[Barthayn]

How do you calculate the maximum number of electrons with principal quantum number:
a) 1
b) 2

There is more, but I list two because I want to learn how to do it. How do you show your work mathematically and what is is the principal quantum number?

[BetaAmyloid]

The principal quantum number represents the potential energy of the electrons at n position. n can be 1 and higher, the lower n is, the closer the potential energy is to the nucleus of that atom.

The formula n² allows you to calculate the number of orbitals at a specific energy level (principal quantum number).

Since each orbital can contain an up spin electron and a down spin electron, each orbital can hold two electrons. This gives us the formula 2(n²) to calculate the maximum number of electrons within a certain principal quantum number.

So for a):

There is 1 orbital. 1² = 1.
There can be a maximum of 2 electrons when n = 1. 2(1²) = 2.

Hope this helps!