Question

Calculate the number of electrons which constitute one coulomb of charge.

Answer 1

- Hint- Here, we will proceed by defining the term electric charge along with the general relation between electric current and electric charge. Then, we will be using the law of quantization of charge to find the required number of electrons.
Formula Used- Electric current = ${\displaystyle \frac{\text{Electric charge}}{\text{Time}}}$ and Q = ne where Q represents charge, n represents number of electrons and e represents charge of 1 electron.

Complete step-by-step solution -

Electric charge is a physical property of matter that causes it to experience a force when kept in an electromagnetic field. Positive and negative are the two types of electric charges, commonly carried by charge carriers which are protons and electrons. S.I unit of electric charge is Coulomb.
As we know that electric current is defined as charge per unit time.
i.e., Electric current = ${\displaystyle \frac{\text{Electric charge}}{\text{Time}}}$ where S.I unit of electric current is Amperes and that of time is seconds.
One coulomb of charge is equal to the quantity of charge that passes through a cross-section of a conductor in one second, given that a current of one ampere flows through the conductor.
We know that the charge on any electron is given by e = $-1.6\times {10}^{-19}$ Coulomb
Here, we have to find the number of electrons which will together give a charge of 1 Coulomb.
Also we know that according to quantization of charge (i.e., charge in the form of packets),
Charge Q = ne where n represents the number of electrons and e represents charge on 1 electron
Here, Q = 1 Coulomb and e = $1.6\times {10}^{-19}$ Coulomb (we have neglected the negative sign because it only represents that the charge on an electron is negative i.e., taking only magnitude).
By putting these values in the law of quantization of charge, we get
$$\begin{gathered} \Rightarrow 1=n\left(1.6\times {10}^{-19}\right) \\ \Rightarrow n={\displaystyle \frac{1}{1.6\times {10}^{-19}}} \\ \Rightarrow n=0.625\times {10}^{19} \\ \Rightarrow n=625\times {10}^{16} \end{gathered}$$
Therefore, a total of $625\times {10}^{16}$ electrons will constitute one coulomb of charge.

Note- There are basically two types of electric charges i.e., positive charge and negative charge. Neutral charges just refers to the region between positive and negative charges. Like charges repel each other (i.e., two positive charges and two negative charges will repel each other) whereas unlike charges attract each other (i.e., one positive and one negative charge will attract each other).