What is the relationship between n and the total number of sublevels in a main energy level?

Answer 1

An electron in an atom is described by four quantum numbers:

• n, the principal quantum number
• l, the azimuthal quantum number
• ml, the magnetic quantum number
• ms, the spin angular momentum quantum number

The principal quantum number is a positive integer: 1, 2, 3, etc.

The azimuthal quantum number is a non-zero integer: 0, 1, 2, 3, etc.

The relationship between n and l is that l must always be strictly less than n. So, for n=1, the only permissible l value is 0. For n=2, l can be 0 or 1. So the number of types of orbitals per level is equal to n.

The relationship between l and ml is that ml is an integer between -l and +l. There are 2l+1 values of ml for any given value of l.

Since each n, l, ml triple specifies an orbital, if you work it out it turns out that there are n2 orbitals with a given principal quantum number n.

Each orbital can have two electrons (ms = +1/2 or -1/2), so there are twice that number of electrons.

Answer 2

The variable n here represents the Principal Quantum Number. This means the maximum number of electrons can be from 2 to 14 in naturally occurring materials

Answer 3

The number of sublevels is equal to n.

Answer 4

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