Question

How many electrons will constitute $32\;C$ of charge?
A.$2 \times 10^{19}$
B.$2 \times 10^{18}$
C.$2 \times 10^{17}$
D.$2 \times 10^{20}$

Answer 1

Hint: Recall that the charge possessed by a single electron is of the magnitude $1.6 \times 10^{-19}C$. Now, given the total charge, we know that this total charge is equally divided among the number of electrons that constitute the charge. Using this, find out the number of electrons that are required to produce the 32C of charge.
Formula Used:
The number of electrons n carrying a charge q is given by:
$n = \dfrac{q}{e}$

Complete answer:
We know that there are two kinds of electric charges, positive and negative. Like charges repel each other and unlike charges attract. For a current to be produced, there has to be some charge-related motion. This is generally established by the negative charges. The charge carriers of electricity via electric currents are basically electrons travelling through the circuit.
Now, coulomb is the standard unit for the quantity of electric charge or electricity, in the SI system. One coulomb can be defined as the quantity of electricity transported in one second by a current of one ampere, i.e.,
$q = I\times t$, when t=1 $\Rightarrow q=I$
Now, we know that the magnitude of charge possessed by a single electron is $e = 1.6 \times 10^{-19}\;C$
Given that the total charge is $q = 32\;C$, the number of electrons n carrying that charge can be calculated by :
$n = \dfrac{q}{e} = \dfrac{32}{1.6 \times 10^{-19}} = 2\times 10^{20}$

Therefore, the correct choice would be D. $2\times 10^{20}$ electrons.

Note:
Remember that in general, one coulomb of electric charge is equivalent to the charge carried by $6.281 \times 10^{18}$ electrons. Using this information at hand, we can solve the above problem alternatively, where the number of electrons will now be given by:
$n = 32 \times 6.281 \times 10^{18} = 2.009 \times 10^{20} \approx 2 \times 10^{20}$, which yields the same result.