Spin Quantum Number - s	+ ½	- ½
As long as you are consistent, you can have the up arrow either +1/2 or - 1/2.  The down arrow must have the opposite sign of the up arrow.

Quantum Number Limits

n     must be a positive integer

l       0  through  (n - 1)

m     -l through  +l      (this is the letter l  not the number 1)

s      + ½ or - ½

These limits are used to determine if a set of quantum numbers is possible.  Start with the n value, it must be a positive integer.  If it is not a positive integer, the whole set is wrong and you do not have to look at the other values.  

If n is correct, l must be from 0 through (n-1).   Example: if n is 5, l must be either 0, 1, 2, 3, or 4.   If it is, move on to the m value, if it is wrong, the whole set is wrong and you do not have to look at the other values.  

If l is correct, m must be -l through +l.  Example: if l is 2, m must be either -2, -1, 0, +1, or +2.  If it is, move on to the s value, if it is wrong, the whole set is wrong and you do not have to look at the other values. 

If m is correct, s must be either +1/2 or -1/2.  The sign of s is not dependent on any other value.

No other limits apply unless it specifies ground state electrons. If ground state electrons are specified, the quantum numbers must match values for electrons in the ground state.  Example: l will not be greater than 3 for ground state electrons because the ground state does not go past the f subshell.  However, excited electrons do go past the f subshell.

If the directions ask for the quantum numbers for an element, you must give four quantum for each electron.  Fermium has 100 electrons, it would take 400 quantum numbers to give the quantum numbers for the element fermium.  

Many times, you will be asked for the quantum numbers for the last electron (outermost, last subshell, etc.).  This will only require four quantum numbers.   If you are giving these values, first find the electron configuration of the last subshell.  This will allow you to give the n and s values.

To get the m value create the Magnetic Quantum Number charge for the specified subshell.  As long as you use Hund's Rule, the pattern in which you add electrons is not important.  This means there is no definite answer for the m value.  However, you can base the m value on your chart.

If the last electron is an up spin, , the s value is +1/2.  
If the last electron is a down spin, , the s value is -1/2.

Table of Contents

Quantum Number Problems

 Table of Contents

Quantum Number Answers

1.

Are the following possible sets of quantum numbers.    Quantum Number Limits

n

l

m

s

A.

6

4

-1

+½

This is a possible set.  All values fit within the limits.

B.

5

0

0

-½

This is a possible set.  All values fit within the limits.

C.

3

3

-2

+½

l must be between 0 and 2.  This is an impossible set.

D.

5

3

+4

+½

m must be between -3 and +3.   This is an impossible set.

E.

8

7

-6

+½

This is a possible set.  All values fit within the limits.

F.

4

5

-2

-½

l must be between 0 and 3.  This is an impossible set.

G.

5

2

1

-2/3

s must be either +1/2 or -1/2.

H.

6

5

-2

+2/4

+2/4 is the same as +1/2.  This is a possible set.  All values fit within the limits.

I.

1

0

0

-½

This is a possible set.  All values fit within the limits.

J.

2

1

2

+½

m must be between -1 and +1.  This is an impossible set.

2.

Give the quantum numbers for the last electron of the following elements in their ground state. Principal Quantum Number, Orbital Quantum Number, Magnetic Quantum Number, and Spin Quantum Number

A.

iron

The last subshell is 3d6     n = 3  and l = 2         -2 -1 0 +1 +2 The blue electron is the last electron.  m = -2  and s = -1/2

B.

tellurium

The last subshell is 5p4     n = 5     p = 1        -1 0 +1 The blue electron is the last electron.   m = -1  and s = -1/2

C.

argon

The last subshell is 3p6      n = 3   and l = 1        -1 0 +1 The blue electron is the last electron.   m = +1 and s = -1/2

D.

cesium

The last subshell is 6s1       n = 6   and l = 0            The blue electron is the last electron.         m = 0  and s = +1/2     0

E.

gadolinium

The last subshell is 4f7   n = 4  and  l = 3     -3 -2 -2 0 +1 +2 +3 The blue electron is the last electron.    m = +3  and s = +1/2

F.

palladium

The last subshell is 4d8   n = 4  and l = 2        -2 -1 0 +1 +2 The blue electron is the last electron.    m = 0  and s = -1/2

G.

fermium

The last subshell is 5f11   n = 5   and l = 3      -3 -2 -1 0 +1 +2 +3 The blue electron is the last electron.    m = 0  and s = -1/2

H.

nitrogen

The last subshell is 2p3     -1 0 +1 The blue electron is the last electron.    m = +1  and s = +1/2

I.

magnesium

The last subshell is 3s2       n = 3   and l = 0            The blue electron is the last electron.         m = 0  and s = -1/2     0

J.

tungsten

The last subshell is 5d4   n = 5  and l = 2        -2 -1 0 +1 +2 The blue electron is the last electron.    m = +1  and s = +1/2

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