Quantum Numbers and Electron Configuration _basic and shorthand_ by cuiliqing

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```									                                               Quantum Mechanical Theory

-    Allows us to predict the probability of finding an electron at various points in space
-    Allows us to explain both the atomic spectra of elements better, the arrangement of elements on the
periodic table of elements, and understand chemical bonding

Bohr’s theory                                Quantum Mechanical theory
Term used: orbits                                  Term used: orbital
2-D path                                        3-D region in space
Fixed distance from the nucleus                 Variable distance from the nucleus
Circular or elliptical path                     No path: varied shape of region
2n2 electrons per orbit                         2 electrons per orbital

Quantum Numbers
- Used to describe an electron in an atom
- There are four quantum numbers:

1)    Principal Quantum Number (n)
- Aka: Principal energy level
- Tells you the energy of the electron in an atom
- Positive number (1,2,3,…)
- The smaller the n, the lower the energy
- The size of an orbital also depents on n
- Orbitals with the same n are said to belong to the same shell
- Are sometimes designated by letters

Letter         K       L        M        N…
n              1       2        3        4…

2)    Secondary Quantum Number (l)
- Aka: Sublevel
- Distinguishes orbitals of a given n as having different shapes
- An integer value from 0 to n – 1
- For a given n, the energy of an orbital increases with l
- Orbitals of the same n but different l are said to belong to different subshells of a given shell
Letter         s       p        d        f
l              0       1        2        3

The subshells are split up into 4 different types
s subshell – hold a max of 2 electrons
p subshell – hold a max of 6 electrons
d subshell – hold a max of 10 electrons
f subshell – hold a max of 14 electrons

-      Shapes of the subshells
s subshell – sphere
p subshell – 3 dumbbells

The shape of the subshells become harder to predict and the mathematical calculations are
more complex as the principal quantum number increases
s (l=0)              p (l=1)                                   d (l=2)                                                 f (l=3)

m=0        m=0                 m=±1          m=0            m=±1                 m=±2         m=0          m=±1            m=±2                 m=±3

s             pz         px           py     dz2     dxz          dyz     dxy      dx2-y2     fz3    fxz2    fyz2    fxyz      fz(x2-y2) fx(x2-3y2) fy(3x2-y2)

n=1

n=2

n=3

n=4

n=5                                                                                                 ...     ...     ...     ...        ...      ...        ...

n=6                                                ...     ...       ...        ...       ...       ...     ...     ...     ...        ...      ...        ...

n=7             ...        ...          ...        ...     ...       ...        ...       ...       ...     ...     ...     ...        ...      ...        ...
3) Magnetic Quantum Number (ml)

-   Distinguishes one orbital from another in the same sublevel
-   Distinguishes orbitals given n and l → that is, given energy and shape but having a different
orientation in space
-   Integers from –l to +l
-   Each orbital of a given subshell has the same energy

Table 1. Permissible Values of Quantum Numbers for Atomic Orbitals
n              l             ml *                           Subshell       Number of
Notation       Orbitals in the
Subshell
1               0            0                                1s            1
2               0            0                                2s            1
2               1            -1, 0, +1                        2p            3
3               0            0                                3s            1
3               1            -1, 0, +1                        3p            3
3               2            -2, -1, 0, +1, +2                3d            5
4               0            0                                4s            1
4               1            -1, 0, +1                        4p            3
4               2            -2, -1, 0, +1, +2                4d            5
4               3            -3, -2, -1, 0, +1, +2, +3        4f            7
* Any one of the mi quantum numbers may be associated with the n and l quantum numbers on the
same line.
- NOTE: there are 2l + 1 orbitals in each subshell of quantum number l

4)    Spin Quantum Number (ms)
- Refers to the two possible orientations of the spin axis of an electron
- Possible values are + ½ or – ½

Table 2. Key Experimental Work in Creating the Four Quantum Numbers
Key Experimental work               Theoretical Explanation             Quantum Theory
low-resolution line spectra         principal quantum number (n)        All electrons in all atoms can
be described by four quantum
high-resolution line spectra        secondary quantum number (l)        numbers

spectra in magnetic field           magnetic quantum number (ml)
ferro- and paramagnetism            spin quantum number (ms)

Electron Configuration
- Shows the order of filling of the orbitals

1s2
Energy level        Sublevel/subshell       Number of electrons in that sublevel
(n)                     (l)

Do examples: sulphur, iron, bismuth
Shorthand of Electron Configurations
- Write the symbol of the preceding noble gas in square brackets
- Just the remaining electrons following that noble gas need to be included

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