Question

Why Avogadro's number is only 6.022*10 to the power of 23

Answer 1

Because it was chosen to be that way.

The picture is that at some point in chemical history it was realised that atoms are made up of a nucleus containing protons and neutrons, and electrons that have little mass in comparison in ‘shells’ around the outside. (Beware: this picture is a simplification!) It was, at some point found out how heavy these particles were.

Things like the Law of Constant Proportions and the Law of Multiple Proportions were also known, the first stating that a fixed mass ratio of two different compounds would only be able to react (with extraneous mass of one compound remaining as unreacted residue) and the second stating that if compounds or elements reacted in different ways, the mass proportions would be integer ratios of each other. So obviously the idea of particles which have a mass was correct.

Now how do we ‘count atoms’? Similar to ‘counting sugar’. A recipe won’t tell you to mix xx sugar crystals with butter, eggs and flour to make a cake, it will state a value in grams (or ounces, if you’re in that part of the world). It is common to do that for large amounts where you can’t count the individuals. Taken to atoms, this meant that at one point in history it was defined to take the amount that weighs z gz g of element YY as a value for ‘one count’ — one mole. That definition was changed and currently, 12 g12 g of 12C12C atoms is the number of atoms in a mole.

Because of these choices, the Avogadro constant now had a fixed value and could be calculated. It was calculated to be the well-known 6.022×10236.0221023. Had a different choice been made, it would have been a different number.

Also, this is due to change. The SI unit system is to be modified at some point in the future. From thence, the value of NANA will be fixed much like the speed of light in vacuum are fixed. The definition of the mole will then depend on the fixed constant.