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The mass of an electron is a fundamental property of matter and is extremely small compared to everyday objects. Specifically, the mass of a single electron is about \(9.109 \times 10^{-31}\) kilograms. This tiny mass plays a crucial role in understanding many physical and chemical phenomena, particularly in contexts involving atomic and subatomic particles.
The small mass means that electrons, which are negatively charged particles, will typically have a negligible effect on the overall mass of an object in macroscopic terms. However, in calculations at the atomic scale, the electron's mass must be considered to determine quantities like the number of electrons present in a given mass. Understanding the mass of an electron helps bridge microscopic concepts to macroscopic applications.

The coulomb is the standard unit of electric charge in the International System of Units (SI). It is used to measure the quantity of charge in a given system. One coulomb is defined as the amount of charge transferred by a current of one ampere flowing for one second.

• When dealing with subatomic particles, such as electrons, the standard unit becomes very practical.
• The elementary charge, which refers to the charge of a single electron, is approximately \(-1.602 \times 10^{-19}\) coulombs.

The negative sign indicates an electron carries a negative charge, which is opposite in sign to the positive charge carried by protons. This measure is crucial in calculating electrical interactions in physical systems, such as the total charge in a given number of electrons.

Calculating the number of electrons in a given mass involves dividing the total mass by the mass of an individual electron. This can be expressed with the formula \(N = \frac{M}{m}\), where \(M\) is the total mass and \(m\) is the mass of one electron.
In the problem statement, we had a mass of \(75.0\) kg of electrons. By using the known electron mass \(9.109 \times 10^{-31}\) kg, we can easily find the number of electrons:

• Numerator (total mass): 75.0 kg
• Denominator (mass of one electron): \(9.109 \times 10^{-31}\) kg/electron

This results in an immense count of electrons, about \(8.233 \times 10^{31}\). Understanding this conversion is fundamental to calculating the overall charge a system of electrons, based on the elementary charge.

To compute the total charge from a given number of electrons, you multiply the number of electrons by the charge of a single electron. This concept can be formalized as \(Q = N \times e\), where \(Q\) is the total charge, \(N\) is the number of electrons, and \(e\) is the elementary charge (negative for electrons: \(-1.602 \times 10^{-19}\) coulombs).

• The previously calculated number of electrons: \(8.233 \times 10^{31}\)
• Charge of one electron: \(-1.602 \times 10^{-19}\) C

This results in a total charge of approximately \(-1.319 \times 10^{13}\) coulombs.
It's important to remember the negative sign indicates the charge is carried by electrons, which are negatively charged particles. Calculating the total charge helps in understanding the systemic and cumulative effect of electrical charges in large collections of particles.