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, m _{l} = 0, m_{s} = +^{1}/_{2}*

*b) n = 4, l = 3, m _{l} = -3, m_{s} = -^{1}/_{2}*

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* = 0,1,2,3,4…,(n−1)

** **

**m_{l} **: Magnetic quantum number (m

For ground state electrons :

if *l* = 0 (s-subshell), then m* _{l}* = 0

if *l* = 1 (p-subshell), then m* _{l}* = -1, 0,+1

if *l* = 2 (d-subshell), then m* _{l}* = -2, -1, 0, +1, +2

if *l* = 3 (f-subshell), then m* _{l}* = -3, -2, -1, 0, +1, +2, +3

** **

**m _{s}** : Unlike n,

Step 2

*a) n = 1, l = 1, m _{l}= 0, m_{s}= +^{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, m*l* = -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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