How many orbitals are in each sublevel?

1 Answer
Oct 19, 2015

Answer:

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.

http://www.green-planet-solar-energy.com/electron-details.html

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 -># the first shell only has one subshell, s
  • #n = 2 implies l = 0, 1 -># the second shell has two subshells: s and p
  • #n = 3 implies l = 0, 1, 2 -> # 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 = {-1, 0, 1} -># the 2p-subshell contains 3 orbitals.

How about the 3d-subshell?

For the 3d-subshell, you know that #l = 2#. This means that #m_l# can be

#m_l = {-2, -1, 0, 1, 2} -># 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#.