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

Hint: 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.