Question

Charge on an electron is$1.6 \times {10^{ - 19}}C$. How many electrons are required to accumulate a charge of one Coulomb?

Answer 1

Hint The total amount of charge possessed by the accumulation of a particle in a system is simply the total amount of charge possessed by one particle multiplied by the number of particles accumulated in the system.
In this solution we will be using the following formula;
$\Rightarrow Q = ne$, where $Q$ is the total amount of charge in coulomb, $n$ is the number of electrons (or other particles) contained in the system, $e$ is the amount of charge possessed by an electron.

Complete step by step answer
In general, when a particle with a non zero charge is within a system, the total amount of charge in that system due to the accumulation of the said charge particles is simply the total amount of charge possessed by one particle multiplied by the number of particle accumulated in the system.This is mathematically given as
$\Rightarrow Q = nq$.
Hence, the total amount of charge possessed by the accumulation of a particle in a system is simply the total amount of charge possessed by one particle multiplied by the number of particles accumulated in the system.
For an electron, the equation can become
$\Rightarrow Q = ne$, where $e$ is the charge of an electron.
Hence, to calculate the number of an electron, we have
$\Rightarrow n = \dfrac{Q}{e}$. Then by inserting known values
$\Rightarrow n = \dfrac{1}{{1.6 \times {{10}^{ - 19}}C}} = 6.25 \times {10^{18}}electrons$
$\therefore n = 6.25 \times {10^{18}}electrons$

Note
For clarity, we shall derive the formula $Q = ne$ from a more general case:
In general, the total amount of charge in a system of different charged particles, is the sum of the individual charges. Mathematically,
$\Rightarrow Q = \sum\limits_{i = 1}^n {{q_{1n}}} + \sum\limits_{i = 1}^n {{q_{2n}}} + ... + \sum\limits_{i = 1}^n {{q_{3n}}}$where${q_1},{q_2},...{q_n}$ are the individual charge of different types of particles, and $n$ is the total number of the particular charge.
Since, particles of the same kind have the same number of charge, then it becomes,
$\Rightarrow Q = n{q_1} + n{q_2} + ... + n{q_3}$.
If only one type of particle is in the system or being considered, then, by eliminating all other particles, we have
$\Rightarrow Q = nq$. Hence, the total amount of charge possessed by the accumulation of a particle in a system is simply the total amount of charge possessed by one particle multiplied by the number of particles accumulated in the system.
For electrons, $q = e$, then
$\Rightarrow Q = ne$.