Problem 83 - Master Resource Book in JEE Main Physics

Question

Millikan's oil drop experiment establish that (a) electric charge depends on velocity (b) electron has wave nature (c) electric charge is quantised (d) electron has particle nature (e) electron has wave nature

Step-by-Step Solution

Answer

Millikan's oil drop experiment demonstrated that electric charge is quantised (option c).

Step 1: Understanding the Context

Millikan's oil drop experiment was a famous experiment conducted to measure the charge of an electron. The context of the question revolves around recognizing what fundamental property of electricity was demonstrated through this experiment.

Step 2: Identifying the Concept

To understand the results of Millikan's experiment, recall that it was significant because it determined the discrete nature of electric charge. Through the experiment, Millikan calculated the charge of an electron as a multiple of a fundamental charge unit.

Step 3: Choosing the Correct Option

Given the key concept identified, the correct answer should reflect the understanding that the electric charge is quantised, meaning it exists in discrete packets rather than continuous values. Among the provided options, this matches with option (c): electric charge is quantised.

Key Concepts

Quantization of Electric Charge

The idea of quantization of electric charge is a cornerstone in understanding the nature of electricity itself. Quantization refers to the concept that electric charge is not continuous, but rather exists in distinct, separated units. This concept emerged vividly from Millikan's oil drop experiment, showing that there is a smallest unit of charge, known as the elementary charge, that cannot be divided further.

In more familiar terms, think of quantization like counting steps on a staircase. You can take a whole step up or down, but you cannot take a fraction of a step. Similarly, the electric charge is observed in multiples of a basic, indivisible unit. This revelation from Millikan’s experiment led to further investigations and a deeper understanding of atomic and subatomic structures.

• Electric charge appears only in integer multiples of the elementary charge.
• The smallest charge unit is the charge of an electron or proton.

The experiment essentially proved that electrons have a fixed charge, reinforcing the theory of quantization, which is fundamental to the field of quantum mechanics.

Electron Charge Measurement

Millikan's innovative oil drop experiment directly led to the precise measurement of the electron’s charge. By observing tiny oil droplets in an electric field and measuring their fall and rise, Millikan could calculate the charge carried by each droplet. This was achieved by balancing gravitational forces with electrical forces.

The measurement process involved adjusting the voltage across two plates and observing how individual droplets behaved. As Millikan meticulously altered voltages to hold the droplets in equilibrium, he gained insights into the exact magnitude of the charge.

• The charge of the electron was determined to be approximately \(1.602 imes 10^{-19}\) coulombs.
• This value is fundamental to calculations involving atomic and molecular phenomena.

The accuracy of this experiment allowed scientists to standardize the elementary charge across diverse scientific fields, ensuring consistency in physical calculations and theories.

Discrete Charge Units

Through Millikan's oil drop experiment, the existence of discrete charge units was confirmed. This concept means that charges appear in specific, quantifiable amounts rather than on a sliding scale of infinite possibilities. Each droplet in Millikan's experiment had a total charge that was a whole number multiple of a basic charge unit.

This discrete nature allows for standardization in scientific inquiry and engineering, enabling precise calculations and predictions. It also laid the groundwork for developments in theoretical physics, such as quantum electrodynamics, where such discrete units are essential for models describing how charges interact with forces and fields.

• Discrete charge units explain the stability of atoms.
• The atomic structure relies on charges being in these fixed increments.

Millikan’s discovery confirmed what was hypothesized in atomic theory, proving empirically that charge is not just any quantity, but comes in these neat, discrete packages, shaping our modern understanding of the microscopic world.