Tuesday, December 4, 2012

Quantum Numbers


The energy state of an electron in an atom may be described by a set of four quantum numbers. Quantum numbers describe the orbital the electron occupies in terms of: 1) distance from the nucleus; 2) shape; 3) position with respect to the three axes in space; and 4) the direction of the electron on the orbital.

1.      Principle  quantum number (n)

This is the main energy level

n will equal positive whole numbers

 

ex: n=2 indicates that the electron being described is in the second energy level

note: The number of possible orbital shapes in an energy level is equal to the value of the principal quantum number (n)

            ex: the third energy level can contain three differently shaped types of orbitals

                        first energy level- only has an s orbital

                        second energy level- has s and p orbitals

                        third energy level- has s, p, and d orbitals

                        fourth energy level- has s, p, and d orbitals

2.      Orbital Quantum Numbers ( l )

this indicates the shape of the orbital which the electron occupies

l= 0,1,2,3,… where     l= 0 indicates the electron is in an s orbital

                                    l= 1 indicates the electron is in a p orbital

                                    l= 2 indicates the electron is in a d orbital

                                    l= 3 indicates the electron is in an f orbital

            n= 3     l= 2      indicates the electron being describes is in a d orbital in the third energy level

Note:   -there is 1 s orbital per energy level

            -if an energy level has p orbitals (level 2 and above) then it will have three p orbitals in that energy level

            -if an energy level has d orbitals (level 3 and above) then it will have five d orbitals in that energy level

            -if an energy level has f orbitals (level 4 and above) then it will have seven f orbitals in that energy level

3.      Magnetic quantum number (m)

-This indicates the position about the three axes in space by indicating which orbital of a particular shape the electron is in

-for the single s orbital is in an energy level m=0

s orbital  __   If l= 0 then m= 0

                0

-for the three p in an energy level m= -1, 0, +1

p orbitals __ __ __  If l= l then m= -1, 0, +1

               -1   0  +1

            - for the five d orbitals in an energy level m= -2, -1, 0, +1, +2

            d orbitals __ __ __ __ __ If l= 2 then m= -2, -1, 0, +1, +2

                            -2  -1  0  +1 +2

            - for the seven f orbitals in an energy level m= -3, -2, -1, 0, +1, +2, +3

            f  orbitals __ __ __ __ __ __ __ If l= 3 then m= -3, -2, -1, 0, +1, +2, +3
                            -3  -2  -1  0  +1 +2 +3
Note: each line represents an orbital

4.      Spin quantum number (s)

This represents a quantity which can be thought of as the electron spinning on its axis;

There are two possibilities, clockwise and counterclockwise.

            S= +½  or –½  represent the two possibilities

Note:  -an orbital can hold a maximum of two electrons (if it has two they must have opposite spins)

            -the orbitals fill one electron at a time before pairing

            -no two electrons within an atom can be described by the same four quantum numbers

            -the total number of orbitals in an energy level equals n2

                        Ex. Third energy level n= 3 n2= 9

                                    1 s orbital

                                    3 p orbitals

                                    5 d orbitals

                                    9 orbitals total

-the total number of electrons which an energy level can hold equals 2n2

            Ex. Third energy level n=3  9 total orbitals, each with a maximum of two electrons

                        2 x 9= 18 or 2(3)2=18

Questions: For odd numbers, circle the electron indicated, identify element. For even numbers, draw orbital notation and assign quantum numbers to the last electron represented.

1)      2          _       __ __ __          n=2

1                      ↑↓                               l =0

 s               p                m=0

                                   s = +½

                                   element= ___

2)      2          __        __ __ __          n=

1          __                                l=

             s                p                m=

                                                s =

                                                element= Ne

3)      2          ↑↓        ↑_ ↑_ ↑_          n= 2

1          ↑↓                                l = 1

             s               p                 m= +1

                                                s = +½

                                                element= ___

4)      2          __        __ __ __          n=

1          __                                l =

             s                p                m=

                                                s =

                                                element= Be

5)      3          ↑↓        ↑_ __ __          __ __ __ __ __            n= 2

2          ↑↓        ↑↓ ↑↓ ↑↓                                              l = 1

1          ↑↓                                                                    m= 0

             s                p                          d                        s = +½

                                                                                    element=

6)      3          __        __ __ __          __ __ __ __ __            n=

2          __        __ __ __                                              l =

1          __                                                                    m=

             s               p                           d                        s=

                                                                                    element= S

7)      4          ↑↓        ↑_ ↑_ __          __ __ __ __ __            __ __ __ __ __ __ __  n=3

3          ↑↓        ↑_ __ __          __ __ __ __ __                                                l = 2

2          ↑↓        ↑↓ ↑↓ ↑↓                                                                                  m= -1

1          ↑↓                                                                                                        s = +½

             s                p                          d                                         f                  element=  

8)      4          __        __ __ __          __ __ __ __ __            __ __ __ __ __ __ __  n=

3          __        __ __ __          __ __ __ __ __                                                l =

2          __        __ __ __                                                                                  m=

1          __                                                                                                        s =

             s                p                            d                                      f                   element= Mn

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