Question

Calculate the number of electrons constituting $1\;Coulomb$ of charge?

Answer 1

The number of electron is calculated by using the formula of quantization of charge, quantization of charge is a basic principle which states that any body can only have charge $Q$ which is always an integral multiple $n\;\;\left( {where\;n = 0,1,2,3......} \right)$ of basic charge $e$ , where basic charge $e$ is the charge on one electron.
Mathematically, we can write it as: $Q = ne$

Formula Used:
Quantization of charge:
$Q = ne$
Where $Q$ is the total amount of charge; $n$ is the number of charges (here number of electrons) and $e$ is charged on one electron.

Complete answer:
Given:
Total amount of charge $Q = 1\;Coulomb$
And Charge on one electron $e = 1.602 \times {10^{ - 19}}\;Coulomb$
We know that the charge on one electron is given as: $e = 1.602 \times {10^{ - 19}}\;Coulomb$
Substituting the value of $Q = 1\;Coulomb$ and$e = 1.602 \times {10^{ - 19}}\;Coulomb$, in given formula of quantization of charge:
$Q = ne$
We get,
$1\;Coulomb = n \times \left( {1.602 \times {{10}^{ - 19}}\;Coulomb} \right) \\\ n = \dfrac{{1\;Coulomb}}{{1.602 \times {{10}^{ - 19}}\;Coulomb}} \\\ n = 6.24 \times {10^{18}}\;electrons \\\$

Therefore, $1\;Coulomb$ of charge is constituted by $6.24 \times {10^{18}}\;electrons$.

Additional Information:
1 coulomb of charge is defined as the amount or quantity of charge transferred by an electric current of one ampere in one second given by using the formula of electric current $I$ as follows:
$I = \dfrac{Q}{t} \\\ or\;Q = I \times t \\\$
So when $I = 1\;Ampere$ and $t = 1\;\sec$, we have,
$Q = 1\;A \times 1\;s \\\ Q = 1\;Coulomb \\\$
Remember that the transfer of charge from one body to other also follows quantization of charge, but in all the processes of charge transfer or flow of current we simply ignore it because the basic charge is so small that in a single coulomb of charge $6.24 \times {10^{18}}\;$ times of basic charge $e$ is transferred which is a very big number so it is wise to ignore quantization of charge in most of the processes.

Note:
Alternative method:
We can find the number of electron constituting $1\;Coulomb$ of charge, by using unitary method as follows:
$1.602 \times {10^{19}}Coulomb$ Charge is constituted by $1$ electron
Then, $1\;Coulomb$ charge is constituted by $\dfrac{1}{{1.602 \times {{10}^{ - 19}}}}\;electrons$
Thus, $1\;Coulomb$ charge is constituted by $6.24 \times {10^{18}}\;electrons$