Quantum Numbers

Quantum Numbers

In solving quantum numbers we always should always use specific representations for determining the quantum numbers of an electron. These specific representations are n, l, ml, ms.

Principal quantum numbers

•  Represented by “n”.
• You can identify it by looking at the energy level or shell where the last electron of a specific element is located.

For example: 2p⁶, the principal quantum number is 2 because 2p⁶ is located at the 2^nd shell.

Azimuthal Quantum number

• represented by “l”.
• You can identify it by looking at the subshell. Subshells are the s, p, d and f from the electron configuration.

The subshells have different kinds of shapes.

S is a sphere shaped area, 

P is a dumbbell shaped area, 

D is a clover shaped area, and 

F is a fundamental shaped area. 

• We also have representations for subshells s, p, d and f when looking for the azimuthal quantum number.

s= 0

p= 1

d= 2

f= 3

For example: 2p⁶, its subshell is p and therefore its azimuthal quantum number is 1.

The magnetic quantum number

• Represented by “ml”.
• It is somehow connected with the azimuthal quantum number.
• You can identify it by looking at the compartment of the element. Every subshell has different numbers of compartments.

                      S= 1 compartment,

                      P= 3 compartments  

                      D= 5 compartments

                     F=  7 compartments

• The center of the compartment is always zero, so if you’re going to look at the left side it means that it is negative and if you are going to look at the right side it means that it is positive.

For example: 2p⁶, its magnetic quantum number is 1 because the 6^th electron of 2p⁶ is located at the 3^rd compartment.

Magnetic Spin

•  The representation for magnetic spin is “ms”.
• Inside of every compartment, there are 2 arrows but their direction is opposite:

               

1.  Upwards which means that arrow is going to a clockwise direction and it denotes +1/2 or having a positive spin.
2. Downwards which means that arrow is going to a counter clockwise direction and it denotes -1/2 or having a negative spin.

• These 2 spins are called magnetic spins

Example for this quantum number: 2p⁶, the magnetic spin of it is -1/2 because the last arrow is going to a counter clockwise direction. 

Illustration

        1. Look for the electron configuration of Carbon:

        1s² 2s² 2p²

                      2.   Look for n, l, m_l, m_s:

                             _{n= 2}

                   1s² 2s² 2p²

                            ^{2 is the last electron shell of the element}

                        l= 1

                   1s² 2s² 2p²

                                                     The last subshell of the electron is p. There for L=1 

                 Representation for subshells

 

        S= 0

           

        P= 1  

                           

        D= 2

                    F= 3

                   m_{l =} 0

                              

                           The last electron is on the 2^nd or the middle compartment therefore m_l= 0

                            

              m_s = +1/2

 

            The Last arrow points upward there for it spins clockwise and it is positive. m_s= +1/2

Exercise!

 
   Look for the quantum numbers of the following:

1. Potassium 

2. 3d7 

3. 5f10 

4. n= 3, l=0,ml=0,ms=-1/2 

5. 4d7

MEMBERS

• Audrey Carbonel
• Derika Catapang
• Jenina Chua
• Cheska Cornelio
• Cathlyn Dumpit

Sources --> http://www.meta-synthesis.com/webbook/34_qn/qn_to_pt.html