Download Unit 7 - Hicksville Public Schools

AP Chemistry
Unit 7 Atomic Structure and Periodicity
Unit 7: Atomic Structure and Periodicity
You should be able to:
Characteristics of waves
Light Spectrum order
3 light equations
Atomic Spectrum
Bohr’s Model
Rydberg equation
Schrodinger model/quantum mechanical model
o Compare and contrast between the two
Heisenberg uncertainty principle
Quantum #’s
Orbital shapes and energies
Electron configuration
o Short hand - "Noble Gas Configuration"


Reading the periodic table
o Long hand - Complete Electron Configuration


Arrows - Orbital Notation
History of the periodic table
Periodic groups
Representative vs. transition elements
Periodic Trends
o Ionization Energy
o Electronegativity
o Atomic Size
o Ionic Size
o Shielding
o Electron Affinity
Know what a metalloid is
7.1 Electromagnetic Radiation
Read and outline 7.1
Define:
•
Electromagnetic Radiation
•
Wavelength
•
Frequency
•
Amplitude
•
Trough
•
Crest
How does frequency and wavelength relate to each other?
How fast does light travel?
How does a microwave work?
7.1 Notes
One way energy travels thought space is by electromagnetic radiation. Wavelength (λ) is the distance between two
consecutive peaks. Frequency () is the amount of wave cycles per second that pass a given point. The unit for
frequency is hertz (Hz) which are inverse seconds.
c=λν
c = 2.99 x 108 m/s
λ = Wavelenght (m)
ν = Frequency (1/s)
Short wavelengths have high frequencies and high energy
Long wavelengths have low frequencies and low energy
“c”—the speed of light; 2.99792458 [just call it 3] × 108 m/s;
ALL EM RADIATION TRAVELS AT THIS SPEED!
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Example 7.1a
The brilliant red colors seen in fireworks are due to the emission of light with wavelengths around 650 nm when
strontium salt such as strontium nitrate and strontium carbonate are heated. Calculate the frequency of this red
light with a wavelength of 6.50 x 102 nm.
υ = 4.61 × 1014 Hz
7.2 The Nature of Matter
Read and outline 7.2
Define:
Planck’s Constant
Quantized
Photons
Dual Nature of Light
Diffraction
Diffraction Pattern
What are particles described as?
What are waves described as?
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What did “old physics” say about matter and energy?
How can a system transfer energy according to Planck?
If a beam of light can be consider to be a stream of particles, do photons have mass? Why or why not?
How does white light’s diffraction grading and Hydrogen’s spectrum differ?
What does all matter exhibit?
What are the conclusions of Planck’s and Einstein’s experiments?
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7.2 Notes
At the end of the 19th century, physicists were feeling rather smug. All of physics had been explained [or so they
thought]. Matter and Energy were distinct: Matter was a collection of particles and Energy was a collection of
waves. Enter Max Planck stage left…
Max Planck solved the "Ultraviolet catastrophe" problem - the fact that a glowing hot object did not emit UV light
as predicted. He made an incredible assumption: There is a minimum amount of energy that can be gained or lost
by an atom, and all energy gained or lost must be some
integer multiple, n, of that minimum. (As opposed to just any old value of energy being gained or lost.)
Energy is in fact is quantized and can occur only in discrete units of h.
∆Energy = n(hν)
where h is a proportionality constant, Planck's constant, h = 6.6262 x 10-34 J*s . This ν is the lowest frequency that
can be absorbed or emitted by the atom, and the minimum energy change, hν, is called a quantum of energy. Think
of it as a “packet” of E equal to hυ. There is no such thing as a transfer of E in fractions of quanta, only in whole
numbers of quanta.
Example
The blue color in fireworks is often achieved by heating copper (I) chloride to about 1200OC. Then the compound
emits a blue light having a wavelength of 450. nm. What is the increment of energy that is emitted?
= 4.41 × 10-19 J
Example
What is the energy of the red light that has a wavelength of 675 nm?
= 2.94 × 10-19 J
de Broglie’s equation:
You know Einstein for the famous E = mc2 from his second “work” as the special theory of relativity published in
1905. Such blasphemy, energy has mass?! That would mean:
m=
therefore,
m=
E
h
hC/λ
=
=
2
2
C
Cλ
C
E
C2
or...... λ =
h
Cxm
Light can have wave like properties, and have certain characteristics of particulate matter.
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Example
Compare the wavelength for an electron (mass = 9.31 x 10-31 kg) traveling at a speed of 1.0 x 107 m/s with that for a
ball (mass = 0.10 kg) traveling at 35 m/s.
Worksheet 7.01
Light Equations
1. Calculate the wavelength of a wave whose frequency is 6.4 × 1022 s−1.
2. Find the energy of a light beam that has a frequency of 5.4 × 1022 Hz.
3. Find the frequency of a particle that has an energy of 1.6 × 10−19 J.
4. Calculate the frequency of a wave that has a wavelength of 3.4 × 107 m.
5. A beam of light has a wavelength of 4.3 × 10−7 m. Find the energy of the light beam.
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Worksheet7.02
Light Equations
Name______________________________
Solve the following problems using the de Broglie equation:
1. If a particle has a mass of 0.0045 kg, and is traveling at a velocity of 35.5 m/s, find its wavelength, in meters.
2. A 0.200 kg baseball has a wavelength of 1.0 × 10−34 m. Find its velocity, in m/s.
3. A rock has a wavelength of 3.4 × 10−35 m. It is moving at 56 m/s. Find its mass, in kg.
4. What is the wavelength of an electron that has a mass of 9.11 × 10−31 kg and is traveling at a velocity of
4.4 × 106 m/s?
5. If a proton has a mass of 1.67 × 10−27 kg, and is traveling at a velocity of 4.2 × 104 m/s, find its frequency, in Hz.
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7.3 The Atomic Spectrum of Hydrogen
Read and outline 7.3
Define:
•
Continuous Spectrum
•
Line Spectrum
What is significant of the line spectrum of hydrogen?
7.3 Notes
Diffraction results when light is scattered from a regular array of points or lines. A continuous spectrum is made
from white light shined through a prism, and a diffraction grating is made from exciting electrons.
Emission spectrum—the spectrum of bright lines, bands, or continuous radiation that is provided by a specific
emitting substance as it loses energy and returns to its ground state OR the collection of frequencies of light given
off by an "excited" electron.
Absorption spectrum—a graph or display relating how a substance absorbs electromagnetic radiation as a function
of wavelength
Line spectrum--isolate a thin beam by passing through a slit then a prism or a diffraction grating
which sorts into discrete frequencies or lines
What is the significance of the line spectrum of hydrogen? It indicates that only certain energies are allowed for the
electron in the hydrogen atom. In another words, the energy of the electron in the hydrogen atom is quantized. The
discrete line spectrum of hydrogen shows that only certain energies are possible; that is, the electron energy levels
are quantized, in contrast, if any energy level were allowed, the emission spectrum would be continuous.
Niels Bohr connected spectra, and the quantum ideas of Einstein and Planck: the single electron of the hydrogen
atom could occupy only certain energy states, stationary states
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7.4 The Bohr Model
Read and outline 7.4
Define:
• Quantum Model
What is significant of the line spectrum of hydrogen?
What quantum number did Bohr find to fit his model?
What are two important points to the Bohr Model?
Why does Bohr’s Model only work for Hydrogen?
7.4 Notes
An electron in an atom would remain in its lowest E state unless otherwise disturbed.
• Energy is absorbed or emitted by a change from this ground state
• an electron with n = 1 has the most negative energy and is thus the most strongly
attracted to the positive nucleus. [Higher states have less negative values and are not
as strongly attracted to the positive nucleus.]
• ground state--n = 1 for hydrogen
E photon = hγ =
hC
λ
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•
To move from ground level to n = 2 the electron/atom must absorb no more or no less than
0.75 Rhc. [that’s a collection of constants]
•
•
•
•
•
So, a move of n = 2 to n = 1 emits 985 kJ of energy.
What goes up must come down. Energy absorbed must eventually be emitted.
The origin or atomic line spectra is the movement of electrons between quantized energy states.
IF an electron moves from higher to lower E states, a photon is emitted and an emission line is observed.
Bohr’s equation for calculating the energy of the E levels available to the electron in the hydrogen atom:
E = - 2.178 x 10
•
•
•
•
•
-18
 Z2 
J 2 
n 
where n is an integer [larger n means larger orbit radius, farther from nucleus], Z is the nuclear charge
The NEGATIVE sign simply means that the E of the electron bound to the nucleus is lower that it would be if the
electron were at an infinite distance [n = ∞] from the nucleus where there is NO interaction and the energy is
zero.
ΔE is simply the subtraction of calculating the energy of two different levels, say n=6 and n=1.
If the difference is negative, E was lost. If the difference is positive, E was gained.
As the electron becomes more tightly bound, its energy becomes more negative related to the zero-energy
reference state (corresponding to the electron being at infinite distance from the nucleus). As the electron is
brought closer to the nucleus, energy is released for the system.
TWO Major defects in Bohr's theory:
1) Only works for elements with ONE electron.
2) The one, lonely
electron DOES NOT orbit the nucleus in a fixed path!!
Example
Calculate the energy required to excite the hydrogen electron from level n = 1 to level n=2. Also calculate the
wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state.
ΔE = 1.633 × 10-18 J
λ = 1.216 × 10-7 m
Example
Calculate the energy required to remove the electron for a hydrogen atom in its ground state.
ΔE = 2.178 × 10-18 J
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Worksheet 7.03
Bohr’s Orbitals
Name______________________________
1. Calculate the wavelengths of the light emitted when each of the following transitions occur in the hydrogen
atom.
a. n = 3 → n = 2
b. n = 4 → n = 2
c. n = 5 → n = 3
2. Using vertical lines, indicate the transition form the above problem on an energy – level diagram for the
hydrogen atom (see fig 7.8)
3. An excited hydrogen atom emits light with a frequency of 1.141 x 1014 Hz to reach the energy level for which
n = 4. In what principle quantum level did the electron begin?
4. From the Heisenberg uncertainty principle, calculate Δx for a baseball (mass = 145g) with Δv 0.100m/s. How
does this Δx compare to the size of the baseball?
5. Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom form the
energy state characterized by n = 4 to n = 10.
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7.5 The Quantum Mechanical Model of the Atom
Read and outline 7.5
Define:
•
Standing Wave
•
Wave Function
•
Orbital
•
Quantum Mechanical Model
•
Heisenberg Uncertainty Principle
•
Probability Distribution
•
Radial probability distribution
7.5 Notes
Quantum Mechanics--- to Schrodinger and de Broglie the electron bound to the nucleus seemed similar to a
standing wave. Standing waves can be looked at like playing an instrument. The wave is kept between two or more
nodes. We can have a whole number of half wavelengths. Only certain circular orbits have a circumference into
which a whole number of wavelengths of the standing electron wave will fit.
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THE WAVE MECHANICAL VIEW OF THE ATOM
Schrodinger equation: ĤΨ = EΨ
Schrodinger equation Ψ is the wave function. Each solution consists of a wave function that is characterized by a
particular value of E (energy). A specific wave function is often called an orbital. The wave function does not know
the pathway of the electron.
•
solutions are called wave functions--chemically important. The
electron is characterized as a matter-wave
•
sort of standing waves--only certain allowed wave functions
(symbolized by the Greek letter, ψ, pronounced “sigh”)
•
Each ψ for the electron in the H atom corresponds to an allowed
energy (−Rhc/n2). For each integer, n, there is an atomic state
characterized by its own ψ and energy En.
In English? Points 1 & 2 above say that the energy of electrons is
quantized.
•
The hydrogen electron is visualized as a standing wave around the nucleus [above right]. The
circumference of a particular circular orbit would have to correspond to a whole number of wavelengths, as shown
in (a) and (b) above, OR else destructive interference occurs, as shown in (c). This is consistent with the fact that
only certain electron energies are allowed; the atom is quantized. (Although this idea encouraged scientists to use
a wave theory, it does not mean that the electron really travels in circular orbits.)
Heisenberg uncertainty principle - There is a fundamental limitation to just how precisely we can know both
the position and momentum of a particle at a given time.
Δx is the uncertainty of the position
Δ(mv) is the uncertainty of the
momentum
h is Planck’s constant.
The more accurately we know the
position of an electron the less
accurately we know the momentum.
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7.6 Quantum Numbers
Read and outline 7.6
Define:
•
Quantum Numbers
•
Principle Quantum Number
•
Angular Momentum Quantum Number
•
Magnetic Quantum Number
•
Subshell (Sublevel)
•
Magnetic Spin Quantum Number
7.6 Notes
•
Quantum numbers
o Orbitals made for the Schrödinger equation.
•
Principle quantum number (n)
o Energy level
o Related to the size and the energy of
the orbital.
•
Angular momentum quantum number (l)
o Integers from 0 to n-1
o Related to the shape of the orbital
 s=0
 p=1
 d=2
 f=3
•
Magnetic quantum number (ml)
o Integer value between l and –l
o Related to the orientation of the orbital
•
Magnetic Spin (ms)
o Electrons need to spin opposite ways
o ms = -½ or ½
Example
For principle quantum level n = 4, determine the number of allowed subshells (l), and the given designation of each
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Worksheet 5.04
Quantum numbers
Name______________________________
1. Circle the following designations that are incorrect : 1s, 1p, 7d, 9s, 3f, 4f, 2d.
2. Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets that are
incorrect, state which is wrong in the set.
a. n = 2 l = 1 ml = -1
b. n = 1 l = 1 ml = 0
c. n = 8 l = 7 ml = -6
d. n = 1 l = 0 ml = 2
3. Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets that are
incorrect, state which is wrong in the set.
a. n = 3 l = 2 ml = 2
b. n = 4 l = 3 ml = 4
c. n = 0 l = 0 ml = 0
d. n = 2 l = -1 ml = 1
4. Give the maximum amount of electrons in an atom that can have their quantum numbers:
a.
n=4
b.
n=5
ml = +1
c.
n=5
ms = +1/2
d.
n=3
l=2
e.
n=2
l=1
f.
n=0
l=0
ml = 0
g.
n=2
l=1
ml = -1
h.
n=3
ms = +1/2
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7.7 and 7.8 Orbital Shapes and Energies and Electron Spin and the Pauli Exclusion Principle
Read and outline 7.7 and 7.8
Define:
• Nodal Surfaces
•
Nodes
•
Degenerate
•
Electron Spin
•
Electron spin quantum number
•
Pauli Exclusion Principle
Summarize the Hydrogen Atom:
1.
2.
3.
4.
1
What does 2px mean?
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7.7 Notes
The electron probability distribution for a 1s orbital
Node is an area that the electron has no probability of being in.
THE SHAPES OF ATOMIC ORBITALS
There is no sharp boundary beyond which the electrons are never found!!
• s--spherical; the size increases with n. The nodes you see at left represent
ZERO probability of finding the electron in that region of space. The number of
nodes equals n-1 for s orbitals.
•
•
•
p--have one plane that slices through the nucleus and divides the region of
electron density into 2 halves. Nodal plane--the electron can never be found
there!!
3 orientations: px, py, and pz.
d--2 nodal planes slicing through the nucleus to create four sections; 5 orbitals.
- The dz2 orbital is really strange!
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7.9 Polyelectronic Atoms and 7.10 The History of the Period Table
Read and outline 7.9 and 7.10
Define:
• Polyelectronic Atoms
•
Degenerate Orbitals
What are the three energy contributions that must be considered when describing a helium atom?
1.
2.
3.
The repulsions of the electrons cause ______________________ (more/less) of an uncertainly in the pathway and
they ________________________ (can/cannot) be calculated exactly. This is called the electron correlation
problem.
Es < Ep < Ed < Ef
"Penetrates"
closest to the
nucleus
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THE HISTORY OF THE PERIODIC TABLE
in the 1800's Johann Dobereiner
arranged the periodic table by
_____________________________
In 1864 John Newlands arranged the
periodic table by
_____________________________
In 1870--Dmitrii Mendeleev & Julius
Lothar Meyer arranged the periodic
table according to
___________________ __________
and in 1913, Mosley arranged the
elements by
_______________________
The modern Periodic table of the elements contain ______________ groups (families) and _____________
periods.
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7.11 Electron Configuration
Read and outline 7.11
Define:
• Aufbau Principle
•
Hund’s Rule
•
Core electrons
•
Valence electrons
•
Transistion Metals
•
Lanthanide series
•
Actinide series
•
Representative elements
ATOMIC ORBITAL ENERGIES AND ELECTRON ASSIGNMENTS
So How do we do that?
Order of Orbital Assignments:
"Long hand" electron configuration
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Orbital Notation:
"Short hand" (Noble Gas) electron configuration
Electron configuration for ions:
Isoelectronic species -- contain the same number of electrons
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7.12 Periodic Trends in Atomic Properties
Read and outline 7.12
Define:
•
First ionization energy
•
Second ionization energy
•
Electron affinity
•
Atomic Radii
On page 309 there are ionization energies for Aluminum. Look at the I values, how can you tell that the stable
Aluminum ion has a 3+ charge?
What are the trends for:
Atomic Radii -
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Ionic Radius
Ionization energy
Successive Ionization energies
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Electron Affinity
Electronegativity
Summary of period trends. Add the ones that are not on this
chart.
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Worksheet 7.07
Periodicity
Name______________________________
For each of the following pairs, circle the atom or ion that is larger. Use the periodic table to assist you.
Magnesium atom or Sodium atom
Cs1+ ion or Ca2+ ion
Iodine atom or Chlorine atom
Silicon atom or Fluorine atom
Positive Sr2+ ion or Neutral Sr atom
Selenium atom or Gold atom
Fluorine atom or Sulfur atom
Aluminum atom or Helium atom
Sodium atom or Barium atom
Xenon atom or Silver atom
Neutral Co atom or Positive Co2+ ion
N3− ion or S2− ion
P3− ion or Al3+ ion
Cobalt atom or Cesium atom
For each of the following pairs, circle the element that has the larger ionization energy. Use the periodic table to
assist you.
Li or N
Cl or Se
Li or K
Cl or B
Li or Sc
Br or Pd
Mg or Rb
F or Fe
Mg or C
F or Na
Mg or Cl
V or Mo
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Worksheet 7.08
Periodicity
Name______________________________
Answer the following questions.
1. Restate in one or two words: “The amount of energy required to remove the first electron from the valence
shell of a neutral atom.”
2. Restate in one or two words: “The tendency of an atom to hold on to its valence electrons while engaged in a
chemical bond.”
3. Restate in one or two words: “The actions of the non-valence electrons, diluting the force of the attraction
between nucleus and valence electrons.”
4. Which atom has a greater shielding, Au or Cu? Why?
5. Which has a larger atomic eadius, Au or Cu? Why?
6. Which has greater first ionization energy, Cu or Ag? Why?
7. Which has greater shielding, Xe or Ar? Why?
8. Which is a larger ion, sulfur ion or phosphorus ion? Why?
9. Which has greater shielding, Ge or Ra? Why?
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