Chapter 5.Periodicity and the Periodic Table

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Chapter 5. Periodicity and the Periodic Table
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Chapter 5. Periodicity and the Periodic
Table Many properties of the elements follow a
regular pattern. In this chapter, we will look at
theory that has been developed to explain this
periodicity
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Much of what we have learned about atomic and
molecular structure, has come from our
understanding of how matter interacts with
light. What is light? The interaction of light
with matter forms the foundation of our
understanding of atomic structure, molecular
structure, and the structure of the universe! IR
tutor
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The interaction of light with matter forms the
foundation of our understanding of molecular
structure. How so?
Wave properties of light c ?? where c
3x1010 cm/s speed of light in vacuum ?
wavelength of light and ? frequency of
light Particle properties of light E h?
where E is the energy of a photon of light and
h 6.626 x 10-34 J.s
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Heisenberg uncertainty principle
(uncertainty in position)(uncertainty in
momentum (mv)) ? h/4?
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What happens if we take a hydrogen atom and heat
it up, or for that matter, any element?
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The emission spectrum of H and sodium atoms in
the visible region of the spectrum
The significance of observing discrete line may
not be immediately apparent but these atomic
species when heated do not give off all
wavelengths of light but only discrete wavelengths
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http//jersey.uoregon.edu/vlab/elements/Elements.h
tml
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The interpretation of these observations is that
upon heating H atoms, the hydrogen does not emit
any light until a certain amount of energy is put
into the atom. Since an atom of hydrogen consists
of only a proton and an electron, it is believed
that the emission of light by the hydrogen is due
to excitation of the electron.
Excited hydrogen
energy
Unexcited hydrogen
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The interpretation of these observations is that
upon heating H atoms, the hydrogen does not emit
any light until a certain amount of energy is put
into the atom. Since an atom of hydrogen consists
of only a proton and an electron, it is believed
that the emission of light by the hydrogen is due
to excitation of the electron. Alternatively, we
cant excite hydrogen electronically unless we
put in the correct amount of energy.
Excited hydrogen
energy
h? given off
Unexcited hydrogen
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Balmer equation 1/ ? R1/22-1/n2 where R
1.097x10-2 nm-1 and n is some integer gt 2 The
energy of the light observed in the visible
region is only a portion of the light emitted by
a hydrogen atom

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ionization potential I.E.
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Balmer Rydberg equation 1/ ? R1/m2-1/n2
where R 1.097x10-2 nm-1 and n is some integer gt
m. This equation accounts for the lines observed
for hydrogen both in the visible region and
elsewhere.
Why are these other lines also included?

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Why are the orbital energies of hydrogen written
as 1s, 2s, 2p, 3s, 3p, 3d.? Also why the
difference in energy between the 2s and 2p level,
for example, in a multi-electron atom? Many more
emission lines are observed in multi electron
atoms. These terms are used to describes the
levels an electron can occupy
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How does the emission spectrum of multi-electron
atoms look like? http//jersey.uoregon.edu/vlab/e
lements/Elements.html
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States needed to explain emission lines in
multi-electron states in a magnetic field
multi-electron atom

Absorption lines were observed to increase in
magnetic field
3d 3p 3s 2p 2s 1s
3d 3p 3s 2p 2s 1s
Energy
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What is observed in the spectra of multielectron
atoms are multiple lines closely spaced followed
by big gaps. The number of lines observed with
other atoms are numerous and beyond our concern.
We will be interested in summarizing the theory
that has been developed to explain these emision
lines.
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Attempts to explain the emission (and absorption
spectra) of atomic hydrogen and the other atoms,
resulted in discovery/development of a
mathematical equation with properties that
mimicked the observed spectra of
atoms. Schroedinger Equation is a differential
equation Properties of a differential equation
1. the equation may have more than one solution.
2. any combination of solutions (sum or
difference) is also a solution Solutions to
this equation are found only when certain terms
in the equation have unique values these terms
have been called quantum numbers and have been
given the symbols n, l, m, and s.
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The quantum numbers have names and also must have
certain relationships between each other,
otherwise the equation vanishes (has no
solution) n principle quantum number, must
have integer values of 1, 2, 3, L is called
the angular momentum quantum number and must have
integer values from (n-1), -(n-2), 0 m is
called the magnetic quantum number and can have
values from L, (L-1),..0,..L (cap L used
because lowercase l looks like the number 1) s
is called the spin quantum number, must be 1/2
or 1/2
Each electron in an atom is assigned 4 quantum
numbers no two electrons can have the same 4
quantum numbers or the solution vanishes?
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What do the solutions to the Schroedinger
Equation look like and what information do they
provide. The solutions are mathematical
equations often described in spherical
coordinates. What are spherical coordinates?
What are Cartesian coordinates?
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Cartesian Coordinates
z
. (x1,y1,z1)
y
x
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Spherical Coordinates
z
. (r,?,?)
y
?
x
?
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Some solutions to the Schroedinger Equation
Solution to this equation are called ?
(psi) What do they look like ?1s
(1/?a3)(2.718)r/a where a is a constant
5.2910-9 cm and r is the distance of the
particle from the origin (n1, l 0) ?2s
1/4(1/2?a3).5(2-r/a)(2.718)r/2a (n 2,
l0) ?2p 1/4(1/2?a3).5(r/a)(2.718)r/2acos ?
(n 2, l1) What is the physical
interpretation of the information they
provide? The functions ? (psi) are amplitude
functions, when squared and multiplied by an
element of volume, they provide the probability
of finding an electron at some location ((r,?,?)
in space. What do these functions look like?
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1s n 1, l 0
2s n 2, l 0
3s n 3, l 0
-
-

?3s
?2s
?1s
a node is a region where the function 0
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What do the p orbital look like?
How do they compare in energy to s orbitals?
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P orbitals n 2, l 1, m -1 n 2, l 1, m
0 n 2, l 1, m 1
-
-
-
?2p
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What do the d orbitals look like and how many are
there? How do they compare in energy to p
orbitals?
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?3d
?4f
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• Why are these orbitals significant
• These orbitals are solutions to the Schroedinger
  Equation for the hydrogen atom. However they are
  very useful because they provide a model to mimic
  the behavior observed for the remaining element
  in the periodic table.
• Rules for predicting the electronic properties of
  the remaining elements of the periodic table
• Electrons want to occupy orbitals with the lowest
  energy possible
• No two electrons can have the same four quantum
  numbers
• Electrons repel each other and prefer to go in
  orbitals of equal energy that are unoccupied
  they prefer to go in with the same spin (Hunds
  rule)
• A maximum of 2 electron are possible in any given
  orbital

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H 1 proton and 1 electron Designation 1s1
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Remember, if we excite hydrogen, we can excite it
to a 2s level, 3s level, 4s level, and then it
can decay from any one of these leves to a lower
level by emitting a specific wavelength of light.
This model explains the observed spectra of
hydrogen, both emission (light given off from an
exited state to one of lower energy) or
absorption (light aborbed in going from the
ground state to an excited state)
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He has 2 protons and 2 electrons note that the
orbital energy scale will change because each
electron will be attracted to a nucleus that has
2 protons Designation 1s2
Also note that this fills the 1s level the next
level is much higher in energy
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Li has 3 protons and 3 electrons note that the
orbital energy scale will change again because
each electron will be attracted to a nucleus that
has 3 protons Designation 1s2 2s1
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Be has 4 protons and 4 electrons note that the
orbital energy scale will change because each
electron will be attracted to a nucleus that has
4 protons Designation 1s2 2s2
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B has 5 protons and 5 electrons note that the
orbital energy scale will change because each
electron will be attracted to a nucleus that has
5 protons Designation 1s2 2s2 2p1
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C has 6 protons and 6 electrons note that the
orbital energy scale will change because each
electron will be attracted to a nucleus that has
6 protons Designation 1s2 2s2 2p2 Note Hunds
rule electrons occupy different orbitals with
the same spin
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N 7 has protons and 7 electrons note that the
orbital energy scale will change because each
electron will be attracted to a nucleus that has
7 protons Designation 1s2 2s2 2p3
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O has 8 protons and 8 electrons note that the
orbital energy scale will change because each
electron will be attracted to a nucleus that has
8 protons Designation 1s2 2s2 2p4
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F has 9 protons and 9 electrons note that the
orbital energy scale will change because each
electron will be attracted to a nucleus that has
9 protons Designation 1s2 2s2 2p5
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Ne has 10 protons and 10 electrons note that the
orbital energy scale will change because each
electron will be attracted to a nucleus that has
9 protons Designation 1s2 2s2 2p6
Also note that this fills this level
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Na has 11 protons and 11 electrons note that the
orbital energy scale will change because each
electron will be attracted to a nucleus that has
11 protons Designation 1s2 2s2 2p6 3s1
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Name the element with the following electronic
configurations 1s2 2s2 2p6 3s1 (Ne
3S1) Na 1s2 2s2 2p6 3s2 Mg 1s2 2s2 2p6 3s2
3p6 Ar 1s2 2s2 2p6 3s2 3p6 4s1 K 1s2 2s2
2p6 3s2 3p6 4s23d5 Mn 1s2 2s2 2p6 3s2
3p6 4s2 3d103p3 As
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In a multi-electron atom, which orbital shape do
you think shields the nucleus best to an electron
further out in space? s orbital p orbital d
orbital f orbital
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Some anomalous electron configurations Stability
associated with half filled and fully filled
shells Cr Ar 4s2 3d4 ? Ar 4s1 3d5 Cu
Ar 4s2 3d9 ? Ar 4s1 3d10
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Which of the following combination of quantum
numbers can refer to any electron in a ground
state Co atom (Z 27)?1. n 3, l 0, ml 2
2. n 4, l 2 ml -23. n 3, l 1, ml 0
Using the periodic table to assist in determining
electric configurations
ground state Co 1s2 2s2 2p6 3s2 3p6 4s2 3d7 n
3, l 0 is a s orbital, ml 0 n 4, l 2 is a 4d
orbital, ml -2, -1, 0, 1, 2 n 3, l 1 3p
orbital, ml -1, 0 ,1
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Which of the following electron configurations
refer to an excited state of V? Ne3s2 3p6 4s2
3d3 Ne3s2 3p6 4s2 3d2 3f1 Ne3s2 3p6 4s2 3d2
4p1 ground state V 1s2 2s2 2p6 3s2 3p6 4s2
3d3 Ne3s2 3p6 4s2 3d2 4p1
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Which of the following electron configurations
refer to an excited state of V3? Ne3s2 3p6
4s2 Ne3s2 3p6 4s2 3d2 4f1 Ne3s2 3p6 4s1 3d0
4p1 ground state V3 1s2 2s2 2p6 3s2 3p6 4s2
3d0 Ne3s2 3p6 4s1 3d0 4p1
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What is the electronic configuration of Se? 1s2
2s2 2p6 3s2 3p6 4s2 3d10 4p4
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• How many unpaired electrons are there in
• K?
• Cr?
• Fe?