# How many f orbitals are present in n=3?

Nov 6, 2015

Zero.

#### Explanation:

As you know, the number of orbitals you get per energy shell is given by the equation

color(blue)("no. of orbitals" = n^2)" ", where

$n$ - the energy level, also known as energy shell

Now, the third energy level, characterized by $n = 3$, will have a total of

$\text{no. of orbitals} = {3}^{2} = 9$

orbitals. But how many of these orbitals will be f-orbitals?

As it turns out, none.

Each energy level contains a number of subshells given by the angular momentum quantum number, $l$, which can take values ranging from $0$ to $n - 1$.

$l = 0 , 1 , 2 , \ldots , n - 1$

This means that the third energy level will have a total of three subshells

• one s-subshell, for which $l = 0$
• one p-subshell, for which $l = 1$
• one d-subshell, for which $l = 2$

The f-subshell, for which $l = 3$, doesn't come around until the fourth energy level, $n = 4$.

Therefore, you can say that the third energy level contains no f-orbitals since it contains no f-subhsell.