light and planck's constant do now: using your textbooks answer the following 1. what is mass...

LIGHT and Planck's Constant

DO NOW: Using your textbooks answer the following 1. What is mass spectrometry and how is it used?

2. Define light3. What is the formula for Planck’s constant and what

does each variable represent

Light

The study of light led to the development of the quantum mechanical model.

Light is a kind of electromagnetic radiation. (radiant energy)

Electromagnetic radiation includes many kinds of waves

All move at 3.00 x 108 m/s ( c)

Parts of a wave

Wavelength

Amplitude

Orgin

Crest

Trough

Parts of WaveOrgin - the base line of the energy.Crest - high point on a waveTrough - Low point on a waveAmplitude - distance from origin to crestWavelength - distance from crest to crestWavelength - is abbreviated l Greek letter

lambda.

Waves

To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation.

The distance between corresponding points on adjacent waves is the wavelength ().

Waves

The number of waves passing a given point per unit of time is the frequency ().

For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

Electromagnetic RadiationAll electromagnetic radiation travels

at the same velocity: the speed of light (c), 3.00 108 m/s.

Therefore, c =

Frequency

The number of waves that pass a given point per second.

Units are cycles/sec or hertz (hz)Abbreviated n the Greek letter nu

c = ln

Frequency and wavelength

Are inversely relatedAs one goes up the other goes down.Different frequencies of light is different

colors of light.There is a wide variety of frequenciesThe whole range is called a spectrum

Radiowaves

Microwaves

Infrared . Ultra-violet

X-Rays GammaRays

Low energy High energy

Low Frequency High Frequency

Long Wavelength Short Wavelength

Visible Light

Wave model of light cannot explain several phenomena:

◦Emission of light from hot objects (black body radiation)

◦Emission of electrons from metal surfaces on which light shines (photoelectric effect)

◦Emission spectra of light from electronically excited gas atoms (emission spectra)

The Nature of Energy

The wave nature of light does not explain how an object can glow when its temperature increases.

Max Planck explained it by assuming that energy comes in packets called quanta.

Light is a Particle

Energy is quantized.Light is energyLight must be quantizedThese smallest pieces of light are called

photons.Energy and frequency are directly related.

Energy and frequencyE = h x n E is the energy of the photon n is the frequencyh is Planck’s constant h = 6.6262 x 10 -34 Joules sec.joule is the metric unit of Energy

The Nature of EnergyEinstein used this

assumption to explain the photoelectric effect.

He concluded that energy is proportional to frequency:

E = hwhere h is Planck’s constant, 6.63 10−34 J-s.

Photoelectric effect

Light shining on a clean surface causes the surface to emit electrons

A minimum frequency of light, different for different metals, is required for the emission of electrons

Einstein deduced each photon must have an energy equal to Planck's constant times the frequency of the light


Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:

c = E = h

The Math

Only 2 equations

c = λνE = hνPlug and chug.

ExamplesWhat is the wavelength of blue light with a frequency of 8.3 x 1015 hz?

What is the frequency of red light with a wavelength of 4.2 x 10-5 m?

What is the energy of a photon of each of the above?

PES

PHOTOELECTRON SPECTROSCOPY (PES)Interpret spectroscopic data and extract

information on atomic structure Low resolution PES of atoms provides

evidence of shell model

HOW DOES PES WORK?

Light consists of photons, each of which has energy E = hv, where h is Planck’s constant and v is frequency of light

IN PHOTOELECTRIC EFFECT

Incident light ejects electrons from material

This requires the photon to have sufficient energy to eject the electron

PES determines energy needed to eject electrons

PES

Measurement of these energies provides a method to deduce the shell structure of an atom

PES

Intensity of photoelectron signal at a given energy is a measure of # of electrons in that energy level

PES

Electron structure of atoms with multiple electrons can be inferred from evidence provided by PES

6.11, 6.12, 6.14, 6.17, 6.18

HW

Line Spectra and the Bohr model

How color tells us about atoms

Atomic Spectrum

How color tells us about atoms

Prism

White light is made up of all the colors of the visible spectrum.

Passing it through a prism separates it.

If the light is not white

By heating a gas with electricity we can get it to give off colors.

Passing this light through a prism does something different.

Atomic SpectrumEach element

gives off its own characteristic colors.

Can be used to identify the atom.

How we know what stars are made of.

• These are called discontinuous spectra

• Or line spectra• unique to each element.• These are emission spectra• The light is emitted given off.


Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.


One does not observe a continuous spectrum, as one gets from a white light source.

Only a line spectrum of discrete wavelengths is observed.


Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:1. Electrons in an atom can

only occupy certain orbits (corresponding to certain energies).


Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:2. Electrons in permitted

orbits have specific, “allowed” energies; these energies will not be radiated from the atom.


Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:3. Energy is only absorbed

or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by

E = h

The Nature of EnergyThe energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:

E = −RH ( )1nf

2

1ni

2-

where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron.

Limitations of the Bohr Model

Electrons exist only in certain discrete energy levels, which are described by quantum numbers

Energy is involved in the transition of an electron from one level to another

The Wave Nature of Matter

Louis de Broglie suggested that if light can have material properties, matter should exhibit wave properties.

He demonstrated that the relationship between mass and wavelength was

h = Planck’s constant and v = velocityQuantity mv is called its momentum

=hmv

The Uncertainty Principle

Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known:

In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

(x) (mv) h4

HOMEWORK

6.23, 6.24, 6.30, 6.33, 6.35a,

Quantum Theory

1. What did Schrödingers equation lead to?2. What is the principal reason we must consider the

uncertainty principle when discussing electrons and other subatomic particles but not when discussing our

macroscopic world?

Quantum Mechanics

Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated.

It is known as quantum mechanics.

Quantum MechanicsThe wave equation is

designated with a lower case Greek psi ().

The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.

Quantum MechanicsElectron density refers to the

probability of finding an electron in a specified location

High dot density, high

Ψ2 value, high

probability of finding an electron in this region

Low dot density, low Ψ2

value, low probability of

finding an electron in this

region

Quantum Numbers

Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies.

Each orbital describes a spatial distribution of electron density.

An orbital is described by a set of three quantum numbers.

Principal Quantum Number, n

The principal quantum number, n, describes the energy level on which the orbital resides.

The values of n are integers ≥ 0. Increase in n means the electron has a

higher energy and is therefore less tightly bound to the nucleus

For Hydrogen En= -2.178x10-18 / n2 (Bohr calculated the energies corresponding to the allowed orbits for the electron)

Azimuthal Quantum Number, l

This quantum number defines the shape of the orbital.

Allowed values of l are integers ranging from 0 to n − 1.

We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

Azimuthal Quantum Number, l

Value of l 0 1 2 3

Type of orbital s p d f

Magnetic Quantum Number, ml

Describes the three-dimensional orientation of the orbital.

Values are integers ranging from -l to l: −l ≤ ml ≤ l.

Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.

Magnetic Quantum Number, ml

Orbitals with the same value of n form a shell.

Different orbital types within a shell are subshells.

Questions:

1. Without referring to Table 6.2 predict the number of subshells in the fourth shell, that is for n = 4?

2. Give the label for each of these subshells?

3. How many orbitals are in each of these subshells?

Questions:

1. What is the designation for the subshell with n=5 and l=1?

2. How many orbitals are in this subshell?3. Indicate the values of m1 for each of

these orbitals

HOMEWORK:

1. 6.49, 6.51, 6.52

AIM: QUANTUM THEORY

DO NOW:

Textbook #6.53, 6.54, 6.55

s OrbitalsValue of l = 0.Spherical in shape.Radius of sphere

increases with increasing value of n.

s Orbitals

Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.

p Orbitals

Value of l = 1.Have two lobes with a node between

them.

d Orbitals

Value of l is 2.

Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

F orbitals

Summary

s

p

d

f

# of shapes Max electrons Starts at energy level

1 2 1

3 6 2

5 10 3

7 14 4

Spin Quantum Number, ms

In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.

The “spin” of an electron describes its magnetic field, which affects its energy.

Spin Quantum Number, ms

This led to a fourth quantum number, the spin quantum number, ms.

The spin quantum number has only 2 allowed values: +1/2 and −1/2.

Pauli Exclusion Principle

No two electrons in the same atom can have exactly the same energy.

For example, no two electrons in the same atom can have identical sets of quantum numbers.

Pauli Exclusion Principle

To put more than one electron in an orbital and satisfy the Pauli Exclusion principle, need to assign different ms value (only 2 possible values for ms)

Orbital can have a max of 2 electrons and they must have opposite spins

Energies of Orbitals

For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.

That is, they are degenerate.


The presence of more than one electron greatly changes the energies of the orbitals


As the number of electrons increases, though, so does the repulsion between them.

Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.

By Energy Level

First Energy Level

only s orbitalonly 2 electrons1s2

Second Energy Level

s and p orbitals are available

2 in s, 6 in p2s22p6

8 total electrons

By Energy LevelThird energy

levels, p, and d

orbitals2 in s, 6 in p,

and 10 in d3s23p63d10

18 total electrons

Fourth energy level

s,p,d, and f orbitals

2 in s, 6 in p, 10 in d, and 14 in f

4s24p64d104f14

32 total electrons

By Energy LevelAny more than

the fourth and not all the orbitals will fill up.

You simply run out of electrons

The orbitals do not fill up in a neat order.

The energy levels overlap

Lowest energy fill first.

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

HOMEWORK

6.8, 6.61, 6.62, 6.64, 6.65

Aim: Electron Configurations

DO NOW: answer the following questions:1. What information does an electron

configuration give us?2. What are valence electrons and where

are they located in the electron configuration?

3. What do you think core electrons are?

Electron Configurations

Distribution of all electrons in an atom

Consist of ◦ Number denoting the

energy level


Distribution of all electrons in an atom


energy level◦ Letter denoting the

type of orbital


Distribution of all electrons in an atom.


energy level.◦ Letter denoting the

type of orbital.◦ Superscript denoting

the number of electrons in those orbitals.

Orbital Diagrams

Each box represents one orbital.

Half-arrows represent the electrons.

The direction of the arrow represents the spin of the electron.

Hund’s Rule

“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

Electron ConfigurationsThe way electrons are arranged in atoms.Aufbau principle- electrons enter the

lowest energy first.This causes difficulties because of the

overlap of orbitals of different energies.Pauli Exclusion Principle- at most 2

electrons per orbital - different spins

PARAMAGNETISM Diamagnetism - All of the electrons are

spin-paired in diamagnetic elements so their subshells are completed, causing them to be unaffected by magnetic fields.

Paramagnetism - Paramagnetic elements are strongly affected by magnetic fields because their subshells are not completely filled with electrons.

PARAMAGNETISM Which of the following elements would be expected to be paramagnetic? Diamagnetic?He, Be, Li, N

He: 1s2 subshell is filledBe: 1s22s2 subshell is filledLi: 1s22s1 subshell is not filledN: 1s22s22p3 subshell is not filledAnswerLi and N are paramagnetic. He and Be

are

Electron Configuration

Hund’s Rule- When electrons occupy orbitals of equal energy they don’t pair up until they have to .

Let’s determine the electron configuration for Phosporus

Need to account for 15 electrons

The first to electrons go into the 1s orbital

Notice the opposite spins

only 13 more

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

The next electrons go into the 2s orbital

only 11 more

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The next electrons go into the 2p orbital• only 5 more

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The next electrons go into the 3s orbital• only 3 more

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

Incr

easi

ng e

nerg

y

1s

2s

3s

4s

5s

6s

7s

2p

3p

4p

5p

6p

3d

4d

5d

7p 6d

4f

5f

• The last three electrons go into the 3p orbitals.

• They each go into seperate shapes• 3 upaired electrons

•1s

22s

22p

63s

23p

3

The easy way to remember

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2

• 2 electrons

Fill from the bottom up following the arrows

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2

• 4 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

• 12 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2

• 20 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2

• 38 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2 4d10 5p6 6s2

• 56 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2 4d10 5p6 6s2

4f14 5d10 6p6 7s2• 88 electrons


1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2 2s2 2p6 3s2

3p6 4s2 3d10 4p6

5s2 4d10 5p6 6s2

4f14 5d10 6p6 7s2

5f14 6d10 7p6 • 108 electrons

Exceptions to Electron Configuration

Orbitals fill in order

Lowest energy to higher energy.Adding electrons can change the energy

of the orbital.Half filled orbitals have a lower energy.Makes them more stable.Changes the filling order

Write these electron configurations

Titanium - 22 electrons1s22s22p63s23p64s23d2

Vanadium - 23 electrons

1s22s22p63s23p64s23d3

Chromium - 24 electrons1s22s22p63s23p64s23d4 is expectedBut this is wrong!!

Chromium is actually

1s22s22p63s23p64s13d5

Why?This gives us two half filled orbitals.Slightly lower in energy.The same principal applies to copper.

Copper’s electron configurationCopper has 29 electrons so we expect1s22s22p63s23p64s23d9

But the actual configuration is1s22s22p63s23p64s13d10

This gives one filled orbital and one half filled orbital.

Remember these exceptions

Periodic Table

We fill orbitals in increasing order of energy.

Different blocks on the periodic table, then correspond to different types of orbitals.

Some Anomalies

Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.

Some Anomalies

For instance, the electron configuration for copper is[Ar] 4s1 3d5

rather than the expected[Ar] 4s2 3d4.

Some Anomalies

This occurs because the 4s and 3d orbitals are very close in energy.

These anomalies occur in f-block atoms, as well.

AP CHEM PRACTICE – finish for HW

Complete the circled problems in the packet

Text #6.68, 6.69, 6.70, 6.73STUDY TEST ON WED!

light and planck's constant do now: using your textbooks answer the following 1. what is mass...

Documents

emission of light

minimum frequency of

study of light

wave nature of light

wave model of light

photoelectric effect

different frequencies

different colors of