Topic 12: Quantum numbers Heisenberg, Schrodinger, Quantum Theory, Quantum numbers, Practice
Quantum Mechanics We left off by saying Bohr s model only explained the electron arrangement of Hydrogen... A new model was needed. Because of observations made regarding ionization energy and line spectra, it was concluded that we needed to take into consideration more than just the energy level of an electron Enter - QUANTUM MECHANICS!
Ionization energy The first ionization energy of an element is the energy required to remove one electron from an atom We can see a repeating pattern Why is there a difference between Li and Ne? This provides evidence that the levels can contain different numbers of electrons before they become full
Heisenberg Uncertainty Principle Electrons behave as both waves and particles. Heisenberg determined that it is impossible to know BOTH the exact position and momentum of an electron. W. Heisenberg 1901-1976 He observed that on cannot simultaneously define the position and momentum (= m v) of an electron. If we define the energy exactly of an electron precisely we must accept limitation that we do not know exact position.
So you can either know the position or the energy of an electron --- but you can t know both!
Quantum or Wave Mechanics E. Schrodinger 1887-1961 Schrodinger applied idea of electrons behaving as a wave to the problem of electrons in atoms. He developed the WAVE EQUATION which describe the 3D shapes of the atomic orbitals where there is a high probability that electrons are located. His claim to fame is his cat...he put a cat in box and said it was simultaneously dead AND alive until you actually prove either. So all possibilities are true until proven.
Heisenberg + Schrondinger = QUANTUM THEORY But remember, we can t say EXACTLY where the electron is! We can only define the 3D shape (orbital) where we are most likely to find it! 4 numbers are needed to describe an electron!
The 4 Quantum Numbers These four numbers together provide the address of an electron within an atom Principal (n) ---> energy level Angular Momentum (l) ---> shape of orbital Magnetic (m l ) ---> designates a suborbital Spin (ms) 8 ---> spin of the electron
RULES TO FOLLOW Only 2 electrons per orbital! The Pauli Exclusion Principle says that no two electrons within an atom (or ion) can have the same four quantum numbers. If two electrons are in the same energy level, the same sublevel, and the same orbital, they must have opposite spins! Spin can be +1/2 or - 1/2 11
Principal Quantum Number Each energy level (think: shell) has a number called the PRINCIPAL QUANTUM NUMBER, n Currently n can be 1-7, because there are 7 periods on the periodic table If an electron is in the first shell, n=1 12
Energy Levels n = 1 n = 2 n = 3 n = 4 13
Types of Orbitals Each energy level has between 1 and 4 sublevels (orbitals) Each sublevel is associated with a particular shape of probability: 4 shapes are s, p, d, and f Possible values of l = 0 to n-1 When n=1, then l = 0 When n=2, then l = 0 OR l = 1
SHAPES l = 0 l = 1 l = 2
S Orbitals When l = 0, the orbital is called s 16
Types of Orbitals (l) When l = 1, the orbital is called p 17 planar node There is a PLANAR NODE thru the nucleus, which is an area of zero probability of finding an electron
P ORBITALS The p sublevel has 3 orbitals They are designated as p x, p y, and p z The three p orbitals lie 90 o apart in space 18
Magnetic (m l ) How do we know p orbitals have 3 sublevels? Magnetic number represents the sublevels ml = -l to +l So for the p orbital ml = 1, possible sublevels are -1, 0, 1 1 2 3
D ORBITALS When l = 2, the orbital is called d d sublevel has 5 orbitals ml = -2, -1, 0, 1, 2 20
The shapes & labels of the five d orbitals 21
F ORBITALS When l = 3, the orbital is called f ml = -3, -2, -1, 0, 1, 2, 3 22
Spin Ms! Lastly, spin! Recall the Pauli exclusion principle, which says no two electrons can have the same value Spin is used to differentiate when 2 electrons are paired in the same orbit Arbitrarily assign +1/2 or -1/2
You made it! Let s try writing some quantum numbers! Write a set of 4 quantum numbers for an electron in 1s 1,0,0,+1/2 OR 1,0,0,-1/2 2s 2,0,0,+1/2 OR 2,0,0,-1/2 3p 3,1,0,+1/2 OR 3,1,0,-1/2 3,1,-1,+1/2 OR 3,1,-1,-1/2 3,1,1,+1/2 OR 3,1,1,-1/2 3,2,2,-1/2 3,2,1, -1/2 3,2,0, -1/2 3,2,-1, -1/2 3,2,-2, -1/2 3d 3,2,2,+1/2 3,2,1, +1/2 3,2,0, +1/2 3,2,-1, +1/2 3,2,-2, +1/2
Homework!