Calculating Electrons in One Coulomb Charge

To find the number of electrons equivalent to one Coulomb (C) of charge, we use the fundamental relationship between electric charge and the elementary charge of an electron.

Key Concepts

• Charge (Q): Measured in Coulombs (C). In this problem, Q = 1 C.
• Elementary Charge (e): The magnitude of the electric charge carried by a single electron (or proton). Its approximate value is \(1.602 \times 10^{-19}\) C.
• Number of Electrons (n): The total charge is the number of electrons multiplied by the charge of one electron.

Formula and Calculation

The relationship is given by the formula:

\(Q = n \times e\)

To find the number of electrons (n), we rearrange the formula:

\(n = \frac{Q}{e}\)

Substituting the given values:

\(n = \frac{1 \text{ C}}{1.602 \times 10^{-19} \text{ C/electron}}\)

Performing the calculation:

\(n \approx \frac{1}{1.6 \times 10^{-19}}\)

\(n \approx \frac{1}{1.6} \times 10^{19}\)

\(n \approx 0.625 \times 10^{19}\)

\(n \approx 6.25 \times 10^{18} \text{ electrons}\)

Conclusion

The calculated value of approximately \(6.25 \times 10^{18}\) electrons is closest to the option \(6 \times 10^{18}\).

Therefore, one Coulomb charge is equal to the charge of about \(6 \times 10^{18}\) electrons.