Topic 12: Quantum numberslorenowicz.weebly.com/uploads/4/6/1/6/4616010/sch3u7-quantumnum… · Topic 12: Quantum numbers Heisenberg, Schrodinger, Quantum Theory, Quantum numbers,

Topic 12: Quantum numbers

Heisenberg, Schrodinger, Quantum Theory, Quantum numbers, Practice

Thursday, October 4, 2012

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”

W. Heisenberg

1901-1976

• Electrons behave as both waves and particles.

• Heisenberg determined that it is impossible to know BOTH the exact position and momentum of an electron.

• 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!


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.

E. Schrodinger

1887-1961

Quantum or Wave Mechanics


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!


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The 4 Quantum Numbers

These four numbers together provide the “address” of an electron within an atom

• Principal (n)

• Angular Momentum (l)

• Magnetic (ml)

• Spin (ms)

---> energy level

---> shape of orbital

---> designates a suborbital

---> spin of the electron


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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


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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


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Energy Levels

n = 1

n = 2n = 3n = 4


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


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S Orbitals

When l = 0, the orbital is called s


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Types of Orbitals (l)When l = 1, the orbital is called p

planar node

There is a PLANAR NODE thru the

nucleus, which is an area of zero

probability of finding an electron


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• The three p orbitals lie 90o apart in space

P ORBITALS

The p sublevel has 3 orbitals

They are designated as px, py, and pz


Magnetic (ml)

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


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•d sublevel has 5 orbitals

• ml = -2, -1, 0, 1, 2

D ORBITALS

When l = 2, the orbital is called d


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The shapes & labels of the five d orbitals


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F ORBITALS

When l = 3, the orbital is

called f

ml = -3, -2, -1, 0, 1, 2, 3


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

1,0,0,+1/2 OR 1,0,0,-1/2

2,0,0,+1/2 OR 2,0,0,-1/2

3,1,0,+1/2 OR 3,1,0,-1/23,1,-1,+1/2 OR 3,1,-1,-1/23,1,1,+1/2 OR 3,1,1,-1/2

3,2,2,+1/23,2,1, +1/23,2,0, +1/23,2,-1, +1/23,2,-2, +1/2

3,2,2,-1/23,2,1, -1/23,2,0, -1/23,2,-1, -1/23,2,-2, -1/2

1s 2s

3p 3d


Homework!


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Topic 12: Quantum numberslorenowicz.weebly.com/uploads/4/6/1/6/4616010/sch3u7-quantumnum… · Topic 12: Quantum numbers Heisenberg, Schrodinger, Quantum Theory, Quantum numbers,