How many coulombs of charge do 25 × 10 31 electrons possess?
40 × 10 12 C
Coulombs Calculation: Total Charge of Electrons
To determine the total charge possessed by a given number of electrons, we use a fundamental principle of electrostatics: the total charge is the product of the number of charge carriers and the charge of a single charge carrier. In this specific problem, the charge carriers are electrons.
Understanding the properties of an electron, particularly its elementary charge, is crucial for solving this type of problem.
Electron Charge Fundamentals
An electron is a subatomic particle that carries a negative elementary electric charge. The magnitude of this elementary charge, often denoted by \(e\), is a fundamental physical constant.
- The charge of a single electron \(e\) is approximately \(1.6 \times 10^{-19}\) Coulombs (C).
- This value represents the smallest unit of charge that can exist freely.
Given Data for Charge Problem
Let's identify the information provided in the question:
- Number of electrons (\(N\)) = \(25 \times 10^{31}\) electrons
- Charge of one electron (\(e\)) = \(1.6 \times 10^{-19}\) C (This is a known constant)
Formula for Total Electric Charge
The total charge (\(Q\)) is calculated using the following formula:
\[Q = N \times e\]
Where:
- \(Q\) is the total charge in Coulombs (C).
- \(N\) is the number of electrons.
- \(e\) is the charge of a single electron in Coulombs (C).
Step-by-Step Charge Determination
Now, let's substitute the given values into the formula and perform the calculation:
- Substitute the values:
\[Q = (25 \times 10^{31}) \times (1.6 \times 10^{-19} \text{ C})\]
- Separate the numerical and exponential terms:
\[Q = (25 \times 1.6) \times (10^{31} \times 10^{-19}) \text{ C}\]
- Multiply the numerical terms:
\[25 \times 1.6 = 40\]
- Combine the exponential terms using the rule \(a^m \times a^n = a^{m+n}\):
\[10^{31} \times 10^{-19} = 10^{(31 - 19)} = 10^{12}\]
- Combine the results:
\[Q = 40 \times 10^{12} \text{ C}\]
Comparing Calculated Charge with Options
The calculated total charge is \(40 \times 10^{12}\) C. Let's compare this with the provided options:
| Option | Charge Value |
|---|---|
| 1 | \(80 \times 10^{12}\) C |
| 2 | \(4 \times 10^{12}\) C |
| 3 | \(40 \times 10^{12}\) C |
| 4 | \(8 \times 10^{12}\) C |
The calculated charge of \(40 \times 10^{12}\) C perfectly matches the third option.
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