Unit 4 – Unit 4 – Quantum Quantum MechanicsMechanics

Cartoon courtesy of NearingZero.net

Light and Energy

• Much of what we know about electrons comes from study of light

– Light behaves as waves – Light also behaves as particles

(photons)

Wave properties

• Light waves are part of the electromagnetic spectrum

• Can be characterized by 5 properties:– Amplitude– Wavelength– Frequency– Speed– Energy

c = C = speed of light, a constant (3.00 x 108 m/s)

= frequency, in units of hertz (hz, /s, s-1)

= wavelength, in meters

Electromagnetic radiation Electromagnetic radiation propagates through space as a wave propagates through space as a wave moving at the speed of light.moving at the speed of light.

Types of electromagnetic radiation:Types of electromagnetic radiation:

Calculating the color of light…

• Given that a beam of light has frequency of 6.0 x 1014 /s

• what is the wavelength of this light? • What color is it? –use p.129

E = h EE = Energy, in units of Joules (kg·m= Energy, in units of Joules (kg·m22/s/s22))

hh = Planck’s constant (6.63 x 10= Planck’s constant (6.63 x 10-34-34 J·s) J·s)

= frequency, in units of hertz (hz, /s, s= frequency, in units of hertz (hz, /s, s-1-1))

The energy (The energy (E E ) of electromagnetic ) of electromagnetic radiation is directly proportional to the radiation is directly proportional to the frequency (frequency () of the radiation. This is ) of the radiation. This is the energy of a photon of a particular the energy of a photon of a particular frequency.frequency.

Long Wavelength

= Low Frequency

= Low ENERGY

Short Wavelength

= High Frequency

= High ENERGY

Wavelength TableWavelength Table

…produces all of the colors in a “continuous spectrum”

Spectroscopic analysis of the visible Spectroscopic analysis of the visible spectrum…spectrum…

(such as seen from an incandescent light (such as seen from an incandescent light bulb)bulb)

……produces a “bright line” or “produces a “bright line” or “emission spectrumemission spectrum””

Spectroscopic analysis of the hydrogen Spectroscopic analysis of the hydrogen spectrum…spectrum…

(as given off by a hydrogen gas-filled (as given off by a hydrogen gas-filled fluorescent light bulb)fluorescent light bulb)

When they ‘fall’ back to their ’’‘ground state’ they emit photons of light with distinct wavelengths, visible as bands on an ‘emission spectrum’(not all are in the visible range).

Electron Electron transitionstransitionsoccur when occur when electrons absorb electrons absorb energy in a energy in a ‘‘quantum jump’ quantum jump’ to an ‘excited to an ‘excited state’. state’.

VISIBLEVISIBLEJUMPSJUMPS

The Bohr Model of the AtomThe Bohr Model of the Atom

Neils Bohr

I pictured electrons orbiting the nucleus much like planets orbiting the sun.But it turns

out they’re more like

bees around a hive.

WRONG!!!

Quantum MechanicalQuantum MechanicalModel of the AtomModel of the Atom

Mathematical laws were used to identify the regions outside of the nucleus where

electrons are most likely to be found.

These laws are beyond the scope of this class…

But here are two important examples:

Schrodinger Wave EquationSchrodinger Wave Equation

22

2 2

8dh EV

m dx

Equation for probabilityprobability of a single electron being found along a single axis (x-axis)Erwin Schrodinger

Heisenberg Uncertainty Heisenberg Uncertainty PrinciplePrinciple

You can find out where the electron is, but not where it is going.

OR…

You can find out where the electron is going, but not where it is!

“One cannot simultaneously determine both the position and momentum of an electron.”

Werner Heisenberg

Electron Energy Level (Shell)Electron Energy Level (Shell)Generally symbolized by n, it denotes the average distance of the electron from the nucleus.

Number of electrons that can fit in a shell:

2n2

1 holds 2 2 holds 8 3 holds 18 etc.

Orbital shapes are defined as the space that contains the electron 90% of the time.

An orbital is a region within an energy level An orbital is a region within an energy level where there is a probability of finding an where there is a probability of finding an electron. This is a probability diagram for the… electron. This is a probability diagram for the…

s orbitals orbital…… in the in the first energy levelfirst energy level..

Quantum Numbers: Electron Quantum Numbers: Electron Addresses!Addresses!

1st: Energy Level (n = 1, 2, 3, 4 …) Average distance of the electron in the electron cloud from the nucleus.

2nd: Sublevel (l = s, p, d, f) Shape of electron cloud.energy levels have n sublevels.

3rd: Orbital (ml) Orientation of the cloud in 3-D space.

s sublevels have 1 orbital (spherical)p sublevels have 3 orbitals(dumb bell

shape)d sublevels have 5 orbitals(varied)f sublevels have 7 orbitals (varied)

4th: Spin (ms = +1/2 or -1/2) Direction of electron spin. Each orbital holds 2 electrons, one with each spin.

Pauli Exclusion PrinciplePauli Exclusion Principle: Each : Each electron of an atom has its own electron of an atom has its own

unique set of quantum numbers. unique set of quantum numbers. They may have three that are the They may have three that are the

same, but never all four.same, but never all four.

Orbitals of the same shape (s, for instance) grow larger as n increases…

Nodes are regions of low probability within an orbital.

Sizes of Sizes of ss orbitals orbitals

The s orbital has a spherical shape centered

around the origin of the three axes in space

There is only one orientation for this shape

There are three dumbbell-shaped p orbitals in each energy level above n = 1, each assigned to its own axis (x, y and z) in space.

PP orbital shape orbital shape

Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3. To remember the shapes, think of “double dumbells” …and a “dumbell with a donut”!

d orbital shapes

In case you are too curious, In case you are too curious, here is what the f orbitals look here is what the f orbitals look

like.like.

Energy Level (n)

Sublevels in main energy

level (n sublevels)

Number of orbitals per

sublevel

Number of Electrons

per sublevel

Number of electrons

per main energy level (2n2)

1

2

3

4

Energy Levels, Sublevels, Energy Levels, Sublevels, ElectronsElectrons

s 1 2 2

s 1 2 p 3 6 8

s 1 2 p 3 6 d 5 10 18

s 1 2 p 3 6 d 5 10 f 7 14 32

5g18

6f14

7d10

8p6

8s2

The Diagonal Rule: Sublevels The Diagonal Rule: Sublevels in order of increasing energyin order of increasing energy

1s2 2s2 3s2 4s2 5s2 6s2 7s2

2p6 3p6 4p6 5p6 6p6 7p6

3d10 4d10 5d10 6d10

4f14 5f14

Aufbau PrincipleAufbau Principle: Electrons fill the : Electrons fill the lowest energy position available.lowest energy position available.

1s1s222s2s222p2p663s3s223p3p664s4s223d3d10104p4p665s5s224d4d10105p5p666s6s224f4f14145d5d10106p6p667s7s225f5f1414……

Energy levels and sublevels Energy levels and sublevels on the Periodic Tableon the Periodic Table

Hund’s RuleHund’s Rule: Electrons fill : Electrons fill orbitals so that there are a orbitals so that there are a

maximum number of orbitals maximum number of orbitals with a single electron. with a single electron.

Element Configuration notation

Orbital notation Noble gas notation

Lithium 1s22s1 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s1

Beryllium 1s22s2 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2

Boron 1s22s22p1 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2p1

Carbon 1s22s22p2 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2p2

Nitrogen 1s22s22p3 ____ ____ ____ ____ ____

1s 2s 2p

[He]2s2p3

Oxygen 1s22s22p4 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2p4

Fluorine 1s22s22p5 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2p5

Neon 1s22s22p6 ____ ____ ____ ____ ____ 1s 2s 2p

[He]2s2p6

Electron configuration of the Electron configuration of the elements of the first three elements of the first three

periodsperiods