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The mass of an electron is an extremely small quantity. In scientific notation, the mass of a single electron is approximately \(9.109 \times 10^{-31} \text{ kg}\). This tiny mass is fundamental in understanding calculations involving large quantities of electrons. When dealing with total mass, such as in the problem where we have \(75 \text{ kg}\) of electrons, the small mass of each individual electron becomes crucial. By dividing the total mass by the mass of a single electron, we can find the total number of electrons.

To find the number of electrons in a given mass, we use the formula: \[ \text{number of electrons} = \frac{\text{Total mass}}{\text{Mass of one electron}} \].

For instance, if we have \(75 \text{ kg}\) of electrons, and knowing that one electron's mass is \(9.109 \times 10^{-31} \text{ kg}\), the calculation will be: \[ \frac{75.0 \text{ kg}}{9.109 \times 10^{-31} \text{ kg/electron}} \].

This gives us approximately \(8.23 \times 10^{31} \text{ electrons}\). This number represents how many electrons are in \(75 \text{ kg}\). Understanding this step is crucial before moving on to calculate the total charge.

The charge of a single electron is known to be negative and is specifically \(-1.602 \times 10^{-19} \text{ C}\).

This value is fundamental in physics and helps in calculating the total or net charge of a system containing multiple electrons. When dealing with large quantities of electrons, recognizing this constant charge value allows for straightforward charge calculations. Multiply the total number of electrons by this charge per electron, and you'll get the overall total charge.

Coulombs (C) is the SI unit of electric charge. The total charge in any system can be expressed in coulombs.

For example, if we have approximately \(8.23 \times 10^{31} \text{electrons}\), each with a charge of \(-1.602 \times 10^{-19} \text{ C}\), we use multiplication to find the total charge. The formula is: \[ \text{total charge} = \text{number of electrons} \times \text{charge of one electron} \]

Calculating, we get: \[ (8.23 \times 10^{31}) \times (-1.602 \times 10^{-19} \text{ C}) \]

Which gives us approximately \(-1.32 \times 10^{13} \text{ C}\) as the total charge. Understanding how to express charges in coulombs is essential for many physics and electrical engineering problems.