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Modern Atomic Theory

Chapter 10

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Electromagnetic Radiation• Classical physics says matter made up of

particles, energy travels in waves

• Electromagnetic Radiation is radiant energy, both visible and invisible

• Electromagnetic radiation travels in waves

• All waves are characterized by their velocity, wavelength, amplitude, and the number of waves that pass a point in a given time

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Figure 10.1 (a): A light wave

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Electromagnetic Waves• velocity = c = speed of light

– 2.997925 x 108 m/s– all types of light energy travel at the same speed

• amplitude = A = measure of the intensity of the wave, “brightness”

• wavelength = = distance between two consecutive peaks or troughs in a wave– generally measured in nanometers (1 nm = 10-9 m)– same distance for troughs

• frequency = = the number of waves that pass a point in space in one second– generally measured in Hertz (Hz), – 1 Hz = 1 wave/sec = 1 sec-1

• c = x

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Figure 10.2: The different wavelengths of electromagnetic radiation

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Planck’s Revelation

• Showed that light energy could be thought of as particles for certain applications

• Stated that light came in particles called quanta or photons

• Particles of light have fixed amounts of energy– Basis of quantum theory

• The energy of the photon is directly proportional to the frequency of light– Higher frequency = More energy in photons

hc

EhE

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Figure 10.3: Electromagnetic radiation

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Problems with Rutherford’s Nuclear Model of the Atom

• Electrons are moving charged particles

• Moving charged particles give off energy

• Therefore the atom should constantly be giving off energy

• And the electrons should crash into the nucleus and the atom collapse!!

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Atomic Spectra• Atoms which have gained extra energy release that

energy in the form of light• The light atoms give off or gained is of very

specific wavelengths called a line spectrum– light given off = emission spectrum

– light energy gained = absorption spectrum

– extends to all regions of the electromagnetic spectrum

• Each element has its own line spectrum which can be used to identify it

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Figure 10.5: Absorption and Emission Processes

Absorption

Emission

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Figure 10.6: When an excited H atom returns to a lower energy level, it emits a photon that contains

the energy released by the atom

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Atomic Spectra• The line spectrum must be related to energy

transitions in the atom.– Absorption = atom gaining energy

– Emission = atom releasing energy

• Since all samples of an element give the exact same pattern of lines, every atom of that element must have only certain, identical energy states

• The atom is quantized– If the atom could have all possible energies, then the

result would be a continuous spectrum instead of lines

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Figure 10.7: When excited hydrogen atoms return to lower energy states, they emit photons of certain

energies, and thus certain colors

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Figure 10.9: Each photon emitted by an excited hydrogen atom corresponds to a particular energy change in the hydrogen atom

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Bohr’s Model• Explained spectra of hydrogen• Energy of atom is related to the distance

electron is from the nucleus• Energy of the atom is quantized

– atom can only have certain specific energy states called quantum levels or energy levels

– when atom gains energy, electron “moves” to a higher quantum level

– when atom loses energy, electron “moves” to a lower energy level

– lines in spectrum correspond to the difference in energy between levels

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Figure 10.10: (a) Continuous energy levels. (b) Discrete (quantized) energy levels.

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Figure 10.11: The difference between continuous and quantized energy levels

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Bohr’s Model• Atoms have a minimum energy called the ground state

– therefore they do not crash into the nucleus• The ground state of hydrogen corresponds to having its one

electron in an energy level that is closest to the nucleus• Energy levels higher than the ground state are called excited

states– the farther the energy level is from the nucleus, the higher its

energy• To put an electron in an excited state requires the addition of

energy to the atom; bringing the electron back to the ground state releases energy in the form of light

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Figure 10.13: The Bohr model of the hydrogen atom

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Bohr’s Model• Distances between energy levels decreases as the

energy increases– light given off in a transition from the second energy

level to the first has a higher energy than light given off in a transition from the third to the second, etc.

– Electrons “orbit” the nucleus much like planets orbiting the sun

• 1st energy level can hold 2e-1, the 2nd 8e-1, the 3rd 18e-1, etc.– farther from nucleus = more space = less repulsion

• The highest energy occupied ground state orbit is called the valence shell

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Figure 10.9: Each photon emitted by an excited hydrogen atom corresponds to a particular energy change in the hydrogen atom

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Problems with the Bohr Model

• Only explains hydrogen atom spectrum– and other 1 electron systems

• Neglects interactions between electrons

• Assumes circular or elliptical orbits for electrons - which is not true

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Wave Mechanical Model of the Atom

• Experiments later showed that electrons could be treated as waves– just as light energy could be treated as particles

– de Broglie

• The quantum mechanical model treats electrons as waves and uses wave mathematics to calculate probability densities of finding the electron in a particular region in the atom– Schrödinger Wave Equation

– can only be solved for simple systems, but approximated for others

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Figure 10.15: The probability map, or orbital, that describes the hydrogen electron in its lowest possible energy state

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Orbitals• Solutions to the wave equation give regions in space

of high probability for finding the electron - these are called orbitals– usually use 90% probability to set the limit

– three-dimensional

• Orbitals are defined by three integer terms that are added to the wave equation to quantize it - these are called the quantum numbers

• Each electron also has a fourth quantum number to represent the direction of spin

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Figure 10.16: The hydrogen 1s orbital

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Orbitals and Energy Levels• Principal energy levels identify how much energy

the electrons in the orbital have– n– higher values mean orbital has higher energy– higher values mean orbital has farther average distance

from the nucleus• Each principal energy level contains one or more

sublevels– there are n sublevels in each principal energy level– each type of sublevel has a different shape and energy– s < p < d < f

• Each sublevel contains one or more orbitals– s = 1 orbital, p = 3, d = 5, f = 7

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Figure 10.17: The first four principal energy levels in the hydrogen atom

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Figure 10.18: Principal levels can be divided into sublevels

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Figure 10.19: Principal level 2 shown divided into the 2s and 2p sublevels

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Figure 10.20: The relative sizes of the 1s and 2s orbitals of hydrogen

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Figure 10.21: The three 2p orbitals: (a) 2px, (b) 2pz, (c) 2py.

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Figure 10.22: A diagram of principal energy levels 1 and 2 showing the shapes of orbitals that compose

the sublevels

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Figure 10.23: The relative sizes of the spherical 1s, 2s, and 3s orbitals of hydrogen

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Figure 10.24: The shapes and labels of the five 3d orbitals

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Pauli Exclusion Principle• No orbital may have more than 2 electrons

• Electrons in the same orbital must have opposite spins

• s sublevel holds 2 electrons

• p sublevel holds 6 electrons

• d sublevel holds 10 electrons

• f sublevel holds 14 electrons

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• for a many electron atom, build-up the energy levels, filling each orbital in succession by energy

• ground state• 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d <

5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p• degenerate orbitals are orbitals with the same

energy– each p sublevel has 3 degenerate p orbitals

– each d sublevel has 5 degenerate d orbitals

– each f sublevel has 7 degenerate f orbitals

Orbitals, Sublevels & Electrons

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Figure 10.28: A box diagram showing the order in which orbitals fill to produce the atoms in the periodic table

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Hund’s Rule

• for a set of degenerate orbitals, half fill each orbital first before pairing

• highest energy level called the valence shell– electrons in the valence shell called valence electrons

– electrons not in the valence shell are called core electrons

– often use symbol of previous noble gas to represent core electrons

1s22s22p6 = [Ne]

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Electron Configuration• Elements in the same column on the

Periodic Table have – Similar chemical and physical properties – Similar valence shell electron configurations

• Same numbers of valence electrons• Same orbital types• Different energy levels

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s1

s2

d1 d2 d3 d4 d5 d6 d7 d8 d9 d10

p1 p2 p3 p4 p5 s2

p6

f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14

1234567

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Figure 10.25: The electron configurations in the sublevel last occupied for the first eighteen

elements

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The Modern Periodic Table• Columns are called Groups or Families

• Rows are called Periods– Each period shows the pattern of properties

repeated in the next period

• Main Groups = Representative Elements

• Transition Elements

• Bottom rows = Lanthanides and Actinides– really belong in Period 6 & 7

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Figure 10.26: Partial electron configurations for the elements potassium through krypton

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Figure 10.27: The orbitals being filled for elements in various parts of the periodic table

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Metallic Character

• Metals– malleable & ductile

– shiny, lustrous

– conduct heat and electricity

– most oxides basic and ionic

– form cations in solution

– lose electrons in reactions - oxidized

• Nonmetalsbrittle in solid statedullelectrical and

thermal insulatorsmost oxides are

acidic and molecular form anions and

polyatomic anionsgain electrons in

reactions - reduced

• MetalloidsAlso known as

semi-metalsShow some

metal and some nonmetal properties

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Figure 10.31: The classification of elements as metals, nonmetals, and metalloids

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Metallic Character• Metals are found on the left of the table,

nonmetals on the right, and metalloids in between• Most metallic element always to the left of the

Period, least metallic to the right, and 1 or 2 metalloids are in the middle

• Most metallic element always at the bottom of a column, least metallic on the top, and 1 or 2 metalloids are in the middle of columns 4A, 5A, and 6A

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Reactivity

• Reactivity of metals increases to the left on the Period and down in the column– follows ease of losing an electron

• Reactivity of nonmetals (excluding the noble gases) increases to the right on the Period and up in the column

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Trend in Ionization Energy• Minimum energy needed to remove a valence electron

from an atom– gas state

• The lower the ionization energy, the easier it is to remove the electron– metals have low ionization energies

• Ionization Energy decreases down the group– valence electron farther from nucleus

• Ionization Energy increases across the period– left to right

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Trend in Atomic Size

• Increases down column– valence shell farther from nucleus

• Decreases across period – left to right– adding electrons to same valence shell– valence shell held closer because more protons

in nucleus

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Figure 10.32: Relative atomic sizes for selected atoms. Note that atomic size increases down a group and decreases across a period