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Measuring the Elementary Charge Purpose To determine the elementary charge through analogy and experimental data. Discussion Millikan’s Oil Drop experiment provided evidence that charge was quantized (came in discrete amounts) and was used to determine the charge on an individual electron (sometimes called the elementary charge or e ). Millikan’s experiment was relatively simple to understand, but fiendishly difficult to perform. Oil drops were sprayed into a vacuum. By illuminating the drops with x-rays, the oil drops became charged. A set of parallel plates was used to create a constant electric field that opposed the force of gravity and suspended the oil drops. Inside of the electric field, the force of gravity is equal to the electric force. For an oil drop of mass m, with charge q, suspended between plates with separation d and potential difference ΔV, The charge on the oil drop is given by, (Eq. 1) Materials Film canisters with an unknown number of coins Procedure 1. Measure the mass of each film canister without looking inside or trying to count the number of objects. (You will be given an empty canister; use it to tare your scale.) 2. Design a procedure for predicting the mass of an individual coin contained inside a film canister. Adapted from: Hirsch, Alan, et al. “Nelson Physics 12”, Thomas Nelson, 2003.

Step 1: Measure the mass of each canister, including the empty canister. Step 2: Subtract each canister by the mass of the empty canister. Number each canister from greatest to least weight. Step 3: Assume there are anywhere from 2-4 coins in each canister by shaking it. Step 4: Use the lowest mass found in step 2 and divide it by 2, 3, and 4. Find which of the canisters, after being divided, is the closest to a whole number. That number is the mass of an individual coin. Step 5: Use the mass of the empty container and divide it by the number found in step 4 (Round to the nearest whole number) this will find the number of coins in a container. 3. Use your method to predict the mass of an individual coin. a) Measure the masses of each canister on the electronic balance b) Measured the mass of the empty canister and subtracted that by the masses found in part a) in order to find the mass of the coins. c) Shake the canisters and assume that the number of coins in each canister is between 2 and 4 (2≤x≤4) d) Divide the mass of a canister by the 2, 3, and 4 to find the mass of of a single coin Ex. Smallest mass of coins in canister, in a group of canisters is (M Coins in canister #1 ) 5g. n: Number of coins M Coins in canister #1 / n = M Mass per coin 5g / 2 = 2.5g/coin 5g / 3 = 1.67g/coin 5g / 4 = 1.25g/coin —--------------------------------------------------------------------------------------------------------- A random canister, from the same group of canisters that the 5g one was in is 7.3g (M Coins in canister #2 ) M Coins in canister #2 / M Mass per coin = # of coins in a canister 7.3g / 2.5g/coin = 2.92 coins 7.3g / 1.67g/coin = 4.37 coins 7.3g / 1.25g/coin = 5.84 coins Take the number closest to a whole number and round it to the nearest whole number, in this case, 2.92 coins = 3 coins Adapted from: Hirsch, Alan, et al. “Nelson Physics 12”, Thomas Nelson, 2003.

∴There are 3 coins in canister of 7.3g Observations/Data Separation of plates: d=0.50 cm Table 1 Mass of Oil Drop (kg) Electric Potential Difference (V) Charge on Oil Drop (C) 3.2 x 10 -15 140.0 1.1 x 10 -6 2.4 x 10 -15 147.0 8.0 x 10 -17 1.9 x 10 -15 290.9 3.2 x 10 -17 4.2 x 10 -15 214.4 9.6 x 10 -17 2.8 x 10 -15 428.8 3.2 x 10 -17 2.3 x 10 -15 176.1 6.4 x 10 -17 3.5 x 10 -15 214.4 8.0 x 10 -17 3.7 x 10 -15 566.6 3.2 x 10 -17 2.1 x 10 -15 160.8 8.0 x 10 -17 3.9 x 10 -15 597.2 3.2 x 10 -17 4.3 x 10 -15 263.4 6.4 x 10 -17 2.5 x 10 -15 382.8 3.2 x 10 -17 3.1 x 10 -15 237.3 6.4 x 10 -17 3.4 x 10 -15 173.5 9.6 x 10 -17 2.2 x 10 -15 673.8 1.6 x 10 -17 Analysis 1. Using the data in Table 1, calculate the value of the elementary charge. You will need Eq. 1 from the Discussion. Adapted from: Hirsch, Alan, et al. “Nelson Physics 12”, Thomas Nelson, 2003.

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2. Describe the method you used to determine the elementary charge. Was this method similar to the method you used to find the mass of an individual coin in Part 1 once the charge is determined? How so? 3. What must be true about individual elementary charges for your method for determining their values to be valid? i) The oil drops should be stationary in order to calculate the charge, this is because the force of gravity must equal the electrical force (F g = F e ). ii) Each lost charge should be a multiple of 160 zepto coulombs (1.6 x 10 -19 C), for example, a loss of 3.2 x 10 -19 C, a loss of 4.8 x 10 -19 C… 4. Why must a large number of values be used to get a reliable answer? What error might result if only a few oil drops were used, all containing an even number of charges? Using a substantial number of values is essential to ensure the reliability of the results. This approach is crucial because it allows us to identify any outliers in the data. If the experiment were conducted with only a few oil drops, all of which contained an even number of charges, it could result in a systematic error because the use of a limited sample size may not accurately represent the true distribution of charges on the oil drops. Using a larger set of numbers increases the accuracy of the experiment. It allows us to determine the average value we're seeking by minimizing the impact of any irregular numbers that were used. Evaluation: 1. List some possible sources of random and systematic error in an experiment of this nature. What can be done to minimize the errors? (Millikan’s experiment is an unusually good one for thinking about sources of error. Be creative.) Random Errors for our experiment: 1. Unknown coin type, (Toonies, Loonies, Quarters,..) therefore giving an inaccurate and for all types of coins. 2. Coins could have different masses, depending on material of the coin, alloy percentages, and any abnormal events that could have caused the mass to shift. 3. Canisters could also have different masses, although they will be extremely small as they are made from the same material and not an alloy. 4. Attempted to weigh a canister while the balance was still resetting to zero. Adapted from: Hirsch, Alan, et al. “Nelson Physics 12”, Thomas Nelson, 2003.

Systematic Error in measurements: 1. Balance may have been improperly calibrated, leading to inaccurate calculations Errors in Milikan’s Oil experiment and ways to minimize: 1. Electrical leakage and external electric fields from lightbulbs, wires, and most electricity needing devices can interfere with the experiment. A faraday cage can be used to minimise/prevent these outside sources. 2. Evaporation of oil can lead to change in mass and therefore, incorrect calculations. This can be minimised by doing the experiment in a closed system. 3. Unexpected aircurrents could result in a higher or lower voltage being used in order to balance the oil drop. This can be minimised by securing all exposed holes, making the apparatus air tight 4. Dust particles or other contaminants on the plates can affect the electric field, causing it to have a weaker effect on the oil drops. Regularly clean and maintain the plates to minimize this source of error. Adapted from: Hirsch, Alan, et al. “Nelson Physics 12”, Thomas Nelson, 2003.

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