Well, your collection of quantum numbers is no "allowed" for a details electron because of the worth you have for #"l"#, the angular momentum quantum number.

The values the angular momentum quantum number is permitted to take go from zero come #"n-1"#, #"n"# gift the principal quantum number.

You are watching: How many different values of l are possible for an electron with principal quantum number n = 3?

So, in your case, if #"n"# is same to 3, the values #"l"# should take room 0, 1, and also 2. Because #"l"# is noted as having the worth 3, this put it external the enabled range.

The value for #m_l# deserve to exist, because #m_l#, the **magnetic quantum number, arrays from #-"l"#, to #"+l"#.

Likewise, #m_s#, the spin quantum number, has actually an acceptable value, because it deserve to only be #-"1/2"# or #+"1/2"#.

Therefore, the just value in your collection that is not enabled for a quantum number is #"l"=3#.

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Michael
jan 18, 2015

There room 4 quantum number which define an electron in one atom.These are:

#n# the principal quantum number. This speak you which energy level the electron is in. #n# deserve to take integral worths 1, 2, 3, 4, etc

#l# the angular momentum quantum number. This speak you the kind of below - shell or orbit the electron is in. The takes integral values varying from 0, 1, 2, as much as #(n-1)#.

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

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

#s# is the turn quantum number. Put merely the electron have the right to be thought about to be spinning ~ above its axis. For clockwise turn #s#= +1/2. Because that anticlockwise #s# = -1/2. This is often displayed as #uarr# and also #darr#.

In your inquiry #n=3#. Let"s use those rules to watch what worths the various other quantum numbers have the right to take:

#l=0, 1 and 2#, yet not 3.This provides us s, p and also d orbitals.

If #l# = 0 #m# = 0. This is an s orbitalIf #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 5 d orbitals.

#s# deserve to be +1/2 or -1/2.

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These are all the enabled values for # n=3#

Note that in one atom, no electron deserve to have all 4 quantum numbers the same. This is how atoms are collected and is recognized as The Pauli exclusion Principle.