1 chapter 6 the structure of atoms. 2 electromagnetic radiation mathematical theory that describes...

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CHAPTER 6• The Structure of Atoms

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Electromagnetic RadiationElectromagnetic RadiationMathematical theory that describes all

forms of radiation as oscillating (wave-like) electric and magnetic fields

Figure 7.1Figure 7.1

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Wave PropertiesWavelength (): distance between consecutive crests or troughs

Frequency (): number of waves that pass a given point in some

unit of time (1 sec)

-units of frequency 1/time such as 1/s = s-1 = Hz

Amplitude (A): the maximum height of a wave Nodes: points of zero amplitude

-every /2 wavelength

Amplitude

Node (/2)

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Wave Properties

• c = for electromagnetic radiation

Speed of light (c): 2.99792458 x 108 m/s

Example: What is the frequency of green light of wavelength 5200 Å?

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Electromagnetic SpectrumElectromagnetic Spectrum

wavelength increases

energy increases

frequency increases?

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E = h • E = h •

h = Planck’s constant = 6.6262 x 10-34 J•s

Any object can gain or lose energy by absorbing or emitting radiant energy

-only certain vibrations () are possible (Quanta)

-Energy of radiation is proportional to frequency ()

Maxwell Planck

Planck’s Equation

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Light with a short (large ) has a large ELight with a short (large ) has a large E

Light with large (small ) has a small ELight with large (small ) has a small E

E = h • =hc/E = h • =hc/

Planck’s EquationPlanck’s Equation

Maxwell Planck

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Planck’s Equation

What is the energy of a photon of green light with wavelength 5200 Å?What is the energy of 1.00 mol of these photons?

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Einstein and the Photon

Photoelectric effect: the production of electrons (e-) when light (photons) strikes the surface of a metal

-introduces the idea that light has particle-like properties-photons: packets of massless “particles” of energy-energy of each photon is proportional to the frequency of the radiation (Planck’s equation)

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Atomic Spectra and the Bohr Atom

Line emission spectrum: electric current passing through a gas (usually an element) causing the atoms to be excited

-This is done in a vacuum tube (at very low pressure) causing the gas to emit light

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Atomic Spectra and the Bohr Atom

• Every element has a unique spectrum– -Thus we can use spectra to identify elements.– -This can be done in the lab, with stars, in fireworks,

etc.

H

Hg

Ne

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Adsorption/Emission Spectra

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Atomic Spectra

• Balmer equation (Rydberg equation): relates the wavelengths of the lines (colors) in the atomic spectrum

hydrogen of spectrumemission

in the levelsenergy theof

numbers therefer to sn’

n n

m 10 1.097 R

constant Rydberg theis R

n

1

n

1R

1

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1-7

22

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final int

Principle quantum number

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Atomic Spectra

What is the wavelength of light emitted when the hydrogen atom’s energy changes from

n = 4 to n = 2?

nfinal = 2 ninitial = 4

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Bohr’s greatest contribution to science was in building a simple model of the atom

It was based on an understanding of the SHARP LINE EMISSION SPECTRA of excited atomsNiels Bohr

(1885-1962)

The Bohr Model

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Any orbit should be possible and so is any energy

But a charged particle moving in an electric field should emit (lose) energy

End result is all matter should self-destruct

+Electronorbit

Early view of atomic structure from the beginning of the 20th century -electron (e-) traveled around the nucleus in an orbit

-

--

The Bohr Model

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The Bohr Atom

• In 1913 Neils Bohr incorporated Planck’s quantum theory into the hydrogen spectrum explanation– Here are the postulates of Bohr’s theory:

1. Atom has a definite and discrete number of energy levels (orbits) in which an electron may exist

n – the principal quantum number

As the orbital radius increases so does the energy (n-level) 1<2<3<4<5...

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The Bohr Atom

2. An electron may move from one discrete energy level (orbit) to another, but to do so energy is emitted or absorbed

3. An electron moves in a spherical orbit around the nucleus

-If e- are in quantized energy states, then ∆E of states can have only certain values-This explains sharp line spectra (distinct colors)

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Bohr’s theory was a great accomplishment

Received Nobel Prize, 1922 Problem with this theory- it only

worked for H-introduced quantum idea

artificially-new theory had to developed

Niels Bohr

(1885-1962)

Atomic Spectra and Niels Bohr

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de Broglie (1924) proposed that all moving

objects have wave properties

For light: E = mc2

E = h = hc/ Therefore, mc = h/

For particles: (mass)(velocity) = h/

de Broglie (1924) proposed that all moving

objects have wave properties

For light: E = mc2

E = h = hc/ Therefore, mc = h/

For particles: (mass)(velocity) = h/

Louis de Broglie

(1892-1987)

Wave Properties of the Electron

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The Wave Properties of the Electron

In 1925 Louis de Broglie published his Ph.D. dissertation

Electrons have both particle and wave-like characteristics

All matter behave as both a particle and a wave

– This wave-particle duality is a fundamental property of submicroscopic particles

particle of velocity vparticle, of mass m constant, sPlanck’ h

mv

h

de Broglie’s Principle:

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The Wave Nature of the Electron

Determine the wavelength, in meters, of an electron, with mass 9.11 x 10-31 kg, having a velocity of 5.65 x 107 m/s

Remember Planck’s constant is 6.626 x 10-34 J s which is also equal to 6.626 x 10-34 kg m2/s, because 1 J = 1 kg m2/s2

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Erwin Schrödinger1887-1961

r (pm)0 100 200

200 pm

.50 pm

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Schrödinger applied ideas of e- behaving as a wave to the problem of electrons in atoms

-He developed the WAVE EQUATION-The solution gives a math

expressions called WAVE FUNCTIONS,

-Each describes an allowed energy state for an e- and gives the probability (2) of the location for the e-

Quantization is introduced naturally

Quantum (Wave) Mechanics

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The problem with The problem with defining the nature of defining the nature of electrons in atoms was electrons in atoms was solved by W. Heisenbergsolved by W. Heisenberg

the position and the position and momentum (momentum momentum (momentum = m•v) cannot be define = m•v) cannot be define simultaneously for an simultaneously for an electronelectron

??? we can only ??? we can only define edefine e-- energy exactly energy exactly but we cannot know the but we cannot know the exact position of the eexact position of the e-- to to any degree of certainty. any degree of certainty. Or vice versaOr vice versa

The problem with The problem with defining the nature of defining the nature of electrons in atoms was electrons in atoms was solved by W. Heisenbergsolved by W. Heisenberg

the position and the position and momentum (momentum momentum (momentum = m•v) cannot be define = m•v) cannot be define simultaneously for an simultaneously for an electronelectron

??? we can only ??? we can only define edefine e-- energy exactly energy exactly but we cannot know the but we cannot know the exact position of the eexact position of the e-- to to any degree of certainty. any degree of certainty. Or vice versaOr vice versa

Werner Heisenberg1901-1976

n-levels

Uncertainty Principle

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Schrödinger’s Atomic Model

Atomic orbitals: regions of space where the probability of finding an electron around an atom is greatest

• quantum numbers: letter/number address describing an electrons location (4 total)

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The Principal Quantum Number (n)

n = 1, 2, 3, 4, ...

- electron’s energy depends mainly on n- n determines the size of the orbit the e- is

in- each electron in an atom is assigned an n

value- atoms with more than one e- can have

more than one electron with the same n value (level)- each of these e- are in the same electron energy level (or electron shell)

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Angular Momentum (l)

l = 0, 1, 2, 3, 4, 5, .......(n-1)l = s, p, d, f, g, h, .......(n-1)

-the names and shapes of the corresponding subshells (or suborbitals) in the orbital/energy level (n-level)

– -each l corresponds to a different suborbital shape or suborbital type within an n-level

If n=1, then l = 0 can only exist (s only)If n=2, then l = 0 or 1 can exist (s and p)If n=3, then l = 0, 1, or 2 can exist (s, p

and d)

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Atomic suborbital• s orbitals are spherically symmetric

s orbital properties:

one s orbital for every n-level: l = 0

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The three p-orbitals lie 90o apart in space

There are 3 p-orbitals for every n-level (when n ≥ 2): l = 1

p Orbital

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Magnetic Quantum Number (ml)

ml = - l , (- l + 1), (- l +2), .....0, ......., (l -2), (l -1), +l

– Example: ml for l = 0, 1, 2, 3, …l

– 0, +1 0 -1, +2 +1 0 -1 -2, +3 +2 +1 0 -1 -2 -3, …+l through –l

-This describes the number of suborbitals and direction each suborbital faces

within a given subshell (l) within an orbital (n)-There is no energy difference between each suborbital (ml) set

– If l = 0 (or an s orbital), then ml = 0 for every n • Notice that there is only 1 value of ml.

This implies that there is one s orbital per n value, when n 1

– If l = 1 (or a p orbital), then ml = -1, 0, +1 for n-levels >2• There are 3 values of ml for p suborbitals.

Thus there are three p orbitals per n value, when n 2

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Atomic suborbital• s orbitals are spherically symmetric

s orbital properties:

one s orbital for every n-level: l = 0 and only 1 value for ml

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p Orbital Properties

The first p orbitals appear in the n = 2 shell-p orbitals have peanut or dumbbell shaped volumes-They are directed along the axes of a Cartesian coordinate system.

• There are 3 p orbitals per n-level:– -The three orbitals are named px, py, pz.– -They all have an l = 1 with different ml

– -ml = -1, 0, +1 (are the 3 values of ml)

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When n = 2, then When n = 2, then ll = 0 and/or 1 = 0 and/or 1

Therefore, in n = 2 shell there Therefore, in n = 2 shell there are 2 types of are 2 types of suborbitals/subshellssuborbitals/subshells

For For ll = 0 = 0 mmll = 0 = 0

this is an s subshellthis is an s subshell

For For ll = 1 m = 1 mll = -1, 0, +1 = -1, 0, +1

this is a this is a p subshell with with 3 orientations

When n = 2, then When n = 2, then ll = 0 and/or 1 = 0 and/or 1

Therefore, in n = 2 shell there Therefore, in n = 2 shell there are 2 types of are 2 types of suborbitals/subshellssuborbitals/subshells

For For ll = 0 = 0 mmll = 0 = 0

this is an s subshellthis is an s subshell

For For ll = 1 m = 1 mll = -1, 0, +1 = -1, 0, +1

this is a this is a p subshell with with 3 orientations

planar node

Typical p orbital

planar node

Typical p orbital

When l = 1, there is a single PLANAR NODE thru the nucleus

• p orbitals are peanut or dumbbell shaped

p Orbitals

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d Orbital PropertiesThe first d suborbitals appear in the n = 3 shell

•-The five d suborbitals have two different shapes:– 4 are clover shaped– 1 is dumbbell shaped with a doughnut

around the middle•-The suborbitals lie directly on the Cartesian axes

or are rotated 45o from the axes

222 zy-xxzyzxy d ,d ,d ,d ,dThere are 5d orbitals per n level:

–The five orbitals are named –They all have an l = 2 with different ml

ml = -2,-1,0,+1,+2 (5 values of m l)

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s orbitals l = 0, have no planar node, and so are spherical

p orbitals l = 1, have 1 planar node, and so are “dumbbell” shaped

This means d orbitals with l = 2, have 2 planar nodes, and so have 2 different shapes

(clover and dumbbell with a donut)

typical d orbital

planar node

planar node

Figure 7.16Figure 7.16Figure 7.16Figure 7.16

d Orbitals

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d Orbital Shape

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f Orbitals

• There are 7 f orbitals with l =3

• ml = -3, -2,-1,0,+1,+2, +3 (7 values of ml)

-These orbitals are hard to visualize or describe

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When n = 4, When n = 4, ll = 0, 1, 2, 3 so there are 4 subshells in = 0, 1, 2, 3 so there are 4 subshells in this orbital (energy level)this orbital (energy level)

For For ll = 0, m = 0, mll = 0 = 0

---> s subshell with single suborbital---> s subshell with single suborbital

For For ll = 1, m = 1, mll = -1, 0, +1 = -1, 0, +1

---> p subshell with 3 suborbitals---> p subshell with 3 suborbitals

For For ll = 2, m = 2, mll = -2, -1, 0, +1, +2 = -2, -1, 0, +1, +2

---> d subshell with 5 suborbitals---> d subshell with 5 suborbitals

For For ll = 3, m = 3, mll = -3, -2, -1, 0, +1, +2, +3 = -3, -2, -1, 0, +1, +2, +3

---> f subshell with 7 suborbitals---> f subshell with 7 suborbitals

f Orbitals

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One of 7 possible f orbitals

All have 3 planar surfaces

f Orbital Shape

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Spin Quantum Number (ms)

Describes the direction of the spin the electron has

only two possible values:ms = +1/2 or -1/2

ms = ± 1/2

proven experimentally that electrons have spins

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Spin Quantum NumberSpin quantum number effects:

Every orbital can hold up to two electronsWhy?

The two electrons are designated as having: one spin up and one spin down

Spin describes the direction of the electron’s magnetic fields

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Electron Spin and MagnetismDiamagnetic:

NOT attracted to a magnetic field -they are repelled by magnetic fields-no unpaired electrons

Paramagnetic: are attracted to a magnetic field -unpaired electrons