Transcript APCh7MB

Chapter 7: Atomic Structure and
Periodicity
7.1 Electromagnetic Radiation
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Comes from the sun and the stars
Electromagnetic Radiation – radiant
energy that exhibits wavelike behavior
and travels through space at the
speed of light (3.00 X 108 m/s)
Wavelength – length of a wave (from
crest to crest, trough to trough, or
other corresponding points)
Frequency – number of waves
(cycles) per second that pass a given
point in space
- Page 139
“R O Y G
Frequency Increases
Wavelength Longer
B I V”
Formula!
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v = c/λ OR c = vλ
λ (wavelength) is in meters
v (frequency) is in sec-1 or hertz (hz)
c (speed of light) is in m/s and is a constant
Practice problem
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Given: v = 4.54 X 1014 s-1
λ=?
4.54 X 1014 s-1 = 3.00 X 108 m/s / λ
λ = 6.61 X 10-7 m
7.2 The Nature of Matter
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Δ E = hv
Δ E = change in energy for a system (in
J/photon)
h = Planck’s constant  6.626 X 10-34 J*sec
v = frequency
Δ E = hv = hc / λ
Examples
1) What is the wavelength of blue
light with a frequency of 8.3 x
1015 hz?
2) What is the frequency of red
light with a wavelength of 4.2 x
10-5 m?
3) What is the energy of a photon
of each of the above?
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1)  = c = 3 x 108 m/s = 3.6 x 10-8 m
 8.3 x 1015hz
2)  = c = 3 x 108 m/s = 7.1 x 1012 hz
 4.2 x 10-5 m
3-1) E = h = (6.626 x 10-34 J·s)(8.3 x 1015hz)
= 5.4 x 10-18 J
3-2) E = h = (6.626 x 10-34 J·s)(7.1 x 1012hz)
= 4.7 x 10-21 J
2 ways to excite an electron
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1. Heat
2. Electricity
An electron jumps up an energy level, falls back down
releasing a packet of energy (a photon) with a λ = 589.0 nm
Find change in energy for this photon & per mol of photons.
v=c/λ = 3.00 X 108 m/s / 5.89 X 10-7 m = 5.09 X 1014 hz
Δ E = hv = (6.63x10-34Jsec)(5.09x1014 hz) = 3.37x10-19 J
J/mol = 3.37 X 10-19 J | 6.02 X 1023 photons
1 photon
|
1 mol
Answer = 203.17 kJ/mol
de Broglie’s Equation and the
Dual Nature of Light
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E = mc2 & E = hν & E = hc/λ
m = h/(λv)
OR λ = h/(mv)
v = velocity
Dual nature of light: sometimes
electromagnetic radiation exhibits wave
properties, sometimes it shows characteristics
of particle matter
7.3 Atomic Spectrum of Hydrogen
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Continuous spectrum – contains all the
wavelengths over which the spectrum is
continuous
Line spectrum – contains certain specific
wavelengths which are characteristics of the
substances emitting those wavelengths
There are specific energy levels among which
an e- in a H atom can jump  quantized
7.4 The Bohr Model
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E = -2.178 X 10-18 J [Z2]
[n2]
E = energy in J
Z = nuclear charge/number of protons
n = state energy level (farther away from
nucleus = higher number)
Lowest energy state: n=1
Highest energy state: n=∞ where it’s ionized
Sample Problem
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Calculate E corresponding to n=3 in H atom.
E = -2.178 X 10-18 J [12/32] = -2.42 X 10-19 J
When you move there is a change in energy.
Δ E = Efinal – Einitial
Δ E = -2.178 X 10-18 J [z2/nf2 – z2/ni2]
If going from 13, ni=1 and nf=3
ΔE=(-2.178 X 10-18J [12/32]) – (-2.178 X 10-18J [12/12])
ΔE = -2.178 X 10-18J [12/32 – 12/12 ] = 1.9 x 10-18 J
7.5 Quantum Mechanical Model of
the Atom
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Electron is assumed to behave as a standing
wave.
Wave function of an electron represents the
allowed coordinates where an electron may
reside in the atom  orbital
Heisenberg’s uncertainty principle
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Can only know position or velocity
As one is known more precisely, the other is known
less precisely
Δ x  Δ (mv) ≥ h/4π
Δ x = uncertainty in the particle’s position
Δ (mv) = uncertainty in particle’s momentum
h = Planck’s constant
Smallest possible uncertainty = h/4π
(h/4π)2 = probability distribution
Radius of the sphere encloses 90% of the total
electron probability
Rules to Remember for Orbital
Notation
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Aufbau Principle – electrons are added one at
a time to the lowest energy level available until
all electrons are accounted for
Pauli Exclusion Principle – an orbital can hold
a max of two electrons which have opposite
spins
Hund’s Rule: electrons occupy equal energy
orbitals so that the max number of unpaired
electrons results
Orbital Shapes
S orbital
P orbitals
D orbitals
The Diagonal Rule
An Example of Orbital Notation
What is the orbital notation for nitrogen?
N = 1s2 2s2 2p3
Draw the orbital diagram for nitrogen.
7.6 Quantum Numbers
Name
Designation
Property of
the orbital
Possible
range of
values
Principle
quantum #
Angular
momentum #
N
Energy level
l
Shape
(sublevel)
0 < integers <
7
0  n-1
Magnetic
quantum #
Ml
Position of
orbital
Spin
S
Spin
Integers from
–3 to 3
+1/2 or –1/2
Orbital notation chart
7.12 Periodic Trends in Atomic
Properties
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Ionization energy – energy needed to remove an
electron
1. Metals – low, nonmetals – high
2. Across a period IE increases (because nuclear
force increases with a greater number of protons)
3. Going down a group IE decreases (because of the
added energy levels)
Successive IE:
1. After one e- is taken off, it is harder to take off the
next e2. Shielding effect/penetration effect
3. When all e- are taken away, take away core e-
2.
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Electron affinity – the opposite of IE – change in
energy when adding an electron
1. Across a period EA increases
2. Going down a group EA decreases
Atomic radius – distance from nucleus to outermost
electron
1. Across a period AR decreases Zeff
2. Going down a group AR increases
A metal ion is + and smaller than the original atom
A nonmetal ion is – and larger than the original atom
EXCEPTIONS TO GEN RULES?
7.13 Properties of a Group: Alkali
Metals
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As you go down the
group:
–
–
–
–
–
IE decreases
AR increases
Density increases
Reactivity increases
Melting point and boiling
point decrease
7.13 Properties of a Group: Halogens
Nonmetals
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As you go down the
group:
–
–
–
–
–
IE decreases
AR increases
Density increases
Reactivity decreases
Melting point and boiling
point increase