Question
Asked Jan 30, 2020
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Which of the following sets of quantum numbers are NOT allowed? (There may be more than one correct answer.

 a) n = 1, l = 1, ml = 0, ms = +1/2

b) n = 4, l = 3, ml = -3, ms = -1/2

c) n = 4, l = 0, ml = 0, ms = +3/2
 
d) n = 2, l = 1, ml = 0, ms = +1/2
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Expert Answer

Step 1

n : The principal quantum number, n, designates the principal electron shell. n can be any positive integer starting at 1, n = 1 designates the first principal shell (the innermost shell), n = 2 designates the second principal, n = 3 indicates the third principal shell, n = 4 indicates the fourth principal shell, and so on.

n = 1,2,3,4…

 

l : The orbital angular momentum quantum number l determines the shape of an orbital. Each value of l indicates a specific s (l = 0), p (l = 1), d (l = 2), f (l = 3) subshell (each unique in shape.) The value of l is dependent on the principal quantum number n. Unlike n, the value of l can be zero. It can also be a positive integer, but it cannot be larger than one less than the principal quantum number (n-1):

l = 0,1,2,3,4…,(n−1)

 

ml : Magnetic quantum number (ml) refers to the number of orbitals per subshell. It is given as -l to +l.

For ground state electrons :

if l = 0 (s-subshell), then ml = 0

if l = 1 (p-subshell), then ml = -1, 0,+1

if l = 2 (d-subshell), then ml = -2, -1, 0, +1, +2

if l = 3 (f-subshell), then ml = -3, -2, -1, 0, +1, +2, +3

 

ms : Unlike n, l, and ml, the electron spin quantum number ms does not depend on another quantum number. It designates the direction of the electron spin and may have a spin of +1/2, represented by ↑, or –1/2, represented by ↓.

Step 2

a) n = 1, l = 1, ml= 0, ms= +1/2

When n = 1, l = 0 to (n-1) = 0

l can only be 0 not 1.

Therefore, this set of quantum numbers are NOT allowed.

Step 3

b) n = 4, l = 3, ml= -3, ms= -1/2

When n = 4, l = 0 to (n-1) = 0 to 3 = 0,1,2,3

When l = 3, ml = -3, -2, -1, 0, +1, +2, +3

And ms is always either -1/2 or +1/2

Therefore, this set of quantum numbers are allowed.

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