Question

How many electrons are there in one coulomb of electricity? (a) \(6.023 \times 10^{23}\) (b) \(1.64 \times 10^{-24}\) (c) \(6.24 \times 10^{18}\) (d) \(6.24 \times 10^{-24}\)

Short answer

There are approximately \(6.24 \times 10^{18}\) electrons in one coulomb of electricity.

Step-by-step solution

Identify the charge of one electron

To find out how many electrons constitute one coulomb of charge, we must first know the charge of one electron, which is approximately \( -1.602 \times 10^{-19} \) coulombs.

Calculate the number of electrons

Since the charge of one electron is known, the number of electrons per coulomb can be calculated by dividing one coulomb by the charge of one electron, using the formula \({\text{number of electrons} = \frac{1 \text{ C}}{1.602 \times 10^{-19} \text{ C/electron}}}\).

Perform the calculation

Carry out the division to find the number of electrons per coulombs, which equates to \(\frac{1}{-1.602 \times 10^{-19}} \approx 6.24 \times 10^{18} \) electrons per coulomb.

Key concepts

Electrical Charge

Think of electrical charge as an intrinsic property of particles that facilitates their participation in electromagnetic interactions. It's the reason objects attract or repel each other in the world of electricity and magnetism. There are two types of electric charges, positive and negative, famously carried by protons and electrons, respectively.\(
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Charges can be transferred or shared between objects in various ways, leading to familiar phenomena such as static electricity or the flow of current in electrical circuits. The standard unit for measuring charge is the coulomb (C), named after Charles-Augustin de Coulomb, an eminent French physicist. One coulomb of charge is considerable; for scale, it represents a tremendous number of fundamental charge carriers, which we call electrons.

Elementary Charge

Diving into the concept of elementary charge, it's like uncovering the DNA of electricity. Every charged particle carries a multiple of this fundamental value. The elementary charge, denoted by 'e', is the smallest amount of electric charge that can exist independently without being divisible.\(
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An electron has a negative elementary charge of approximately \( -1.602 \times 10^{-19} \) coulombs, reflecting its minuscule yet critical role in electrical phenomena. Protons carry a positive charge of the same magnitude but opposite sign. This tiny quantity is like the building block for all larger electrical charges and is pivotal in understanding how charges accumulate and interact.

Coulomb's Law

Envision a universe where electrical forces could be predicted with precision—that's what Coulomb's Law provides us. It describes the force between two point charges: the force is proportionate to the product of the two charges and inversely proportional to the square of their separation distance. The law can be mathematically formulated as \(F = k \frac{|q_1 \times q_2|}{r^2}\), where \(F\) is the force in Newtons (N), \(q_1\) and \(q_2\) are the charges in coulombs (C), \(r\) is the distance in meters (m), and \(k\) is Coulomb's constant.\(
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Coulomb's Law is fundamental in explaining the principles of electrostatics, helping us compute forces with unerring exactitude whenever charged particles are involved. It has practical importance in designing electrical systems and understanding intermolecular forces.

Quantitative Calculation in Physics

Physics often requires us to perform quantitative calculations to predict and comprehend the natural world. These calculations involve figuring out precise values, like how many electrons are in one coulomb of charge. Utilizing data such as the elementary charge, we're able to set up proportionality equations and perform division or multiplication to generate answers applicable across physics and engineering.\(
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In the specific exercise at hand, we calculated the number of electrons in a coulomb by dividing the charge of one coulomb by the elementary charge of one electron. It's a superb example of quantitative calculation in physics—taking abstract concepts like charge and converting them into familiar, concrete numbers that quantify the mysteries of our universe.