Can n = 2, l = 2 describe an orbital?

Oct 5, 2016

No, it cannot.

Explanation:

As you know, we use four quantum numbers to describe the position and spin of an electron inside an atom.

The three quantum numbers given to you describe the location of the electron inside an atom.

Now, the thing to notice here is that the value of the angular momentum quantum number, $l$, depends on the value of the principal quantum number, $n$, as given by

$l = \left\{0 , 1 , 2 , \ldots , n - 1\right\}$

This means that $l$ must be smaller than $n$ in order for the value to be valid.

In your case, $n = 2$ would allow only two possible values for $l$

$n = 2 \implies l = \left\{0 , 1\right\}$

Since $l = 2$ is not a valid value for the angular momentum quantum number when the principal quantum number is equal to $2$, the said given to you cannot describe an electron inside an atom.