Problem 18 - Chemistry: The Central Science

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: (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?

Step-by-Step Solution

Answer

The different charges on the oil droplets signify that each drop carries a charge that is an integer multiple of the elementary charge, and by analyzing the data, we can determine the charge of an electron. In the example provided, the smallest charge value of 1.6 x 10^(-19) C represents the charge of the electron, and all other charge values are integer multiples of this value. The student should report the electronic charge value as 1.6 x 10^(-19) C, with two significant figures, or more depending on the precision of the measurements taken.

Step 1: (a) Significance of having different charges on the oil droplets

: Oil drops in this experiment have different charges due to different numbers of excess electrons on each drop. Each oil drop will carry a charge that is an integer multiple of the elementary charge (the charge of one electron). By analyzing the data and finding the relationship among the charges, we can determine the smallest (elementary) charge, representing the charge of an electron.

Step 2: (b) Drawing a conclusion from the data about the charge of the electron

: Examine the given data and find the greatest common divisor, which is the charge of the electron. For example, assuming the data is given in the form of a list of charges as follows: Charge values: 1.6 x 10^(-19) C, 3.2 x 10^(-19) C, 4.8 x 10^(-19) C, 9.6 x 10^(-19) C By examining these values, we can see that the smallest charge value is 1.6 x 10^(-19) C. All other charges are integer multiples of this smallest charge, so we can conclude that the charge of the electron is 1.6 x 10^(-19) C.

Step 3: (c) Reporting the value and significant figures for the electronic charge

: The student should report the smallest charge value obtained, which represents the charge of an electron. In this case, it would be 1.6 x 10^(-19) C. As for the number of significant figures, it depends on the precision of the measurement taken. In our example, the reported value has two significant figures (since 1.6 has two digits while ignoring the powers of 10). If the student has a more precise measurement, she should report more significant figures to reflect that precision. For instance, if the charge value was 1.59 x 10^(-19) C, the student would report three significant figures.

Key Concepts

Millikan Oil Drop Experiment

The Millikan oil drop experiment was a groundbreaking experiment conducted by Robert A. Millikan in 1909 to determine the charge of the electron. The experiment involved observing tiny oil droplets that were electrically charged and suspended between two metal plates. By adjusting the voltage across the plates, Millikan was able to make the oil drops hover in mid-air, allowing precise measurements of their charges.

Each droplet had a unique charge due to varying numbers of electrons. By measuring the charge on many droplets and finding the smallest common charge, Millikan concluded that this represented the charge of a single electron. This experiment fundamentally demonstrated how static charges could be observed and quantified, laying a foundation for modern atomic theory.

• Observation of charged oil droplets under an electric field.
• Adjustment of voltage to balance gravitational and electric forces.
• Identification of the elementary charge as a common factor in droplet charges.

Millikan's work ultimately confirmed that the charge of an electron is quantized, meaning it exists in discrete amounts rather than a continuous spectrum.

Elementary Charge

The elementary charge is the smallest unit of electric charge that is observed in nature, represented by the letter e, and equal to approximately \( 1.6 \times 10^{-19} \) coulombs. This charge is fundamental to the understanding of physics and chemistry as it represents the charge carried by a single proton or the negative of the charge carried by a single electron.

In the context of the Millikan oil drop experiment, recognizing the elementary charge was critical. By determining that every observable difference in the charge on the oil droplets was a multiple of this value, Millikan provided strong evidence for the quantized nature of electric charge. Understanding elementary charge is key to making sense of atomic structure and interactions.

• Smallest possible charge, fundamental to subatomic particles.
• Approximately \( 1.6 \times 10^{-19} \) C, confirming the quantization of charge.
• Foundation for much of modern physics and chemistry.

Grasping the concept of elementary charge aids in conceptualizing how atoms bond and interact at the molecular level.

Significant Figures

Significant figures are the digits in a number that are known with certainty plus one final digit, which is somewhat uncertain or estimated. They are crucial when reporting measurements in scientific experiments. The number of significant figures indicates the precision of a measurement.

In the exercise where the charge of an electron is evaluated, significant figures play a role in how the result is reported. If the measurement gives an electron charge as \( 1.6 \times 10^{-19} \) C, it's reported with two significant figures, showcasing the precision of the measurement.

• Indicate the precision of a measurement.
• Help distinguish exact figures from approximate ones.
• Essential for accurately communicating the results of calculations or measurements.

Understanding how to determine and use significant figures ensures clarity and precision in scientific communication.

Static Charges

Static charges emerge when there is an imbalance of electric charges on the surface of a material. This concept was pivotal in Millikan's oil drop experiment, where the oil droplets acquired static charges that were observed in an electric field. Understanding static charges involves knowing how electrons transfer between materials, either as a result of friction, contact, or induction.

The behavior of static charges is key to a variety of everyday phenomena and technologies, like photocopiers, which harness static electricity to attract ink to paper, or in avoiding electrostatic discharge in electronics.

• Results from imbalance of electric charges on a surface.
• Key to understanding phenomena such as sparks or static cling.
• Invaluable in technological applications and experiments.

Appreciating the role of static charges aids in grasping not only scientific experiments like Millikan's but also a wide range of practical utilities.