Quantum Mechanics Through the Looking Glass Rutherford Bohr-Planetary Model This is how the model of the atom has developed so far:

Correcting Bohr’s Planetary Model …using the Photoelectric Effect

Louis DeBroglie’s insight: If light radiation can have a particle nature then why can’t particles have a wavelike nature? If electrons are particles Electrons must have a wavelike nature = h mv

Werner Heisenberg ( ) There is an uncertainty in either the position or the momentum of an electron that cannot be reduced beyond a certain minimum level Heisenberg’s Uncertainty Principle Is Shrodinger’s cat dead or alive?

The Quantum Mechanical Model Describes the wave properties of electrons and regions of space surrounding the nucleus Called orbitals Where there is a high probability of finding electrons

Describing an electron’s address Bohr’s model places the electron in a quantum energy level (n) Bohr-Planetary Model

Describing an electron’s address using the Quantum Mechanical Model Electrons exist in orbitals A collection of orbitals with the same energy is called an electron shell designated (n) 1 st quantum #-principle quantum number (n) n = (1,2,3,…,  ) describes shell or energy level

Describing an electron’s address using the Quantum Mechanical Model 2 nd quantum # - azimuthal number (l), value 0 to n-1 describes sublevel 3 rd quantum # - magnetic number (m l ), value = l to 0 to - l The orientation of the orbital in space 4 th Quatum # - Spin (m s ), value is + or – ½, describes the spin

The first energy level (n = 1) is constructed from a single orbital (l = 0), also designated ‘1s’, which is spherical ( m l = 0)

The second energy level (n = 2) is constructed from a single orbital (l = 0) also designated ‘2s’ which is spherical ( m l = 0)

The third energy level (n = 3) is constructed from a single orbital (l = 0) also designated ‘3s’ which is spherical ( m l = 0)

Energy level ‘n = 2’ is more complex than energy level ‘n =1’ and is constructed from two kinds of orbitals The innermost part of ‘n =2’ consists of a single spherical orbital designated ‘2s’ The outermost part of ‘n = 2’ consists of three orbitals which are not spherical, (l = 1)

Each dumbbell-shaped orbital (l = 1), also designated ‘2p x, 2p y,2p z ’is oriented along the x, y, and z axes ( m l = -1, 0, 1) Like the ‘s’ orbital, the ‘p’ orbitals also repeat in subsequent energy levels

Energy level ‘n = 3’ is more complex than energy level ‘n =1’ or ‘n = 2’ and consists of an innermost spherical orbital designated ‘3s’ The middle part of ‘n = 3’ consists of three dumbbell-shaped orbitals, (l = 1) The outermost part of ‘n = 3’ consists of five orbitals which are also not spherical, (l = 2)

Each four-lobed orbital (l = 2), also designated ‘3 d orbital ’is oriented along different planes ( m l = -2, -1, 0, 1, 2) Like the ‘s’ and ‘p’ orbitals, the ‘d’ orbitals also repeat in subsequent energy levels

Energy level ‘n = 4’ is more complex than energy level ‘n =1, 2, or 3’ and consists of an innermost spherical orbital designated ‘4s’ The lower middle part of ‘n = 4’ consists of three dumbbell-shaped orbitals, (l = 1) The upper middle part of ‘n = 4’ consists of five orbitals which are also not spherical, (l = 2)

The outermost part of ‘n = 4’ consists of seven orbitals, also designated ‘f ’ orbitals, which are also not spherical, (l = 3) nightmare In fact, they are a real nightmare ( m l = -3, -2, -1, 0, 1, 2, 3)

Describing an electron’s address

Quantum Mechanics: Where ever you go... there you are! Schwartzchild’s Radical which of the following is not an allowable quantum number 1.4,4,3,1/2 2.3,2,2,1 3.5,2,-1,-1/2

What are the maximum number of electrons allowed that have the quantum numbers designated? §1. n=3 §2. n=3, l=2 §3. n= 3, l=2, m l = 1 §4. n= 3, l=2, m l = 1, m s = 1/2

Which of the following are in an excited state and what element do they represent? §1. 1s 2 2s 2 2p 6 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6

How many unpaired electrons are in each of the following. §Cr §Fe 3+ §Cl 1-