Question

The number of electrons present in $1C$ of charge is ______.
A) $4.25\times {10}^{18}$
B) $6.25\times {10}^{18}$
C) $3.25\times {10}^{18}$
D) $2.25\times {10}^{18}$

Answer 1

Hint: We are given with a charge of $1C$ . To find the number of electrons present, we will use the expression of quantization of charge which will give a relation between charge on an electron, number of electrons. Using the given information, we will calculate the number of electrons.

Complete step by step solution:
The charge is given in Coulomb and we know the expression of quantization of charge is given by,
$Q=ne$
Here, Q is the charge on the object
n is the number of electrons present.
And e is the charge on an electron.
The charge is quantized therefore, n will be an integer.
Using the above equation, we have
$n={\displaystyle \frac{Q}{e}}$
Substituting the value of charge on an electron $e=1.6\times {10}^{-19}C$ and $Q=1C$ in the above equation, we get
$n={\displaystyle \frac{1}{1.6\times {10}^{-19}}}$
$\Rightarrow n=6.25\times {10}^{18}$
Therefore, the number of electrons is $6.25\times {10}^{18}$

Thus, option B is the correct option.

Additional Information:
Quantized means anything which is available in fixed amounts. After much effort by physicists, we have come to know that the charge is quantized means charge is available in multiples of some number. This implies that we cannot have the value of charge as half coulomb or one-fourth of coulomb as n in the equation is an integer.

Note: Quantization of charge is the principle which states that charge on any object is the integral multiple of an elementary charge. Thus, charge on an object can be exactly zero or one or two but not in decimals. The charge on an electron is taken for calculating the total charge. Also, the magnitude of charge on an electron and proton is the same.