charge - Why are there $1 / 1.602176634 times 10^{-19}$ electrons in a coulomb?

Why that exact number of electrons in one coulomb? who decided it? there is nothing wrong with the number, it just seems slightly messy. Why didn't the scientific community just settle on an easier number, such as $1\times10^{-19}$ for example?

Answer

The charge of $1C$ was derived from the definition of Ampere. If you look at the SI units, you'll check that, surprisingly, intensity of current is a basic unit, whereas charge is a derived quantity. This is a bit weird, because charge is seen as "more fundamental" than current, current is "charge per unit time".

So why is it? Because measuring the charge of one electron is very hard (electrons are extremely tiny), whereas currents are easily measurable.

Consider two straight and infinite parallel wires. The force exerted between the two per unit length is

$$f=\frac{\mu_0 I_1 I_2}{2\pi r}$$

Where $I$ are the intensities, $f$ is the force per unit length, $r$ is the distance between the wires and $\mu_0$ is a constant of known value. If we make $I_1=I_2=I$, we get

$$ f=\mu_0 I^2 / 2\pi r$$

So $I=\sqrt {2\pi r f /\mu_0}$

If we introduce the SI units: $r=1m, f=1N/m$, we get the definition of one ampere.

And then we define 1 coulomb to be $1C=1A\cdot 1s$.

So the value of $1C$ was derived first. Then, Millikan discovered how many coulombs was the charge of an electron.

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EDIT for clarifiaction:

This is the historical process that led to the definition of one coulomb of charge.

The Ampere definition has recently been modified.

This answer explains the process for which: 1) The formula of the magnetic force between two straight current-carrying conductors was found. $f\propto I^2$ 2) This was used to define the unit of intensity of current. 3) Then the defintion of charge is striaghtforward. $1C=1A\cdot1s$. It was done like this because measuring currents is easier than measuring charges.

4) Millikan found the charge of the electron. He did it using the existing unit: coulombs. It happened to be $\sim 1.6\cdot10^{-19}$.

5) The definition of Ampere has recently been changed, in order to make it less dependent. However, this change has been such that the figure does not change, because we do not want all books and instruments to become wrong.