# How many orbitals are in each sublevel?

Oct 19, 2015

That depends on the subshell.

#### Explanation:

Electrons that surround an atom's nucleus are distributed on specific energy levels, or shells.

Each shell is made up of a different number of subshells. More specifically, the number of subshells a shell can have increases as you move away from the nucleus.

You can use quantum numbers to illustrate this point.

The principal quantum number, $n$, gives you the energy level, or shell.

Now, the number of subshells is given by the angular momentum quantum number, $l$, which can take values from $0$ to $n - 1$.

This means that you will have

• $n = 1 \implies l = 0 \to$ the first shell only has one subshell, s
• $n = 2 \implies l = 0 , 1 \to$ the second shell has two subshells: s and p
• $n = 3 \implies l = 0 , 1 , 2 \to$ the third shell has three subshells, sp, p, and d
$\vdots$

and so on.

The number of orbitals each subshell contains is given by the magnetic quantum number, ${m}_{l}$, which takes values from $- l$ to $l$.

So, for example, how many orbitals would you say the 2p-subshell has?

Well, the 2p-subshell has $l = 1$, which means that ${m}_{l}$ can be

${m}_{l} = \left\{- 1 , 0 , 1\right\} \to$ the 2p-subshell contains 3 orbitals.

For the 3d-subshell, you know that $l = 2$. This means that ${m}_{l}$ can be
${m}_{l} = \left\{- 2 , - 1 , 0 , 1 , 2\right\} \to$ the 3d-subshell contains 5 orbitals.
So, as a conclusion, you get th number of orbitals per subshell from the principal quantum number, $n$, which in turn gives you the value of the angular momentum quantum number, $l$.
The magnetic quantum number, the ones that tells you exactly how many orbitals you get per subshell, will always take values from $- l$ to $l$, so if you know $l$, you automatically know ${m}_{l}$.