quantum theory, part 2 the atom is it a particle or a wave? day 1

Quantum Theory, Part 2Quantum Theory, Part 2

The AtomThe Atom

Is it a particle or a wave?Is it a particle or a wave?

Day 1Day 1

Is it a particle or a wave?Is it a particle or a wave? ParticleParticle

– Defined location at a particular timeDefined location at a particular time

– Can be at rest, moving, or acceleratingCan be at rest, moving, or accelerating

Falling Ball

Ground level

3

Direction of travel, velocity

Up-downoscillations

Wavelength, frequency, velocity and oscillation size defines waves

WaveWave

– Need to see crests and troughs to define them.Need to see crests and troughs to define them.

– Waves are oscillations in space and time.Waves are oscillations in space and time.

Is it a particle or a wave?Is it a particle or a wave?

4

When particles collide, they cannot pass through each other.They can bounce or they can shatter!

Before collision After collision

Another aftercollision stateshatter

Basic difference in behaviourBasic difference in behaviour??

Before collision

5

Watch the collision between a truck with ladder on top and a car at rest !

Note the ladder continue its motion forward …..

6

Head on collision of a car and truck

Collision is inelastic – the small car is pushed along by the truck……

7

The basic difference between Waves The basic difference between Waves and Particles:and Particles:

- Waves can pass through each other!

- As they pass through, they can enhance or cancel each other.

-Afterwards, they regain their original form

8

Waves and Particles:

WavesSpread in space and time

Can be superposed – show interferenceinterference effects

Pass through each other

Particles

Localized in space and time

Cannot pass through each other -they bounce or shatter.

What is Light?!?!?What is Light?!?!?

Planck’s ExperimentPlanck’s Experiment

Einstein’s ExperimentEinstein’s Experiment

Blackbody Radiation

Photoelectric Effect

PARTICLE!

PARTICLE!

– energy is quantized

– light is made up of photons.

Laser Laser

If light is a particle then….If light is a particle then….

Thomas YoungThomas Young

Performed the Double Slit Experiment to test the wave nature of light.

INTERFERENCE (2D)INTERFERENCE (2D)

+ =

+ =

Constructive Interference = more intense (brighter) wave (AMPLIFIED)

Destructive Interference = no amplitude (Node) meaning no wave (CANCELED)

A prism bends light.Different Colors are bent by different amounts.

White Light

4

with two holes

5

with two holes Two Curves

2

A wave moves toward a slit.

3

Comes out as a curve

7

Two Curveswith two holes

Interfere with each other

crests add up

6



7



crests add up

8

Several waves

9

Several wavesSeveral Curves

10

Several wavesSeveral waves

Interference Pattern

Several Curves

Two source interferenceTwo source interference

constructive interference -------destructive interference -------



Path difference =S2P – S1P

S1 S2

P

= 1 wavelength

=



Path difference for constructive interference =

0

2

3

n

(where n is an integer)



½1½

2½

Path difference for destructive interference = (n + ½)

(where n is an integer)

Interference in the ExperimentInterference in the Experiment

CONCLUSION:CONCLUSION:

Light is a wave!

Well along came Louis de Broglie and he said if light can travel in waves and act like particles (energy is given off in packets, called photons) perhaps matter, which is composed of particles can act like waves.

This became known as the Wave-Particle Duality, which led to Quantum mechanics and the discussion that the electron, which is a particle, can move like a wave.

mparticle = h / v (v is velocity)

particle = h / m v h = 6.626 x 10-34 Js = wavelength in m

m = mass in kgv = velocity in m/s

In fact in 1927, a beam of electrons was able to be diffracted thus suggesting that like light, electrons travel in waves. ONLY waves CAN BE DIFFRACTED. (This experimental evidence helped prove de Broglie’s ideas.)

NOTE: Because de Broglie’s hypothesis is applicable to all matter, any object has the characteristics of waves, however the wavelength of an ordinary sized object, such as a golf ball, is so tiny, that it cannot be observed by the human eye.

An electron has mass, so it is matter. A particle can only go through one hole, a wave through both holes. An electron does go through both, and makes an interference pattern. Thus, it behaves like a wave.

Electrons exhibit wave like properties – they can pass through each other!

Phenomenon of electron interference

Dual Nature of LightDual Nature of Light

Waves can bend around small obstacles…

…and fan outfrom pinholes.

Particles effuse from pinholes

Three ways to tell a wave from a particle…

wave behavior particle behavior

waves interfere particle collide

waves diffract particles effuse

waves are delocalized particles are localized

This quantum picture of the world is at odds with our common sense view of physical objects.

We cannot uniquely define what is a particle andwhat is a wave !!

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TRUE UNDERSTANDING OF NATURE REQUIRED THAT PHYSICAL OBJECTS, WHATEVER THEY ARE, ARE NEITHER EXCLUSIVELY PARTICLES OR WAVES

No experiment can ever measure both aspects at the same time, so we never see a mixture of particle and wave.

WHEN ONE OBSERVES A PHYSICAL PHENOMENON INVOLVING A PHYSICAL OBJECT, THE BEHAVIOUR YOU WILL OBSERVE – WHETHER PARTICLE LIKE OR WAVE LIKE – DEPENDS ON YOUR METHOD OF OBSERVATION.

THE OBJECT IS DESCRIBED BY MATHEMATICAL FUNCT IONS WHICH ARE MEASURES OF PROBABILITY .

ALL PHYSICAL OBJECTS exhibit both PARTICLE AND WAVE LIKE PROPERTIES. THIS WAS THE STARTING

POINT OF QUANTUM MECHANICS DEVELOPED INDEPENDENTLY BY ERWIN SCHRODINGER AND

WERNER HEISENBERG.

36

Classical world is Deterministic:Classical world is Deterministic:•Knowing the position and velocity of all objects at a particular time•Future can be predicted using known laws of force•and Newton's laws of motion.

Quantum World is Probabilistic:Quantum World is Probabilistic:•Impossible to know position and velocity with certainty at a given time.

•Only probability of future state can be predicted using•known laws of force and equations of quantum mechanics.

Observer Observed Tied together

BEFORE OBSERVATION IT IS IMPOSSIBLE TO SAYWHETHER AN OBJECT IS A WAVE OR A PARTICLE OR WHETHER IT EXISTS AT ALL !!

QUANTUM MECHANICS IS A PROBABILISTIC THEORY OF NATURE

In order to find the location or momentum (velocity) of the electron, the investigator must interact with the electron.

Heisenberg’s uncertainty principle states you can never know both the location of an electron and its momentum (velocity). If you know the velocity, then you will not know the location; likewise, if you know the location, you cannot know the velocity.

Scientists do not know the exact path that an electron will follow.

Heisenburg’s Uncertainty PrincipleHeisenburg’s Uncertainty Principle

Heisenberg Uncertainty PrincipleHeisenberg Uncertainty Principle

In order to observe an electron, one would need In order to observe an electron, one would need to hit it with photons having a very short to hit it with photons having a very short wavelength.wavelength.

Short wavelength photons would have a high Short wavelength photons would have a high frequency and a great deal of energy.frequency and a great deal of energy.

If one were to hit an electron, it would cause If one were to hit an electron, it would cause the motion and the speed of the electron to the motion and the speed of the electron to change.change.

Lower energy photons would have a smaller Lower energy photons would have a smaller effect but would not give precise information.effect but would not give precise information.

The Quantum Mechanical ModelThe Quantum Mechanical Model

Charge Cloud ModelCharge Cloud Model– Erwin “Werner” SchrErwin “Werner” Schrödingerödinger

» AustrianAustrian

Energy is quantized. It comes in Energy is quantized. It comes in chunks.chunks.

Schrödinger derived an equation Schrödinger derived an equation that described the energy and that described the energy and position of the electrons in an atom.position of the electrons in an atom.

Modern ViewModern View The atom is mostly empty The atom is mostly empty

space.space. Electrons do not follow Electrons do not follow

circular paths.circular paths. Energy levels are Energy levels are 3-dimensional.3-dimensional. Model is based on the Model is based on the

probability of finding an probability of finding an electron a certain distance electron a certain distance from the nucleusfrom the nucleus

Two regionsTwo regions– NucleusNucleus- protons and - protons and

neutrons.neutrons.– Electron cloud-Electron cloud- region region

where you might find where you might find an electron.an electron.

So, unlike the Bohr theory of the atom, the modern quantum theory of the atom does not show the electrons following circular orbits, but shows the regions in which there is a high probability of finding an electron. These regions are called orbitals (90% probability).

This new theory of wave mechanics, or quantum mechanics, was credited to Erwin (Werner) Schrödinger. In your junior year in college, in physical chemistry you will spend 15 weeks studying the mathematics behind Schrödinger’s equation. (In fact, he was given the 1932 Nobel Prize in Physics for it.)

These equations are used to determine the probability of finding a particle at a particular time and a particular place; hence, the location of the electron. Schrödinger’s work shows how the probability of finding the electron varies within the atom.

QUANTIZED WAVELENGTHSStanding Wave

200

150

100

50

0

- 50

-100

-150

-2000 50 100 150 200

Second Harmonic or First Overtone 200

150

100

50

0

- 50

-100

-150

-2000 50 100 150 200

Fundamental mode 200

150

100

50

0

- 50

-100

-150

-2000 50 100 150 200

Electrons as WavesElectrons as Waves

QUANTIZED WAVELENGTHS

n = 4

n = 6

Forbiddenn = 3.3

n = 5

Schrodinger’s CatSchrodinger’s Cat

A compilation of individual electronsA compilation of individual electrons

•The visual concept of the atom now appeared as an electron "cloud" which surrounds a nucleus. •The cloud consists of a probability distribution map

• Determines the most probable location of an electron.

•For example, if one could take a snap-shot of the location of the electron at different times and then superimpose all of the shots into one photo, then it might look something like the view at the top.

Scientists are able to plot the changing probability as points as a three-dimensional representation. You will find that regions with high probability have a dense set of points, while areas of low probability have points that are more spread out. These plots look like diffuse clouds. Thus leading to the present day name of the model of the atom, Charge-cloud.

Solving various wave equations led us to the location and motion of the electron inside the atom. A set of four(4) quantum numbers describe the probability (orbitals) of finding the electron at a certain spot in the atom. Using these four quantum numbers, we are able to describe the energy level, sublevel, orbital, etc. of each electron.

Quantum MechanicsQuantum Mechanics

Orbital Orbital (“electron cloud”)(“electron cloud”)

– Region in space where there is 90% Region in space where there is 90% probability of finding an electronprobability of finding an electron

Electron Probability vs. Distance

Ele

ctro

n P

rob

abil

ity

(%)

Distance from the Nucleus (pm)100 150 200 250500

0

10

20

30

40

Orbital

90% probability offinding the electron

Shapes of s, p, and d-OrbitalsShapes of s, p, and d-Orbitals

s orbital

p orbitals

d orbitals

Atomic OrbitalsAtomic Orbitals

s, p, and d-orbitalss, p, and d-orbitals

As orbitals:

Hold 2 electrons(outer orbitals ofGroups 1 and 2)

Bp orbitals:

Each of 3 pairs oflobes holds 2 electrons

= 6 electrons(outer orbitals of Groups 13 to 18)

Cd orbitals:

Each of 5 sets oflobes holds 2 electrons

= 10 electrons(found in elements

with atomic no. of 21and higher)

(a) Electron probability (b) Contour probability (c) Radial probability

(a) 1s (b) 2s (c) 3s

r r

21s

r r

22s

r r

23s

Distance from nucleus

Quantum NumbersQuantum Numbers

px pz py

x

y

z

x

y

z

x

y

z

p-Orbitalsp-Orbitals

px pypz

2s 2p (x, y, z) carbon

px pz py

x

yz

x

yz

x

y

z

x

yz

s

Electron configurations: Electron configurations: Labeling electrons in atomsLabeling electrons in atoms

Quantum numbers are directions (like an address) to find the location of an electron.

State: Energy Level (n = 1, 2, 3, …, 7)City: Sublevel (s, p, d, f)Street: Orientation of orbital (axis)House: Spin (+1/2 or –1/2)

The First Quantum NumberThe First Quantum Number

The first quantum number is called the primary or principal quantum number, represented by the letter n.

This number describes which energy level the electron occupies. n = 1,2,3,4,5,6, or 7.

A large number indicates more energy and a greater distance from the nucleus. n2 = # of orbitals in the energy level

Relative Sizes 1s and 2sRelative Sizes 1s and 2s

1s 2s

The Second Quantum NumberThe Second Quantum NumberThe second quantum number (azimuthal or angular momentum quantum number) describes the shape of the orbital. s,p,d,f.

These letters just represent the shape of the orbitals. s (sharp) is a sphere; p (principal) is shaped like a dumbbell; d (diffuse) and f (fundamental) have complex shapes and higher energy.

The number of possible orbital shapes in an energy level = the value of n

n orbital shapes1 s2 s, p3 s, p, d4 s, p, d, f:

n n shapes possible

The Second Quantum NumberThe Second Quantum Number

The azimuthal quantum number is represented by the letter l

Value of l describes the shape of the region of space occupied by the electron

Allowed values of l depend on the value of n and can range

from 0 to n–1

All wave functions that have the same value of both n and l form a subshell

Regions of space occupied by electrons in the same subshell have the same shape but are oriented differently in space

s p

df


• n = # of sublevels per level

• n2 = # of orbitals per level

• Sublevel sets: 1 s, 3 p, 5 d, 7 f

n = 3n = 3n = 2n = 2n = 1n = 1PrincipalPrincipallevellevel

SublevelSublevel

OrbitalOrbital

ss ss pp ss pp dd

ppxx ppyy ppzz ddxyxy ddxzxz ddyzyz ddzz22 ddxx22- y- y22ppxx ppyy ppzz

Maximum Capacities of Subshells Maximum Capacities of Subshells and Principal Shellsand Principal Shells

n 1 2 3 4 ...n

l 0 0 1 0 1 2 0 1 2 3

Subshelldesignation s s p s p d s p d f

Orbitals insubshell 1 1 3 1 3 5 1 3 5 7

Subshellcapacity 2 2 6 2 6 10 2 6 10 14

Principal shellcapacity 2 8 18 32 ...2n2

The Third Quantum NumberThe Third Quantum NumberThe third quantum number, magnetic quantum number is

represented by ml. This number tells you the spatial orientation

(position) of the orbital that the electron occupies along the x, y, or z plane.

Allowed values of ml depend on the value of l

ml can range from –l to l in integral steps

ml = l, - l + l, . . . 0 . . ., l – 1, l

Each wave function with an allowed combination of n, l, and ml values describes an atomic orbital, a particular spatial distribution for an electron

The Third Quantum NumberThe Third Quantum Number

l, - l + l, . . . 0 . . ., l – 1, l

If l = 2 (d orbital)

Then ml = -2, -1, 0, 1, 2

The Fourth Quantum NumberThe Fourth Quantum NumberThe fourth quantum number, spin quantum number, tells you the direction of the electron’s spin (+1/2 or –1/2) clockwise or counter-clockwise

So, the 4 quantum numbers tell you:

1. The principal energy level2. The shape of the orbitals3. The orientation of the orbital4. The spin of the electron

Level n 1 2 3

Sublevel l Orbital ml

Spin ms

0 0

0 0 1 0 -1 0 1 0 -1 2 1 0 -1 -2

2101

= +1/2= -1/2

Allowed Sets of Quantum Numbers for Electrons in Atoms

Electron Orbitals:Electron Orbitals:

Electronorbitals

EquivalentElectronshells

(a) 1s orbital (b) 2s and 2p orbitals c) Neon Ne-10: 1s, 2s and 2p


n shell

l subshell

ml orbital

ms electron spin

1, 2, 3, 4, ...

0, 1, 2, ... n - 1

- l ... 0 ... +l

+1/2 and - 1/2

Electron ConfigurationsElectron Configurations

Aufbau Principle states that when filling an atom with electrons, the lowest energy levels, sublevels, and orbitals must be filled before proceeding to the next level.

Pauli Exclusion Principle states that no two electrons can have the same 4 quantum numbers.

Hund’s Rule states that the most stable arrangement of the electrons is that with the maximum number of unpaired electrons, all with the same spin directions.

Degenerate orbitals: same amount of energy, the 3 p orbitals, the 5 d orbitals, the 7 f orbitals, etc.

In atoms of different elements, the arrangement of electrons in orbitals follows a precise pattern. The electrons enter orbitals in order of increasing energy of the orbitals, beginning with the 1s orbital. At higher energy levels, some orbitals overlap.

1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s

How to write an electron configuration:How to write an electron configuration:

•Locate the element whose electron configuration you wish to write in the periodic table.

•Fill orbitals in the proper order with electrons.

•Check that the total number of electrons in the electron configuration equals the atomic number.

Electron Configuration: description of the arrangement of electrons in an atom

s sublevel contains 1 s orbital.

p sublevel contains 3 p orbitals

d sublevel contains 5 d orbitals

f sublevel contains 7 f orbitals

A circle stands for an orbital.

This is an empty orbital.

This is an orbital with 1 electron in it.

This is an orbital with 2 electrons in it. (Notice the opposite spins)

Each orbital can hold a maximum of 2 electrons!!!!!!!!

Hence,s sublevel has 1 orbital therefore it can hold 2 electrons (s1 and s2)

p sublevel has 3 orbitals therefore it can hold 6 electrons (p1 to p6)

d sublevel has 5 orbitals therefore it can hold 10 electrons (d1 to d10)

f sublevel has 7 orbitals therefore it can hold 14 electrons (f1 to f14)

This is an orbital with 2 electrons in it. (Notice the opposite spins)

To write an electron configuration, you must To write an electron configuration, you must know the number of electrons in an atom. This know the number of electrons in an atom. This is the same number as Z, the atomic number of is the same number as Z, the atomic number of

the element.the element.Hydrogen (Z=1) 1s 2s 2p 3s 3p

1s1

Helium (Z=2) 1s 2s 2p 3s 3p 1s2

Lithium (Z=3) 1s 2s 2p 3s 3p

1s22s1

Beryllium (Z=4) 1s 2s 2p 3s 3p 1s22s2

Boron (Z=5) 1s 2s 2p 3s 3p

1s22s22p1

ORBITAL DIAGRAMS

Carbon (Z=6) 1s 2s 2p* 3s 3p

*Hund’s Rule 1s22s22p2

Nitrogen (Z=7) 1s 2s 2p* 3s 3p


Oxygen (Z=8) 1s 2s 2p* 3s 3p


Skipping around the table……………Skipping around the table……………

Potassium (Z=19)

1s22s22p63s23p64s1

1s 2s 2p 3s 3p 4s 3d

Calcium (Z=20)

1s22s22p63s23p64s2

1s 2s 2p 3s 3p 4s 3d

Scandium (Z=21)

1s22s22p63s23p64s23d1

1s 2s 2p 3s 3p 4s 3d

neon's electron configuration (1s22s22p6)

Shorthand ConfigurationShorthand ConfigurationNOBLE GAS METHODNOBLE GAS METHOD

[Ne] 3s1

third energy level

one electron in the s orbital

orbital shape

Na = [1s22s22p6] 3s1 electron configuration

AA

BB

CC

DD

[Ar] 4s2 3d10 4p2

Periodic PatternsPeriodic Patterns

Example -Example - GermaniumGermanium

Ge72.61

32

Shorthand ConfigurationShorthand Configuration

[Ar] 4s2

Electron configurationElement symbol

[Ar] 4s2 3d3

[Rn] 7s2 5f14 6d4

[He] 2s2 2p5

[Kr] 5s2 4d9

[Kr] 5s2 4d10 5p5

[Kr] 5s2 4d10 5p6

[He] 2s22p63s23p64s23d6

Ca

V

Sg

F

Ag

I

Xe

Fe [Ar] 4s23d6

KERNAL (Core of atom) includes the nucleus and the energy levels, EXCEPT the outermost (valence level).

VALENCE is the outermost energy level.

LEWIS DOT STRUCTURES:•Write the chemical symbol.•Indicate the number of electrons in the valence shell using dots around the symbol.

• Shorthand Configuration

S 16e-

Valence ElectronsValence ElectronsCore ElectronsCore Electrons

S 16e- [Ne] 3s2 3p4

1s2 2s2 2p6 3s2 3p4

NotationNotation

Longhand ConfigurationLonghand Configuration

S32.066

16

Electron Dot DiagramsElectron Dot Diagrams

H

Li

Na

K

Be

Mg

Ca

B

Al

Ga

C

Si

Ge

N

P

As

O

S

Se

F

Cl

Br

Ne

Ar

Kr

He

Group

1A 2A 3A 4A 5A 6A 7A 8A

= valence electron

s1 s2 s2p2 s2p3 s2p4 s2p5 s2p6s2p1

1 2 13 14 15 16 17 18

Recall the electron configuration for Oxygen (in its ground state):

When we add heat to oxygen, an electron absorbs the energy and jumps to a higher energy state which is shown below:

1s 2s 2p 3s 3p

However, these last two arrangements are unstable. Therefore the electron must return to its ground state. It accomplishes this by emitting the absorbed energy as visible light (color) within the EM spectrum.

1s 2s 2p 3s 3por, it can be shown as:

1s 2s 2p 3s 3p

There are certain rules of stability that affect the

electron configurations of all of the elements;

thus, certain arrangements of electrons are more stable

than others.

The most stable arrangement is that of a full The most stable arrangement is that of a full energy level.energy level.

Elements that have this arrangement belong to the

_______________________ family.

Second most stable arrangement is that of a full Second most stable arrangement is that of a full sublevel.sublevel.

Elements that have this arrangement belong to the

_______________________ family.

Third most stable arrangement is that of a Third most stable arrangement is that of a half-full sublevel.half-full sublevel.

Finally, the least stable

arrangement is that of no

particular order.

Here are a few special cases:Here are a few special cases:What would you predict to be the electron configuration for Chromium (Cr)?

1s 2s 2p 3s 3p 4s 3d

Is that a particularly stable arrangement? ________

Why would this be a particularly stable arrangement?

In fact, we can rearrange the electrons to make a more stable configuration !!!!!!!

1s 2s 2p 3s 3p 4s 3d

In fact, every element in Group 6 (VIB) will arrange its electrons so that it has this type of configuration. (s1d5)

What would you predict to be the electron configuration for copper (Cu)?

Like Cr, Cu will rearrange its configuration to become more stable.

1s 2s 2p 3s 3p 4s 3d

In fact, every element in Group 11 (IB) will arrange its electrons so that it has this type of configuration. (s1d10)

Why is this configuration very stable?

This fills the valenceshell and tends to givethe atom the stabilityof the inert gasses.

The Octet RuleThe Octet Rule

Atoms tend to gain, lose, or share electrons until they have eight valence electrons.

ONLY ss- and pp-orbitals are valence electrons.

O2- 10e- [He] 2s2 2p6

StabilityStability

Ion Electron ConfigurationIon Electron Configuration

– Write the eWrite the e-- configuration for the closest configuration for the closest Noble GasNoble Gas

» EXEX: Oxygen ion : Oxygen ion O O2-2- Ne Ne

MagnetismMagnetism

Paramagnetic-Paramagnetic-•The atom has unpaired electrons in its orbital diagram• Electron spins will align in an external magnetic field

•Magnetism•AlNiCo Magnets

•Increasing the # of unpaired electrons = increase in magnetism

Diamagnetic-Diamagnetic-•No unpaired electrons in the orbital diagram•Diamagnetic materials are not magnetic

Ferromagnetic-•Many unpaired electrons in the orbital diagram•These materials can remain magnetic after the external magnetic field is removed•Electron spins trend to align spontaneously without any applied field

•Fe, Co, Ni•Rare-earth magnets – lanthanide series of f orbitals

Can a Tattoo React with Magnetic Can a Tattoo React with Magnetic Resonance Imaging (MRI)?Resonance Imaging (MRI)?

•The magnetic force of an MRI machine is so strong, even the “weakest” machine is 10,000 times the strength of the Earth’s magnetic field.

•Yes, there is medical evidence that a tattoo can cause a reaction during an MRI. •The tattoo inks expected to cause a reaction are those containing iron oxide (some black, brown, red, flesh, yellow, orange).

•Magnetic metals can convert the radio-frequency pulses of an MRI machine into electricity.

•The burning sensation felt at the site of the tattoo may be a result of electricity running through the tattoo or from the ‘pull' exerted on the magnetic material in the tattoo.

•To reduce the possibility of burning, your doctor may recommend placing ice packs or cool compresses over your tattoos during the MRI.

•MRI’ s affect any magnetic material on or in your body •Jewelry, Implants (dental or otherwise), Pacemakers or even metal fragments.•Even small metal objects such as paperclips or keys can become projectile weapons if left in an MRI room during a scan.

quantum theory, part 2 the atom is it a particle or a wave? day 1

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