Problem 15 - Chemistry: The Central Science

Question

(a) Figure \(2.5\) shows the apparatus used in the Millikan oil-drop experiment with the positively charged plate above the negatively charged plate. What do you think would be the effect on the rate of oil drops descending if the charges on the plates were reversed (negative above positive)? (b) In his original series of experiments, Millikan measured the charge on 58 separate oil drops. Why do you suppose he chose so many drops before reaching his final conclusions?

Step-by-Step Solution

Answer

(a) If the charges on the plates were reversed, the rate of oil drops descending would increase. Negatively charged oil drops would descend faster due to a stronger net force, and positively charged oil drops would descend slower. (b) Millikan measured the charge on 58 separate oil drops to ensure a statistically significant sample size, minimize errors in measurement, and establish a broader range of evidence to support his conclusion. This helped him determine the value of the elementary charge (the charge of an electron).

Step 1: Understanding the Millikan oil-drop experiment

In the Millikan oil-drop experiment, tiny oil drops were sprayed into a chamber, where the drops become electrically charged due to friction. Then, they were placed between two parallel conducting plates with one being positively charged and the other being negatively charged. The oil drops were subject to gravity and the electric field between the plates. Millikan adjusted the voltage applied on the plates to make the oil drops stay suspended or move up/down to measure the electrical charge on the oil drops. #a# For the first scenario, we will discuss the effect of reversing the charges on the plates.

Step 2: Visualizing the oil drops and plates charges

In the original setup, the positively charged plate was situated above the negatively charged plate, attracting the negatively charged oil drops and repelling the positively charged ones. However, if the charges on the plates were reversed, the negatively charged plate would be above the positively charged plate.

Step 3: Effect on the descending rate of oil drops

When the charges on the plates are reversed, the negatively charged oil drops would be repelled by the negatively charged plate and attracted by the positively charged plate, causing them to descend faster due to a stronger net force acting on them. The positively charged oil drops would be attracted by the negatively charged plate, and their descending rate would slow down due to a decreased net force. Overall, reversing the charges on the plates would result in an increase in the rate of oil drops descending. #b# Now let's examine why Millikan chose to measure the charge on so many oil drops.

Step 4: Statistically significant results

Millikan used a large number of oil drops (58 in total) to measure their respective charges because he wanted to ensure that he had a statistically significant sample size. By using a large number of oil drops, he could minimize the impact of errors in measurement and establish a broader range of evidence to support his conclusions.

Step 5: Identifying the fundamental charge of an electron

Millikan observed that the electric charge on each oil drop was quantized, meaning it was always an integral multiple of a fundamental charge (the charge of an electron). By analyzing the charges of 58 separate oil drops, Millikan could conclude that all the measured charges were multiples of this fundamental charge, helping him determine the actual value of the elementary charge (the charge of an electron). In conclusion, reversing the charges on the plates in the Millikan oil-drop experiment would result in an increased rate of oil drops descending. Millikan measured the charge on 58 separate oil drops to get statistically significant results and determine the value of the elementary charge or the charge of an electron.

Key Concepts

Electric Charge

Electric charge is a fundamental property of matter. It describes the presence of either negative or positive charge in a particle. Electrons possess a negative charge, while protons carry a positive charge.
An object can become charged through various methods, such as friction, conduction, or induction, altering its charge state to either positive, negative, or neutral.
In the context of Millikan's oil-drop experiment, understanding electric charge is crucial as it revolves around how particles become charged and react to electric fields. Millikan discovered that oil drops can carry an excess or deficit of electrons, giving them a net electric charge.

• Charged objects can exert electrostatic forces on each other.
• The electric charge is measured in Coulombs (C).
• Opposite charges attract while like charges repel.

Mastering this concept helps explain how charged particles interact in different environments.

Experimental Physics

Experimental physics involves conducting experiments to discover and understand the laws of nature. This branch of physics uses empirical methods and systematic observations to test scientific theories and hypotheses.
The Millikan oil-drop experiment is a landmark study in experimental physics, demonstrating how meticulous experimentation can lead to significant scientific advancements.
Millikan's work was meticulous, involving precise measurements and control of variables, which showcased the significance of experimental setups.

• Research in experimental physics relies heavily on accurate data collection and analysis.
• Experiments are designed to test theories and validate scientific predictions.
• Advanced technology and equipment often support these endeavors.

Understanding experimental physics is essential for comprehending how theoretical propositions are verified through practical experimentation.

Elementary Charge

The elementary charge is the smallest unit of electric charge, carried by a single proton or electron. It is considered the building block of electric charge, fundamental to understanding atomic and subatomic phenomena.
During the Millikan oil-drop experiment, careful analysis revealed that the charges observed on the oil drops were always multiples of a basic unit—this was identified as the elementary charge.
The elementary charge quantifies the charge of a single electron as approximately \(1.602 \times 10^{-19}\) Coulombs. This discovery was crucial as it provided insight into quantized charge in nature and led to the determination of the charge of an electron.

• Elementary charge allows for calculation of total charges in atoms and molecules.
• It plays a key role in electromagnetic interactions.
• Its measurement was a pioneering achievement in understanding atomic structure.

This concept is fundamental in fields like chemistry, physics, and electrical engineering.

Gravity

Gravity is the force of attraction between two masses, such as the Earth and an object. It is a fundamental force in nature, responsible for giving weight to objects and keeping celestial bodies in orbit.
In the Millikan oil-drop experiment, gravity acts on the oil drops, pulling them toward the ground. The balance between gravitational force and the electric field's force allowed Millikan to make his precise measurements.
Understanding gravity's role is essential for comprehending how Millikan could precisely control the droplets' motion.

• Gravitational force is proportional to the mass of the objects involved and decreases with distance.
• It is one of the four fundamental forces in physics.
• Gravity affects objects irrespective of their charge state.

A solid grasp of gravity helps us understand phenomena from simple freefall to the orbits of planets.

Electrical Field

An electrical field is a region around a charged particle where electrostatic forces can be exerted on other charges. It is central to understanding how charged objects interact within space.
In the Millikan oil-drop experiment, an electrical field was applied between two charged plates. By adjusting the strength of this field, Millikan was able to counteract the force of gravity on the oil drops, allowing them to float or suspend.
This interaction between oil drops and the electrical field is fundamental to the experiment's success.

• Electrical fields are represented by field lines emanating from charges.
• The strength of an electrical field diminishes with distance from the source charge.
• They are calculated by the force per unit charge (V/m).

Understanding electrical fields provides insight into the interaction of charged particles in various applications.

Quantization of Charge

The quantization of charge is a principle stating that the charge of any object is an integer multiple of the elementary charge. It implies that charge comes in discrete amounts, not continuous.
During the Millikan oil-drop experiment, it was observed that all measured charges were integral multiples of a fundamental charge, reinforcing the concept of quantization. This means every charge amount could be described as \(n \times e\), where \(n\) is an integer and \(e\) is the elementary charge.

• Quantization demonstrates that charge cannot exist in arbitrary values.
• This principle is crucial for understanding atomic structure and chemistry.
• The discovery of charge quantization helped confirm theories about the nature of electrons.

This key observation has wide-ranging implications in physics, affecting how we perceive atomic and molecular behavior.