Quantum Mechanics

Parima Shah and Jasmine Wang

(In less than 20 minutes)

Quantum Mechanics?

Well, not anymore

Ugh.

What is Quantum Mechanics?It’s a new way of looking at the atomic world and understanding our universe.

In order to understand chemistry and science, we must start at the fundamentals of physics.

We’ll cover

•Orbitals and shells (an overview)

•Light (Waves and Particles)

•Electromagnetic Spectrum

•Photoelectric Effect

•Line Spectra

•The Atom

Orbitals and Shells: A Quick Review

•Pauli Exclusion: no two electrons have the same four quantum numbers

•Aufbau: “building up”

•Hund’s: electrons occupy separate orbitals and share the same spin, pairing up only after all the orbitals are full

•Quantum Numbers– Principal (n)

• Shell• Integers

– Angular momentum (l)• Subshell

–[0, n-1]

– Magnetic (ml)• Orbital• [-l, +l]

– Spin (ms)• 2 electrons• +/- ½ Paramagnetic: unpaired electrons

Diamagnetic: paired electrons

The Nature of LightThe Nature of LightNewton thought that light behaved like particles while

Christian Huygens believed it behaved like waves.

Waves:

•A pattern of matter, energy, or both

•Waves, unlike particles can be spread out over an immense area

•Frequency is the amount of times the wavelength occurs

Particles:

•A particle is a discrete object.

•Occupies a single, localized volume of space

•All energy is concentrated in that space

•One can tell where it is and how it is moving

The anatomy of a Wavelength

Light as Electromagnetic Waves• Visible light

– narrow bands of frequencies

• Light has a larger spectrum of electromagnetic waves– All

electromagnetic waves travel at the same speed: 300,000,000 m/s

• Can move through a vacuum

Did you Know?

It was believed that light had

to travel through ether

(water moved through waves

and sound moved through

air)

Banana Bread

Cheese Cake: Strawberry

Wavelength & Frequency

are related

c=νλ

c =3.00 x 108 m/s

ν = frequency in /s

λ = wavelength in m

Frequency and wavelength

formula

Let’s see if this recipe actually works…

s

sm

/1009.5

/1000.37

8

Time to cook:

Solution: λ=c/υ

What is the wavelength of a yellow sodium

emission of frequency

5.09 x 10-7/s?= 5.89 x 1014

m

The Blackbody Problem•A blackbody cannot be built, but it can be approximated by using an empty box containing electromagnetic energy.

•Energy must be at equilibrium between walls and interior

•Waves must fit inside the box

Emits all possible radiation

Absorbs all possible radiation

The lowest possible frequency of light has a wavelength that fits the box exactly.

Each consecutive frequency fits into the box depending on its wavelength (the next would be two wavelengths, &c. to infinity)

At infinity, there is an infinite amount of energy because each wave carries energy

Led to discovery of UV light

Max Planck and the beginnings of Quantum Mechanics

POUCH

25¢

Quanta of my money is falling

out!Max Planck: Each quanta must have a minimum of energy that is some proportion of the overall energy of the system

Max Planck and the beginnings of Quantum Mechanics

POUCH

radiation could be

absorbed/emitted in small

amounts called quanta – packets of

energy

•Multiplied by a conversion factor (Planck’s constant (h) = 6.6 x 10-34)•An atom at a particular frequency ν could emit energy only in integer multiples of hν, but nothing less than 1hν.

Lenard’s Photoelectric Experiments:

Paradise. (not really)

Lenard’s Photoelectric Experiments: Paradise. (still

not really)

Philip Lenard• The greater the intensity of

incoming light, the greater number of electrons released

Example: Waves on the Beach• Bigger waves dislodge more

sand than weak waves

Lenard’s Photoelectric Experiments: Paradise. (not

getting realer)

The kinetic energy in each “escaping” electron does not increase with intensity. In other words, intensity does not matter on the speed of the electrons.

More and more sand was being dislodged, but no more violently than the weaker waves

Does this make sense in the world of physics?

Does that make sense for waves?

Lenard’s Photoelectric Experiments: Paradise. (nope)

Does this make sense in the world of physics?

Does this make sense in the world?

NO!Nada, Goose egg, a cookie, etc. etc.

So what?Light must not only work as waves, but

as quanta of energy, or particles

Then he discovered:

Increasing the intensity of the light did

not increase the kinetic energy of the

escaping electron ejection. (Remember:

waves on the beach example)

However, the frequency did.

What does that mean?

Light is a stream of quanta instead of

being a continuous wave. Electrons are

ejected because quanta hit them – the

quanta transfers all its energy to the

electron. This means…

The Photoelectric EffectThe ejection of electrons from the surface of a metal from another material when light shines on it.

Einstein adapted Planck’s quanta theory

Photons- Quanta of light

E= hν where E is energy and h is Planck's constant of

The amount of energy of each photon is miniscule.

Light on sodium metal in vacuum

Electrons ejected from the surface

SODIUM METALm/s106.63 34

Emission Line Spectra

• Continuous Spectrum - all wavelengths

• Line spectrum - only specific wavelengths

Bohr’s Theory of the Hydrogen Atom

atom) (For H 1,2,3...n nR

E 2H J10 2.179R -18

H

Energy Level Postulate: electrons can have only specific energy values in an atom, called energy levels.

Bohr’s rule for the quantization of a electron in the hydrogen atom :

Transitions between Energy Levels: An electron can change energy by transferring

one energy level to another energy level. The emission of light from the atom occurs when

the electron in a higher energy level moves to a lower energy level. The electron loses energy, which is emitted as a photon.

)E-(EE- photon emitted ofEnergy if h

Boh

r’s

Th

eory

of

the H

ydro

gen

A

tom

Example Problem

What is the wavelength of light emitted when the electron in a hydrogen

atom undergoes transition from energy

level n=4 to n=2?

J10 2.179R -18H

atom) (For H 1,2,3...n nR

E 2H

)if E-(EE- photon emitted ofEnergy h

Solu

tion

to E

xam

ple

P

rob

lem

J10 2.179R -18H

atom) H (For the 1,2,3...n n

RE

2H

)E-(EE- photon emitted ofEnergy if h

m104.86/s106.17

m/s103.00

ν

cλ

/s106.17sJ106.63

J102.179

16

3

16h

3Rv

ν.obtain toconstant) s(Planck'h by divide Now

photon). emitted theof(energy hν toequals This

16

3R

16

4RR

64

16R4R

2

R

4

R ν

)E-(EΔE : twoposulate from formula theUse4

R

2

RE and

16

R

4

RE

7-.14

8

1434

18H

HHHHH2H

2H

if

H2H

fH

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i

The CD Player: Energy Levels and the good old days

Flame Test (demo)

Materials• 0.50M solution

Copper Chloride (CuCl2)

• 0.50M solution Lithium Chloride (LiCl)

• Tyrrell Burner

• 0.50M solution Sodium Chloride (NaCl)

• 0.50M solution Potassium Chloride (KCl)

• 4 wood splints• 4 beakers

Flame Test (demo)

• WEAR SAFETY GOGGLES• Tie up hair and loose clothing when using flame• Use care with Tyrrell burners and the flame

Safety Precautions

Flame Test (demo)Procedure

1. Saturate a wood splint in each 0.50 solution of metal

2. Take splint from the NaCl solution and place in hottest part of the flame

3. Observe and record the color4. Repeat for LiCl, CuCl2, KCl

Flame Test (demo)

Flame Colors

Element

Na Sodium

Li Lithium

Cu Copper

K Potassium

Color

Yellow

Crimson

Green

Purple

Flame Test (demo)

• The colors seen in the flame from each substance are a demonstration of the excitement of electrons from each element from their energy levels in order to emit photons.

Why does this relate?

Works Cited•http://www.answers.com•http://www.hi.is/~hj/QuantumMechanics/quantum.html •http://www.800mainstreet.com/spect/emission-flame-exp.html•http://xmm.sonoma.edu/edu/lessons/activity-flame.html•http://www.kent.k12.wa.us/staff/carriewattles/chemistry/flametestlab_inst.htm

•http://www.creative-chemistry.org.uk/activities/documents/flametests.pdf

•http://csep10.phys.utk.edu/astr162/lect/light/absorption.html•How mathematical models, computer simulations, and exploration can be used to study the universe : an anthology of current thought/ edited by Fannie Huang. 1st ed. New York : Rosen Pub. Group, 2006.

•Bynum, Wf, Ej Browne, and Roy Porter, eds. "Quantum." Dictionary of the History of Science. 1st ed. 1 vols. Princeton: Princeton UP, 1981.

•Willett, Edward. The Basics of Quantum Physics: Understanding the Photoelectric Effect and Line Spectra. 1st ed. Vol. 1. New York: The

Rosen Group, Inc., 2005. 6-19, 30-43.