## Background

In chemistry, it’s helpful to quantify the **number of something **that is being measured. It may be a solid, a liquid or a gas, but it’s likely matter that consists of molecules, which are formed from atoms. And there are many, many atoms even in a small container such as a cup of water. In fact, the number is so big, you multiply a million times a million times a million times a million to get to a number in the range of the count of atoms in the cup. Therefore, the mole is used to simplify calculations of a collection of particles (molecules, atoms, ions, etc). One mole is 6.022 x 10^{23}. It’s also known as Avogadro’s number.

**The mole – **a representation of a very large number of particles (6.022 x 10^{23})

In 1834, Michael Faraday found that the mass of a substance altered proportional to the charge in electrolysis, in what became Faraday’s laws of electrolysis. Although the mole and Avogadro’s constant were not known at the time, it eventually established a key relationship between the Faraday constant (F), the elementary charge (e_{e}) and Avogadro’s constant (N_{A}). But it doesn’t explain why the mole is related to charge.

## Explanation

The mole may be the number of granules that occupy the space between a proton and electron in ground state hydrogen that allow the transfer of wave energy, that is known as charge. In energy wave theory, charge is measured as longitudinal wave amplitude, and a *substance* must be waving for this to occur. Faraday detected the relationship between charge and this number (now known as Avogadro’s number). But there’s another relationship with three other constants in physics that lead to more evidence that this could be the physical structure between the charged particles. The other three constants are: the Bohr radius, Planck length and Euler’s number as it will be explained.

### Bohr Radius

The Bohr radius (a_{0}) is the most probable location of the electron in orbit around a single proton – ground state hydrogen.

### Planck Length

The Planck length is a very small unit of length and part of Planck unit system. It’s incredibly small. If the Planck length is the radius of a sphere, the electron’s radius by comparison is 10^{20} larger. That order of magnitude is like comparing the radius of a large beach ball to the radius of the Milky Way galaxy.

**Why radius?** A description of a sphere with Planck radius is used because there are similarities in the *classical forms* of the equations for the electron’s mass and Planck mass. *Note: Planck length in the denominator similar to the electron’s radius in the same denominator position for the two equations found on those pages. *

### Euler’s Number

Euler’s number, otherwise known as the mathematical constant (e), is the base of the natural logarithm. It is an important number that appears in many physics equations, including ones for growth and decay, and also in waves.

### Avogadro – Bohr – Planck – Euler Relationship

Faraday found the relationship between charge and what would become Avogadro’s number. But there’s another relationship that may give more meaning to the number and the mechanism for charge. If the following assumptions are made:

- Granules oscillate, transferring energy spherically and declining in wave amplitude from the source as seen in charge.
- A granule has a radius of Planck length (l
_{P}); therefore the diameter is 2l_{P}. - At equilibrium, the separation distance of each granule is the diameter times Euler’s number (2l
_{P}* e).

**Potential Diameter and Separation Distance of Granules**

Using these assumptions, the number of granules between a single proton and electron can be calculated. Since this is ground state hydrogen, the most probable distance of the electron is the Bohr radius.

**Granules Responsible for Charge in Hydrogen – **not to scale

**How many granules** would there be at this size and separation distance in hydrogen?

**6.022 x 10 ^{23 }**–

**Avogadro’s number – One mole**

**Video – What is a Mole?**

The *What is a Mole* video explains the relationship of Avogadro’s number and charge.