrons for each of our old drops, we can say that the Charge of one electron Is going to be 1/3 of will drop a charge. And so we can go ahead and take oil drops. Sorry, oil drops a charge two point oh six times 10 to the negative 11th power Gaelic and divide it by three, which would give us the charge of a single electron equal to 6. times 10 to the negative 12 power Gaelic. Again, the charge of a single electron. And so here we can say that we have determined our answer the charge of a single electron. But we want to verify that this is correct. So what we can do is confirm that by dividing the charge of a single electron by each of our unit charges of oil drops A through D. So beginning with the check for oil drop A We have again it's unit charge given in the prompt as two point oh six times 10 to the negative 11 power Gaelic, dividing by the charge of a single electron 6.87 times 10 to the negative 12 power Gaelic. We would get a result equal to three which again represents the three electrons that we have making up the charge of our oil drop A. Now moving on to oil drop B. We have its unit charge given in the prompt as 2.75 times 10 to the negative 11th power Gaelic, dividing this by the charge of a single electron 6. times 10 to the negative 12 power Gaelic. We get a result equal to four which represent the four electrons which make up the unit charge of oil drop B. Then for oil drops. See we have again, it's given unit charge 4.13 times 10 to the negative 11 power Gaelic divided by the charge of a single electron 6.87 times 10 to the negative power Gaelic. We yield a value of six which represents six electrons that make up the unit charge of oil drop C. So that checks out. And lastly we have for oil drop D. It's given unit charge of 5.50 times 10 to the negative 11 power Gaelic, dividing this again by the charge of a single electron 6.87 times 10 to the negative 12 power Gaelic. We yield a result of eight which represents the eight electrons that make up the unit charge of oil drop D. So everything checks out and we can confirm that we have the correct answer as the charge on a single electron in units of Gaelic. So our final answer highlighted in yellow corresponds to choice be in the multiple choice. I hope that everything I reviewed was clear. If you have any questions, leave them below and I'll see everyone in the next practice video.

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Key Concepts

Millikan Oil-Drop Experiment

Quantization of Charge

Unit Conversion