Millikan determined the charge on the electron by studying the static charges on oil drops falling in an electric field (Figure 2.5). A student carried out this experiment using several oil drops for her measurements and calculated the charges on the drops. She obtained the following data: Droplet Calculated Charge (C) A 1.60 * 10-19 B 3.15 * 10-19 C 4.81 * 10-19 D 6.31 * 10-19 (c) What value (and to how many significant figures) should she report for the electronic charge?

Verified step by step guidance

1. Identify the smallest charge value from the data, which is the charge on droplet A: 1.60 x 10^-19 C. This value is considered as a fundamental unit of charge, based on Millikan's oil drop experiment.
2. Compare the charges of the other droplets (B, C, D) to see if they are multiples of the charge on droplet A. This will help confirm if the smallest charge is indeed the fundamental charge of an electron.
3. Calculate the ratios of the charges of droplets B, C, and D to the charge of droplet A to check if they are close to whole numbers. For example, for droplet B, calculate (3.15 x 10^-19 C) / (1.60 x 10^-19 C).
4. Determine the precision of the measurements by considering the number of significant figures in the smallest charge value, which is three significant figures (1.60 x 10^-19 C).
5. Report the electronic charge as the charge of droplet A, 1.60 x 10^-19 C, with three significant figures, as it is the fundamental charge unit and the most precise measurement.

Key Concepts

Quantization of Charge

The quantization of charge refers to the principle that electric charge exists in discrete amounts, specifically as integer multiples of the elementary charge (e). In Millikan's oil drop experiment, the charges measured on the oil droplets were found to be whole number multiples of the charge of a single electron, which is approximately 1.60 x 10^-19 coulombs. This concept is fundamental in understanding how charges interact and are measured in experiments.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. In scientific measurements, significant figures indicate the certainty of the measurement and help convey the precision of the data. When reporting the charge of the electron based on the student's measurements, it is essential to determine the appropriate number of significant figures based on the least precise measurement in the data set.

Average Charge Calculation

To report a value for the electronic charge, one must often calculate the average of the measured charges from multiple trials. This involves summing the calculated charges and dividing by the number of measurements. The average provides a more reliable estimate of the charge, reducing the impact of random errors in individual measurements, and is crucial for reporting a final value with the correct significant figures.