Question

Calculate the number of electrons constituting one coulomb of charge.
(a). $1.6\times {{10}^{18}}$
(b). $9.6\times {{10}^{18}}$
(c). $3.25\times {{10}^{18}}$
(d). $6.25\times {{10}^{18}}$

Answer 1

- Hint: We know that electrical charges are quantized or we can say that an arbitrary charge will be an integral multiple of quanta or a basic charge. So we can express any coulomb whether it be low or high in magnitude as the integral multiple of the basic charge.

Complete step-by-step solution -

Any type of charge in the universe is an integral multiple of a quanta of charge. The base charge or the quanta is taken as the charge associated with an electron, which is $1.6\times {{10}^{-19}}$coulombs.
Therefore, if we consider one coulomb of charge, it will be an integral multiple of the electronic charge, given by
$\text{q=n }\!\!\times\!\!\text{ e}$
Where q is the one-coulomb charge in our case, e is the electronic charge and n is the multiple or number of electrons we need to find.
$1\text{coulomb}=\text{n}\times 1.6\times {{10}^{-19}}$
$\therefore \text{n}=\dfrac{1}{1.6\times {{10}^{-19}}}$
$\Rightarrow \text{n}=6.25\times {{10}^{18}}$
Therefore, the number of electrons in 1 coulomb of charge is $6.25\times {{10}^{18}}$electrons.

Additional Information:
Electrons play a huge role in every field of science.
Electrons were used to show that particles show wave nature through electron diffraction. Diffraction which is a wave phenomenon was shown by electrons.
Electron was discovered in 1897 by J. J. Thomson.
Robert Millikan was the first scientist who determined the charge of an electron through his famous oil-drop experiment.
J.J. Thomson proposed the plum pudding model, which was the first atomic model after he discovered the electron.

Note: Electrons are one of the fundamental particles which make up an atom. It has a negative charge whose value is $1.6\times {{10}^{-19}}$coulombs. Electrons in classical terms are a particle of mass $9.1\times {{10}^{-31}}$kg.
In the Standard Model of particle physics, electrons belong to the group of subatomic particles called leptons, which are believed to be fundamental or elementary elements. Electrons have the lowest mass of any charged lepton.