Question

One coulomb is equivalent to the charge contained in nearly

• A. \( 0.6 \times 10^{18} \) electrons
• B. \( 1.6 \times 10^{18} \) electrons
• C. \( 6.25 \times 10^{18} \) electrons
• D. \( 16 \times 10^{18} \) electrons

Hint:

Remember the value of the elementary charge \( e \approx 1.6 \times 10^{-19} \) C. To find the number of electrons in one coulomb, take the reciprocal of this value.

Answer 1

The Correct Option is C

Step 1: Recall the charge of a single electron.
The elementary charge, which is the magnitude of the charge of a single electron (or proton), is approximately \( e = 1.602 \times 10^{-19} \) Coulombs (C). Step 2: Determine the number of electrons required to make one coulomb of charge.
Let \( n \) be the number of electrons whose total charge is equal to 1 Coulomb. The total charge of \( n \) electrons is given by \( n \times e \). We want this total charge to be equal to 1 C: \[ n \times |e| = 1 \text{ C} \] \[ n \times (1.602 \times 10^{-19} \text{ C}) = 1 \text{ C} \] Step 3: Solve for \( n \). \[ n = \frac{1 \text{ C}}{1.602 \times 10^{-19} \text{ C}} \] \[ n = \frac{1}{1.602} \times 10^{19} \] \[ n \approx 0.6242 \times 10^{19} \] Step 4: Express the result in the required format.
We can rewrite the number of electrons in scientific notation: \[ n \approx 6.242 \times 10^{-1} \times 10^{19} \] \[ n \approx 6.242 \times 10^{18} \] Comparing this value with the given options, the closest value is \( 6.25 \times 10^{18} \) electrons.