Question

In an oil drop experiment, the following charges (in arbitrary units) were found on a series of oil droplets: \(4.5 \times 10^{-18}\), \(3.0 \times 10^{-18}, 6.0 \times 10^{-18}, 7.5 \times 10^{-18}\) \(9.0 \times 10^{-18}\). The charge on electron (in the same unit) should be (a) \(3.0 \times 10^{-18}\) (b) \(9.0 \times 10^{-18}\) (c) \(1.5 \times 10^{-18}\) (d) \(1.6 \times 10^{-19}\)

Short answer

The charge on an electron should be option (c) \(1.5 \times 10^{-18}\).

Step-by-step solution

Identify The Smallest Charge

Analyze the given charges on the oil droplets to find the smallest charge value. This value is most likely to be the fundamental charge or an integer multiple of it.

Determine The Common Factor

Check which of the given options can be a common factor for all the charges presented. This will be your candidate for the elementary charge.

Divide The Charges By The Candidate

Divide all the given charges by the candidate elementary charge to see if each result is close to an integer. This supports the idea that the charge of the electron is the one that can divide all charges into whole numbers.

Confirm The Elementary Charge

The correct charge for the electron should be an option that can divide all the provided charges into whole numbers. This is because charges on the oil droplets are expected to be multiples of the elementary charge.

Key concepts

Fundamental Charge

The concept of a fundamental charge refers to the smallest unit of electric charge that is indivisible under normal circumstances. In the context of the oil drop experiment, this is crucial in understanding how electrical charge is quantized. The historical oil drop experiment conduced by Robert Millikan and Harvey Fletcher in 1909 aimed to measure this very charge. By carefully analyzing falling oil droplets in an electric field, they were able to determine the smallest increment of charge on the droplets, which they hypothesized to be the charge of a single electron.

In the exercise, the fundamental charge is represented by the smallest charge observed in the units provided. The listed charges indicate that this charge would be an integer multiple of the electron's charge. This assumption leads to an insightful journey into discovering one of the most critical constants in nature. The identification of the electron charge is a significant foundation for understanding the atomic structure, interactions between particles, and underpins how electricity works in the real world.

Elementary Charge

The elementary charge, often symbolized as 'e', is the charge carried by a single proton or the negative of that carried by a single electron. This charge is considered fundamental because its value is consistent across all known charged elementary particles. In our exercise, the objective is to deduce the value of this elementary charge in arbitrary units by using the charges found on the oil droplets.

Since the elementary charge represents a standard, immutable quantity, the charges on the oil droplets should theoretically be whole number multiples of this value. By devising a methodical test, as described in the exercise's step-by-step solution, one can extract which of the provided options corresponds to this indivisible charge. Therefore, confirming the elementary charge is an analytical process that reinforces the evidence that charge is not freely divisible but comes in discrete 'packets' - a revelation that has profound implications in both physics and chemistry.

Quantization of Charge

The quantization of charge is a principle stating that all electric charges are integers multiples of the elementary charge 'e'. This means that charges in nature appear as whole number units of this elementary charge, and the oil drop experiment was key to demonstrating this phenomenon. This concept is not only countering the idea of arbitrarily small charges but also reinforces the atomic theory that matter—and by extension charge—is composed of discrete units.

In analyzing the oil drop experiment data, we see that charges are always whole number multiples of a smallest charge—the hypothesized fundamental unit of charge. As seen in the exercise solutions, one derives the value of the elementary charge by looking for a common divisor of the measured charges that results in integers. When we obtain only whole numbers upon division, it highlights the quantized nature of charge. This pivotal understanding has cascading effects, contributing significantly to quantum theory and technology that operates on a quantum scale, such as semiconductors and computer processors.