$6×10^{18}$ electrons
Understanding Charge and Electrons
The question asks us to find the number of electrons equivalent to one coulomb (C) of charge. We know that charge is quantized, meaning it exists in discrete units. The fundamental unit of charge is the charge of a single electron (or proton).
Calculating Electron Quantity for 1 Coulomb
The charge of a single electron ($e$) is approximately $1.602 \times 10^{-19}$ Coulombs.
To find the number of electrons ($n$) that make up one coulomb ($Q$) of charge, we can use the formula:
$ Q = n \times e $
Rearranging the formula to solve for $n$:
$ n = \frac{Q}{e} $
Substitute the given values:
- $Q = 1 \, \text{C}$
- $e \approx 1.602 \times 10^{-19} \, \text{C}$
Now, perform the calculation:
$ n = \frac{1 \, \text{C}}{1.602 \times 10^{-19} \, \text{C/electron}} $
$ n \approx 6.24 \times 10^{18} \, \text{electrons} $
Comparing with Options
The calculated value is approximately $6.24 \times 10^{18}$ electrons. Comparing this to the given options:
- Option 1: $6 \times 10^6$ electrons
- Option 2: $6 \times 10^{18}$ electrons
- Option 3: $6 \times 10^{12}$ electrons
- Option 4: $6 \times 10^{10}$ electrons
Option 2, $6 \times 10^{18}$ electrons, is the closest approximation to our calculated value.
Important Questions from Electric Charge
Which of the following expressions correctly represents the SI unit of electric charge, the Coulomb ($C$), in terms of other fundamental or derived SI units?
- Suppose every second 1016 electrons come out of a body and move to another body, then the time is required to get a total charge of 3.2 C on the other body is:
- An object is found to have a net negative charge of $-5 \text{ nC}$. How many excess electrons are present on the object? (Given: elementary charge $e = 1.6 \times 10^{-19} \text{ C}$)
- A metallic sphere, initially possessing a positive electric potential relative to the Earth, is connected to the Earth by a conducting wire. Which of the following accurately describes the primary charge movement that occurs until equilibrium is reached?
Two point charges, $Q_1 = +3 \mu C$ and $Q_2 = -8 \mu C$, are placed at a certain distance apart. They attract each other with a force of $48 N$. If each charge is given an additional charge of $+6 \mu C$, what will be the magnitude and nature of the new force between them?
