Question

How many electrons are required to yield a total charge of 1.00 C?

Short answer

Answer: Approximately 6.242×10^18 electrons are required to accumulate a charge of 1.00 Coulombs.

Step-by-step solution

Make a note of the given information

We have the following information: - Total charge, Q = 1.00 C - Charge of one electron, e = 1.602×10^(-19) Coulombs

Calculate the number of electrons required

To find the number of electrons (n) required to yield a total charge of 1.00 Coulombs, we can use the formula: n = Q/e Substituting the values, n = (1.00 C)/(1.602×10^(-19) C/electron)

Solve for the number of electrons

Divide 1.00 C by 1.602×10^(-19) C/electron: n ≈ (1.00)/(1.602×10^(-19)) = 6.242×10^(18) Thus, about 6.242×10^18 electrons are required to yield a total charge of 1.00 Coulombs.

Key concepts

Electron Charge

The concept of electron charge is fundamental in understanding electrical phenomena. Electrons, the tiny negatively charged particles found in atoms, carry a specific amount of electric charge. The charge of one electron is approximately \(1.602 \times 10^{-19} \) Coulombs. This value is considered a fundamental constant of nature, as it is the same for all electrons.
This charge is negative, which is why electrons are known as negatively charged particles. The concept of charge was first discovered in the context of static electricity, and electrons are critical in enabling this concept in conductive materials. A simple way to visualize this is by thinking of electrons as microscopic carriers of charge, flowing through a conductor like water through a pipe.

Number of Electrons Calculation

Calculating the number of electrons required to achieve a specific charge involves a straightforward use of division. The formula used is:

• \( n = \frac{Q}{e} \)

Where \( n \) is the number of electrons, \( Q \) is the total charge, and \( e \) is the charge of one electron.
For example, if you have a charge of 1 Coulomb, and you know the charge of a single electron is \(1.602 \times 10^{-19} \) Coulombs, you would divide 1 by \(1.602 \times 10^{-19} \) to find the number of electrons needed. The resulting calculation is:

• \( n \approx \frac{1.00}{1.602 \times 10^{-19}} = 6.242 \times 10^{18} \)

This means approximately \(6.242 \times 10^{18} \) electrons make up a charge of 1 Coulomb.
This calculation is crucial in fields ranging from electronics to chemistry, where precise understanding of charge and electron flow is necessary.

Coulomb

The Coulomb is the SI unit of electric charge, symbolized as \(C\). It is one of the key units used in the study of electricity and electromagnetism. Named after Charles-Augustin de Coulomb, the Coulomb quantifies the amount of electric charge. One Coulomb is defined as the charge carried by approximately \(6.242 \times 10^{18} \) electrons.
Understanding the Coulomb is essential for grasping how electric fields and potentials work. It measures the quantity of electricity moved by a current of one ampere flowing for one second, creating a link between static and dynamic electricity concepts.

• The Coulomb helps in converting between charge and electron count.
• It provides a standard for measuring charge that can be universally understood.

Knowing how big a Coulomb is helps in visualizing and calculating electrical properties in circuits and systems.