Question

How many electronic charges form 1 coulomb?

$$A.{\text{ }}9.1 \times {10^{ - 31}} \\\ B.{\text{ }}1.6 \times {10^{18}} \\\ C.{\text{ }}62.5 \times {10^{17}} \\\ D.{\text{ }}1.76 \times {10^{11}} \\\$$

Answer 1

Hint- In order to find the number of electronic charges we will use the charge of electron which is given as $e = 1.6 \times {10^{ - 19}}C$ and we will proceed further by using the formula relating the total charge and the number of charged particles.

Formula used- $q = ne$

Complete step-by-step answer:

We know the charge is negative on an electron, so it is negative $e = 1.6 \times {10^{ - 19}}C$
We need to quantify the number of electrons which constitute one charging coulomb.
Total charge required 1 Coulomb.
Therefore $q = 1C$
We know the formula relating total charge and the number of charged particle is given as:
$q = ne \\\ \Rightarrow n = \dfrac{q}{e}.........(1) \\\$
Where q is the net charge, n is the number of charged particles and e is the charge of each particle.
Substituting the values in equation (1) we get:

$$\because n = \dfrac{q}{e} \\\ \Rightarrow n = \dfrac{{1C}}{{1.6 \times {{10}^{ - 19}}C}} \\\ \Rightarrow n = \dfrac{{1 \times {{10}^{19}}}}{{1.6}} \\\ \Rightarrow n = \dfrac{{100 \times {{10}^{17}}}}{{1.6}} \\\ \Rightarrow n = 62.5 \times {10^{17}} \\\$$

Hence, $62.5 \times {10^{17}}$ electronic charges form 1 coulomb.
So, the correct answer is option C.

Note- One coulomb is equal to the amount of charge from a current of one ampere flowing for one second. One coulomb is equal to the charge on $62.5 \times {10^{17}}$ electrons. The charge on 1 electron is $e = 1.6 \times {10^{ - 19}}C$ of negative charge. Students must remember the value of charge present on one electron to solve such problems. Also $e = 1.6 \times {10^{ - 19}}C$ of positive charge is present on one proton.