Question

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: $$ \begin{array}{cc} \hline \text { Droplet } & \text { Calculated Charge (C) } \\ \hline \text { A } & 1.60 \times 10^{-19} \\ \text {B } & 3.15 \times 10^{-19} \\ \text {C } & 4.81 \times 10^{-19} \\ \text {D } & 6.31 \times 10^{-19} \end{array} $$ (a) What is the significance of the fact that the droplets carried different charges? (b) What conclusion can the student draw from these data regarding the charge of the electron? (c) What value (and to how many significant figures) should she report for the electronic charge?

Short answer

(a) The significance of different charges on the droplets is that the charges are quantized, meaning they are integer multiples of a fundamental charge - the charge of a single electron. (b) The student can conclude that the charge of the electron is the smallest charge value found in the data, which is \(1.60 \times 10^{-19}\) C (from droplet A). (c) The student should report the electronic charge value as \(1.60 \times 10^{-19}\) C, with 3 significant figures.

Step-by-step solution

Analyzing the data

First, let's analyze the charges on the oil droplets: Droplet A: \(1.60 \times 10^{-19}\) C Droplet B: \(3.15 \times 10^{-19}\) C Droplet C: \(4.81 \times 10^{-19}\) C Droplet D: \(6.31 \times 10^{-19}\) C

Finding the relationship between charges

We need to find the smallest charge value that could represent the charge of a single electron, which means we need to find the greatest common factor (GCF) of these charges. To do this, let's divide each charge by the smallest charge of droplet A: Droplet A: \(1.00\) (smallest charge) Droplet B: \(1.97\) Droplet C: \(3.01\) Droplet D: \(3.94\) From these values, we can deduce that droplet A carries the charge of a single electron, droplet B carries approximately 2 times the electron charge, droplet C carries approximately 3 times the charge, and droplet D carries approximately 4 times the charge. This implies that the charge on the oil droplets is quantized in integer multiples of the smallest charge value. (a) The significance of the droplets carrying different charges is that the charges on the oil droplets are quantized, meaning they are integer multiples of a fundamental charge (the charge of a single electron). (b) The student can conclude that the charge of the electron is the smallest charge value found in the data, which is \(1.60 \times 10^{-19}\) C (from droplet A).

Reporting the electronic charge value

(c) The student should report the electronic charge value as \(1.60 \times 10^{-19}\) C, with 3 significant figures.

Key concepts

Understanding the Concept of Electronic Charge

The electronic charge is a fundamental property of matter that describes the charge of a single electron. It is a tiny but crucial value in physics and chemistry since it sets the scale for electromagnetic force between particles. This charge plays a pivotal role in understanding interactions in atomic and subatomic particles.
The value of the electronic charge was determined to be approximately \(1.60 \times 10^{-19}\) coulombs based on experiments and calculations, such as the Millikan oil drop experiment. In the context of this experiment, each oil droplet carried a charge that is a multiple of this fundamental charge.
In the Millikan experiment, Robert Millikan meticulously measured the charge on tiny oil droplets suspended in an electric field, ultimately deducing the value of the electronic charge from these quantized values. This monumental discovery paved the way for numerous advancements in quantum mechanics and physics, lending insight into electrical forces and their fundamental role in nature.

Delving into Quantized Charges

Quantization of charge refers to the fact that charge can occur in discrete packets or quanta rather than in a continuous range. This idea is fundamental in physics and chemistry, particularly in the study of atomic and subatomic particles.
In the Millikan oil drop experiment, the measured charges on different oil droplets were not random but rather exact multiples of the smallest observed charge. This smallest charge corresponds to the charge of a single electron.

• Droplet A, for example, carried a charge of \(1.60 \times 10^{-19}\) C, which is essentially one electronic charge unit.
• Droplet B carried approximately two units, droplet C about three units, and droplet D four units.

This pattern indicates quantization, meaning the charges on the droplets are integer multiples of a minimum quanta—the electronic charge.
The importance of quantized charges lies in its illustration of one of the core principles of quantum theory, where discrete, countable quantities are preferred over continuous variations.

Importance of Significant Figures in Measurements

Significant figures in measurements are crucial because they reflect the precision of the measurement tools employed and the accuracy of the recorded data. When reporting findings from an experiment, such as the Millikan oil drop experiment, the number of significant figures conveys the certainty of the measurements.
For instance, the report of the electronic charge being \(1.60 \times 10^{-19}\) C with three significant figures suggests a high level of precision in the experimental and analytical process. This precision indicates that the instruments used were capable of distinguishing between minute variations in charge, thereby lending credibility to the experimental outcome.

• Each digit in a measured value holds significance, showing the resolution of the measurement.
• In the context of scientific experiments, precise figures help establish consistency and reliability.

Understanding the significance of these figures allows students to appreciate the exactness and reliability of scientific measurements, ensuring a valid interpretation of experimental outcomes.