Chapter 6 Electronic Structure of Atoms or “How I Learned to Stop Worrying and Love the...

Chapter 6Electronic Structureof Atomsor “How I Learned to Stop Worrying and Love the Electron”

ElectronicStructureof Atoms

Problems with the Rutherford Model

1. Classical physics says atoms should emit light and destroy themselves - they don’t

2. Atoms can be induced to emit light, but they give off a line spectrum, rather than a continuous spectrum.

3. Every atom gives off different colours of light.

4. No explanation of why different atoms have different properties, or the same properties.

Let’s Talk About Light

What is Light?

• light is radiant energy.•a better term is electromagnetic energy

(EMR)• includes not only visible light, but many

forms of EMR we cannot see directly:▫heat▫microwaves▫x-rays

• light has properties of both waves and particles.

Wave model of Light

•The distance between corresponding points on adjacent waves is the wavelength

•The symbol is the Greek letter lamda ().•The height of the wave is the amplitude.

It corresponds to the intensity of the light

Waves•The number of waves

passing a given point per unit of time is the frequency,

•The symbol is the Greek letter nu ().

•The longer the wavelength, the smaller the frequency.

Electromagnetic Radiation•EMR is a continuous spectrum of wavelengths.

Using λ and ν to determine “colour”•“Colour” is a term used to describe visible

light.•Visible light is a very small part of the

electromagnetic spectrum:▫radio waves -- ultraviolet▫microwaves -- x-rays▫infrared -- gamma rays▫visible

Colour of Light

•we can identify light by its wavelength or frequency:▫a wave 5.00 x 10-7 m is

green▫a wave 6.80 x 10-7 m is

red▫a wave 2.60 x 10-5 m is

infrared▫a wave 7.80 x 10-10 m is

in the x-ray region.

Speed of Light• is the one thing that is constant in the universe

(sort of).• in a vacuum, the speed of light is 3.00 x 108 m/s• there is a relationship between wavelength and

frequency:

• where ▫c = speed of light▫λ = wavelength▫ν = frequency

•Complete questions 6.13 to 6.18, even

Quantized Energy and Photons

•The wave model of light is good, but it does not explain:▫how an object can glow

when its temperature increases. (Blackbody radiation)

▫emission of electrons by shining light on the surface of a metal. (photoelectric effect)

▫emission of light from electrons of excited gas atoms. (emission spectra)

Blackbody Radiation

•Heated solids emit radiation (blackbody radiation)▫The wavelength distribution depends on

the temperature (i.e., “red hot” objects are cooler than “white hot” objects).

▫Why does wavelength or frequency depend on temperature?

•Max Planck suggested a way out by assuming that energy comes in packets called quanta.

• Planck proposed a relationship between energy and the frequency of light quanta:

•where:▫E = energy in Joules▫h = Planck’s constant (6.6262 x 10-34 J·s)▫ν = frequency, in Hertz (1/s, s-1)

• as energy increases, so does frequency.

•Complete questions 6.21 to 6.28

The PhotoelectricEffect

Photons•Einstein used the quantum to

explain the photoelectric effect:▫Light comes in particles,

called photons.▫The energy of each photon is

determined by Planck’s equation.

•Light shining on the surface of a metal can cause electrons to be ejected from the metal.

•The electrons will only be ejected if the photons have sufficient energy:▫Below the threshold frequency no electrons are

ejected.▫Above the threshold frequency, the excess

energy appears as the kinetic energy of the ejected electrons.

•Light has wave-like AND particle-like properties.

•Complete question 6.30

Line Spectra and the Bohr Model

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

The Nature of Energy

•A white light source produces a continuous spectrum, like a rainbow.

•When elements are excited, only a line spectrum of discrete wavelengths is observed.

Hydrogen Spectrum• has line spectra in 3 regions

of the EM Spectrum:▫Ultraviolet – Lymann Series▫Visible – Balmer Series▫ Infrared - Paschen Series

• Niels Bohr adopted Planck’s ideas about the quantum and applied them to the electrons around a nucleus.

•Bohr’s model is based on three postulates:1. Electrons in an atom can only occupy certain

permitted orbits, or quanta.2. Electrons in permitted orbits have specific,

“allowed” energies; these energies will not be radiated from the atom.

3. Energy is only absorbed or emitted to move an electron from one “allowed” energy state to another; the energy is emitted by a photon:

•An electron in its lowest permissible energy is at ground state

• If an electron accepts a quantum of energy it will move to a higher energy level, or excited state.

•When the electron moves back down to ground state it emits a photon of light of a frequency which correlates to the energy of the quantum.

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

E = −RH ( )1nf2

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.

• this explains the line spectra of hydrogen:▫Lyman series. High

energy, in the UV range. Represents energy transition from higher quanta to ground state.

▫Balmer series. Intermediate energy, in the visible range. Represents energy transition from higher quanta to quantum 2.

▫Paschen series. Low energy, in the IR range. Represents energy transition from higher quanta to quantum 3.

Limitations of Bohr Model

•cannot explain the spectra of atoms other than hydrogen.

•However, the model introduces two important ideas:▫The energy of an electron is quantized:

electrons exist only in certain energy levels described by quantum numbers.

▫Energy gain or loss is involved in moving an electron from one energy level to another.

The Wave Nature of Matter•Louis de Broglie posited that if light can

have material properties, matter should exhibit wave properties.

•He demonstrated that the relationship between mass and wavelength was

What does this mean?

•electrons have wave properties.• the orbits of electrons are multiples of the

electron wavelength▫the first orbit has a circumference of 1 λ, the

second is 2 λ , etc.

The Uncertainty Principle•Heisenberg showed that the

more precisely the momentum of a particle is known, the less precisely is its position known.

•Our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

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.

•The wave function describes the electron’s matter wave; it gives the probability of finding the electron.

•Electron density is another way of expressing probability. ▫A region of high electron density is one

where there is a high probability of finding an electron.

Orbitals and 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•describes the energy level on which the

orbital resides.•The values of n are integers ≥ 0. •correspond to the periods on the

Periodic Table.

Azimuthal Quantum Number, l•defines the shape of the orbital.•Allowed values of l are integers ranging

from 0 to n − 1.• letter designations communicate the

different values of l and, therefore, the shapes and types of orbitals.

Azimuthal Quantum Number, lValue of l 0 1 2 3

Type of orbital s p d f

• Theoretical g, h, i, etc. orbitals exist, but no atoms have been created to use them.

Magnetic Quantum Number, ml• three-dimensional orientation of the

orbital.•Values are integers ranging from -l to

l : −l ≤ ml ≤ l

•on any given energy level, there can be up to:▫ 1 s orbital▫3 p orbitals▫5 d orbitals▫7 f orbitals

Magnetic Quantum Number, ml

•Orbitals with the same value of n form a shell.

•Different orbital types within a shell are subshells.

•Each subshell is designated by a number and a letter. ▫For example, 3p orbitals have n = 3 and l

In Summary

s Orbitals

•Value of l = 0.•Spherical in shape.•Radius of sphere

increases with increasing value of n.

p Orbitals

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

them.•The letters correspond to allowed the

values of ml of –1, 0, and +1.

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.

• The letters correspond to allowed the values of ml of -2, –1, 0, +1 and +2.

f orbitals•Value of l is 3.•7 possible

shapes, including 8 lobes and 2 doughnuts.

•The letters correspond to allowed the values of ml of -3, -2, –1, 0, +1, +2 and +3.

Energies of Orbitals

•Orbitals of the same energy are degenerate.

Spin Quantum Number, ms

• 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

•There is a spin quantum number, ms.

•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.

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

Electron Configurations

• Distribution of all electrons in an atom

• Tell us how the electrons are distributed among the various orbitals of an atom.

• Consist of ▫ Number denoting the energy level

• Distribution of all electrons in an atom

• Consist of ▫ Number denoting the energy level▫ Letter denoting the type of orbital

• Distribution of all electrons in an atom.

• Consist of ▫ Number denoting the energy level.▫ Letter denoting the type of orbital.▫ Superscript denoting the number of

electrons in those orbitals.

Electron Configurations•Electrons tend to occupy the lowest energy orbitals at ground state.

•Thus the electron configuration of an atom is the arrangement of the electrons from the lowest energy level to the highest.

Electron Configurations•For any atom or ion:▫find total number of electrons▫start with the 1s electrons and fill each orbital in

order of energy▫watch the order of filling; energy is all important

•For instance:▫Iron (Fe) – contains 26 electrons▫1s22s22p63s23p64s23d6

Electron Configuration of Period 2 Elements

Element Electron configuration lithium 1s22s1

beryllium 1s22s2

boron 1s22s22p1

carbon 1s22s22p2

nitrogen 1s22s22p3

oxygen 1s22s22p4

fluorine 1s22s22p5

neon 1s22s22p6

Examples:•Potassium - 19 electrons▫1s22s22p63s23p64s1

•Silver - 47 electrons▫1s22s22p63s23p64s23d104p65s24d9

•Tungsten - 74 electrons▫1s22s22p63s23p64s23d104p65s24d105p66s2

4f145d4

•Plutonium - 94 electrons▫1s22s22p63s23p64s23d104p65s24d105p66s2

4f14 5d106p67s25f6

•Write the correct electron configuration for the following:▫S, P, As, Fe, Br, At, U, Na1+, O2-, Ne, Kr,

Si, Al, Ca

Electron Configuration• S - 16 e1- 1s22s22p63s23p4

• P - 15 e1- 1s22s22p63s23p3

• As - 33 e1- 1s22s22p63s23p64s23d104p3

• Fe - 26 e1- 1s22s22p63s23p64s23d6

• Br - 35 e1- 1s22s22p63s23p64s23d104p5

• At - 85 e1-

1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p5

• U - 92 e1- 1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p6 7s25f4

• Na1+ -10 e1- 1s22s22p6

• O2- - 10 e1- 1s22s22p6

• Ne - 10 e1- 1s22s22p6

• Kr - 36 e1- 1s22s22p63s23p64s23d104p6

• Si - 14 e1- 1s22s22p63s13p3

• Al - 13 e1- 1s22s22p63s13p2

• Ca - 20 e1- 1s22s22p63s23p64s14p1

Electron Promotion•movement of an outer ‘s’ electron to the

adjacent ‘p’ orbital at the same energy level.

• turns non-bonding electrons into bonding electrons

•allows atoms to make more chemical bonds and achieve a lower energy

•applies to elements from groups 2, 13 and 14 only

• for these elements promotion is the rule

Electron PromotionElement Unhybridized Hybridized

beryllium 1s22s2 1s22s12p1

boron 1s22s22p1 1s22s12p2

carbon 1s22s22p2 1s22s12p3

Orbital Diagrams• are another way to illustrate the position of

electrons. • They are best learned by comparison with

electron configuration:

• Na (11 protons, 11 electrons)• electron configuration: 1s22s22p63s1

• orbital diagram:

1s 2s 2p 3s

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑

Orbital Diagrams

•Each line represents one orbital.

•Arrows represent the electrons.

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

Hund’s Rule

“In any orbital with more than 1 sub-orbital electrons will half-fill each sub-orbital before pairing up.”

Orbital DiagramsRepresentative

Group Element Electron configuration Orbital Diagram

1s 2s 2p 1 lithium 1s22s1 ↑↓ ↑

2 beryllium 1s22s12p1 ↑↓ ↑ ↑

13 boron 1s22s12p2 ↑↓ ↑ ↑ ↑

14 carbon 1s22s12p3 ↑↓ ↑ ↑ ↑ ↑

15 nitrogen 1s22s22p3 ↑↓ ↑↓ ↑ ↑ ↑

16 oxygen 1s22s22p4 ↑↓ ↑↓ ↑↓ ↑ ↑

17 fluorine 1s22s22p5 ↑↓ ↑↓ ↑↓ ↑↓ ↑

18 neon 1s22s22p6 ↑↓ ↑↓ ↑↓ ↑↓ ↑↓

Note the electron promotion for the elements from groups 2, 13 & 14

•Repeat the last assignment, giving the orbital diagrams for the elements.

• these are examples of electron promotion

Condensed Electron Configurations•Looks mainly at electrons with the highest

energy:▫find element on the Periodic Table.▫find noble gas with lower atomic number▫write electron configuration from that point.

•Example: ▫P is 1s22s22p63s23p3,▫but Ne is 1s22s22p6.▫Therefore, P is [Ne]3s23p3.

Electron Configuration and the Periodic Table•The periodic table can be used as a guide

for electron configurations.▫The period number is the value of n.▫Groups 1 & 2 - s block▫Groups 13 to 18 - p block▫Groups 3 – 12 – d block▫The lanthanides and actinides - f block

•Watch the order of filling!

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.

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