Question

Out of the following set of quantum numbers, choose the one which does not exist.


n = 1, = 0, m = 0, s =


n = 4, = 0, m = 0, s =


n = 3, = 3, m = 0, s =


n = 3, = 0, m = 0, s =

Answer 1

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All you have to do here is to use the definitions of the four quantum numbers that we use to describe the location and spin of an electron inside an atom.
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Notice that the magnetic quantum number, ml, depends on the value of the angular momentum quantum number, l, as described by

ml={−l,−(l+1),...,−1,0,1,...,(l+1),l}

This tells you that the absolute value of the magnetic quantum number cannot exceed the value of the angular momentum quantum number

|ml|≤l

For option C), you have l+2 and ml=−3. This cannot take place because

|−3|≤2

In other words, the d subshell, which is described by l=2, can only hold a total of 5orbitals, since

ml={−2,−1,0,1,2}→ for the d subshell

Therefore, you can say that

n=5,l=2,ml=−3,ms=−12

is not a valid set of quantum numbers.
The other three sets of quantum numbers are indeed valid.

n=1,l=0,ml=0,ms=−12

Describes an electron located on the first energy level, in the s subshell, in the 1s orbital, that has spin-down

n=3,l=2,ml

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