Question

$\dfrac{4}{{25}}$ Coulomb of charge contains _______ electrons
A) ${10^{15}}$
B)${10^{18}}$
C) ${10^{20}}$
D) None of the above

Answer 1

In this solution, we will use the definition of the unit of charge which is the coulomb. The charge of one electron is $1.6 \times {10^{ - 19}}$ Coulomb.

Formula used:
We will use the following formula
$q = ne$ where $q$ is the charge of an object and $e$ is the charge of an electron and $n$is the number of electrons it has.

Complete step by step answer:
We’ve been asked to find the number of electrons in an object containing $\dfrac{4}{{25}}$ Coulomb of charge. We know that the number of electrons in a charged object can be calculated using
$q = ne$
In our case, $q = \dfrac{4}{{25}}$ coulomb. So, the number of electrons will be calculated as
$\dfrac{4}{{25}} = n \times 1.6 \times {10^{ - 19}}$
Dividing both sides by $1.6 \times {10^{ - 19}}$, we get
$n = {10^{18}}$ electrons. This is the number of electrons the charged object will have to have a net charge of $\dfrac{4}{{25}}$ Coulomb.

Hence the correct choice is option (B).

Additional information: The number of electrons that we obtained will be the extra number of electrons that the object will have on its surface. Day to day objects that we see around us are electrically neutral since they have an equal amount of positive and negative electric charge. So, to have a net charge, the object must have extra electrons which are the reason why most day to day objects aren’t electrically charged.

Note: Whenever we come across such questions we should first remember the charge of one electron in Coulombs. Then we can count the number of electrons in a given amount of charge using simple calculations using the formula provided above.