What values of l, m_l, and m_s are possible for n = 3?

2 Answers
Jan 18, 2015

Well, your set of quantum numbers is not "allowed" for a particular electron because of the value you have for "l", the angular momentum quantum number.

The values the angular momentum quantum number is allowed to take go from zero to "n-1", "n" being the principal quantum number.

So, in your case, if "n" is equal to 3, the values "l" must take are 0, 1, and 2. Since "l" is listed as having the value 3, this puts it outside the allowed range.

The value for m_l can exist, since m_l, the **magnetic quantum number, ranges from -"l", to "+l".

Likewise, m_s, the spin quantum number, has an acceptable value, since it can only be -"1/2" or +"1/2".

Therefore, the only value in your set that is not allowed for a quantum number is "l"=3.

Jan 18, 2015

There are 4 quantum numbers which describe an electron in an atom.
These are:

n the principal quantum number. This tells you which energy level the electron is in. n can take integral values 1, 2, 3, 4, etc

l the angular momentum quantum number. This tells you the type of sub - shell or orbital the electron is in. It takes integral values ranging from 0, 1, 2, up to (n-1).

If l = 0 you have an s orbital.
l=1 gives the p orbitals
l=2 gives the d orbitals

m is the magnetic quantum number. For directional orbitals such as p and d it tells you how they are arranged in space. m can take integral values of -l ............. 0.............+l.

s is the spin quantum number. Put simply the electron can be considered to be spinning on its axis. For clockwise spin s= +1/2. For anticlockwise s = -1/2. This is often shown as uarr and darr.

In your question n=3. Let's use those rules to see what values the other quantum numbers can take:

l=0, 1 and 2, but not 3.This gives us s, p and d orbitals.

If l = 0 m = 0. This is an s orbital
If l = 1, m = -1, 0, +1. This gives the three p orbitals. So m = 0 is ok.
If l = 2 m = -2, -1, 0, 1, 2. This gives the five d orbitals.

s can be +1/2 or -1/2.

These are all the allowed values for n=3

Note that in an atom, no electron can have all 4 quantum numbers the same. This is how atoms are built up and is known as The Pauli Exclusion Principle.