Question

write the quantum number of L and M if N=3​

Answer 1

Answer:

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#.