1 CHAPTER 6 • The Structure of Atoms
Dec 18, 2015
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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