Question

How many electronic charges form 1 coulomb?
A.$9.1 \times {10^{ - 31}}$
B.$1.6 \times {10^{18}}$
C.$62.5 \times {10^{17}}$
D.$1.76 \times {10^{11}}$

Answer 1

Use the formula for total charge on a system of charges. This formula gives the relation between the total charge on the system of charges, number of the charged particles and charge on a single charged particle. Use the values of total charge given in the question and charge on a single electron to determine total number of electrons.

Formula used:
The total charge is given by
$q = ne$ …… (1)
Here, $q$ is the total charge, $n$ is the number of charged particles and $e$ is the charge on a single charged particle.

Complete step by step solution:
We have given that the total charge is 1 coulomb.
$q = 1\,{\text{C}}$
We have asked the total number of electrons that will have a total charge of 1 coulomb.
The charge on a single electron is $- 1.6 \times {10^{ - 19}}$.
$e = - 1.6 \times {10^{ - 19}}$
We can determine the number of electrons that will have the charge of 1 coulomb using equation (1).
Rearrange equation (1) for the number of electrons.
$n = \dfrac{q}{e}$
Substitute $1\,{\text{C}}$ for $q$ and $1.6 \times {10^{ - 19}}$ for $e$ in the above equation.
$n = \dfrac{{1\,{\text{C}}}}{{1.6 \times {{10}^{ - 19}}}}$
$\Rightarrow n = 0.625 \times {10^{19}}$
$\Rightarrow n = 62.5 \times {10^{17}}$

Therefore, the number of electric charges that will have 1 coulomb charge is $62.5 \times {10^{17}}$.

So, the correct answer is “Option C”.

Note:
The students may think that the charge on a single electron is $- 1.6 \times {10^{ - 19}}$ then why we have substituted the positive value of this charge. As we have to calculate the number of electrons that will have a combined charge of 1 coulomb, the number of electrons required will be negative if the negative value of charge on a single electron is substituted. Hence, the positive value of the charge of a single electron is used in substitution.