Question

One coulomb of charge is equivalent to the charge contained in:
(A) $26 \times {10^{19}}electrons$
(B) $6.2 \times {10^{19}}electrons$
(C) $2.65 \times {10^{19}}electrons$
(D) $6.25 \times {10^{19}}electrons$

Answer 1

Hint : We need to calculate the charge on one electron. Then by unitary method, we have to calculate the number of electrons required to form one coulomb of charge.

Complete step by step answer
The SI unit of charge is Coulomb. It is represented by C.
It is known to us that the charge on 1 electron is $1.6{\text{ }} \times {10^{ - 19}}C$ .
$\therefore$ The number of electrons that make up 1 C of charge will be, $\dfrac{1}{{1.6 \times {{10}^{ - 19}}}}$ electrons.
On calculating this gives us a value of $6.25 \times {10^{19}}$ electrons
Hence, one coulomb of charge is equivalent to the charge contained in: $6.25 \times {10^{19}}$ electrons.
Therefore the correct answer is Option D.

Additional Information
The unit Coulomb is named after scientist Charles-Augustin de Coulomb.
According to Coulomb’s Law:
$\Rightarrow F = k\dfrac{{{q_1}{q_2}}}{r}$ where $F$ is the force of attraction between two charges ${q_1}$ and ${q_2}$ where both ${q_1}$ and ${q_2}$ have 1 Coulomb charge each, and are separated by a distance of $r$ , when $r = 1m$
Thus the value of force would be some $8.99 \times {10^9}N$ ,
This force is more than enough to lift five hundred thousand cars of 1ton.
The amount of charge travelling through a lightning bolt is typically around 15 C while the charge that travels through a typical alkaline battery is about 5000 C. The 12V battery in a medium sized car, delivers about 200A for half a second every time we use the starter to turn the engine on.

Note
Alternatively, one coulomb is defined as the charge transported by a current of one ampere per second.
$\Rightarrow 1C = 1A \times 1s$ .
We know that Ampere and second both are base units of SI. Thus the value of Coulomb, which is a derived unit, depends on them. Experimentally ( from Millikan’s experiment) it was observed that when 1 Ampere current was applied, about $6.2 \times {10^{19}}$ electrons passed through a unit area of the cross section in 1 second.
Thus, one coulomb of charge is equivalent to the charge contained in: $= 6.25 \times {10^{19}}$ electrons.