Download Atomic Structure: valence electrons, Chemistry and the periodic table

PHYS274 Spring 2017
• Quiz
• Homework #9 due today (Apr. 5)
– Chap 41 in its entirety
1
Q31.1
The Pauli Exclusion Principle states that:
A) No two electrons can occupy the same quantum
state
B) Two electrons can occupy the same quantum state
but no more than two
C) No two electrons can occupy the ground state, but
this is ok for excited states
D) No two photons can occupy the same quantum state.
2
Q31.1
The Pauli Exclusion Principle states that:
A) No two electrons can occupy the same quantum
state
B) Two electrons can occupy the same quantum state
but no more than two
C) No two electrons can occupy the ground state, but
this is ok for excited states
D) No two photons can occupy the same quantum state.
3
Q31.2
Which of the following statements is true?
A. The Zeeman effect refers to the splitting of
atomic energy levels in the presence of an
electric field.
B. The Zeeman effect refers to the splitting of
atomic energy levels in the presence of a
magnetic field.
C. The Zeeman effect refers to the splitting of
atomic energy levels under applied pressure
in one-direction
D. The Zeeman effect refers to the splitting of
atomic energy levels at high temperature.
4
Q31.2
Which of the following statements is true?
A. The Zeeman effect refers to the splitting of
atomic energy levels in the presence of an
electric field.
B. The Zeeman effect refers to the splitting of
atomic energy levels in the presence of a
magnetic field.
C. The Zeeman effect refers to the splitting of
atomic energy levels under applied pressure
in one-direction
D. The Zeeman effect refers to the splitting of
atomic energy levels at high temperature.
5
Q31.3
The n=3 state of a hydrogen like atom has
an energy of -1.51eV.
If a strong magnetic field is applied, how
many hyperfine energy levels are observed?
A.
B.
C.
D.
E.
1
2
3
4
5
6
Magnetic moments and the Zeeman effect
• Electron states with nonzero orbital angular momentum (l = 1, 2, 3,
…) have a magnetic dipole moment due to the electron motion.
Hence these states are affected if the atom is placed in a magnetic
field. The result, called the Zeeman effect, is a shift in the energy of
states with nonzero ml. This is shown below.
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Q31.3
The n=3 state of a hydrogen like atom has
an energy of -1.51eV.
If a strong magnetic field is applied, how
many hyperfine energy levels are observed?
A.
B.
C.
D.
E.
1
2
3
4
5
8
Quantum states and the Pauli exclusion principle
•
The allowed quantum numbers for an atomic electron (see the
Table below) are n ≥ 1; 0 ≤ l ≤ n – 1; –l ≤ ml ≤ l; and ms = ±1/2.
•
The Pauli exclusion principle states that if an atom has more than
one electron, no two electrons can have the same set of quantum
numbers.
9
Implications of Pauli principle for the 1S state.
n=1, l=0, sz1=1/2, sz2=1/2
✔
n=1, l=0, sz1=1/2, sz2=-1/2
Imagine the “Pauli’s” are point-like electrons
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Back to the QM hydrogen atom
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Back to the QM hydrogen atom
In the 1s state, the most likely single place to find the electron is:
A) r = 0
B) r = aB
C) Why are you confusing
us so much?
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Shapes of hydrogen wave functions:
l=1, called p-orbitals: angular dependence (n=2)
l=1, m=0: pz = dumbbell shaped.
l=1, m=-1: bagel shaped around z-axis (traveling wave)
l=1, m=+1
Superposition applies:
Dumbbells
px=superposition (addition of m=-1 and m=+1)
py=superposition (subtraction of m=-1 and m=+1) (chemistry)
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Note: Physics vs Chemistry view of orbits
2p wave functions
(Physics view)
(n=2, l=1)
Dumbbell Orbits
(chemistry)
px
m=1
m=-1
m=0
pz
py
px=superposition
(addition of m=-1 and m=+1)
py=superposition
(subtraction of m=-1 and m=+1)
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Chemistry: Shells – set of orbitals with similar energy
1s2
2s2, 2p6 (px2, py2, pz2)
3s2, 3p6, 3d10
l
n
These are the wave functions (orbitals) we just found:
n=1, 2, 3 … = Principal Quantum Number
En = − E1 / n
2
(for Hydrogen, same as Bohr)
l=s, p, d, f … = Angular Momentum Quantum Number
=0, 1, 2, 3 (restricted to 0, 1, 2 … n-1)
| L |= l (l + 1) 
m = ... -1, 0, 1.. = z-component of Angular
Momentum (restricted to –l to l)
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Energy Level Diagram for Hydrogen
l=0
(s)
n=3
n=2
3s
2s
l=1
(p)
3p
l=2
(d)
3d
2p
In HYDROGEN, energy only
depends on n, not l and m.
(NOT true for multi-electron atoms!)
n=1
1s
l=0,m=0
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Schrodinger’s solution for multi-electron atoms
What’s different for these cases?
Potential energy (V) changes !
(Now more protons AND other electrons)
V (for q1) = kqnucleusq1/rn-1 + kq2q1/r2-1 + kq3q1/r3-1 + ….
Need to account for all the interactions among the electrons
Must solve for all electrons at once! (use matrices)
Is very difficult to solve … huge computer programs!
Solutions change:
- wave functions change
- energy of wave functions affected by Z (# of protons)
We use the central field approximation.
Can use modified single electron solutions.
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Implications of QM for chemistry
Electron configuration in atoms:
How do the electrons fit into the available orbitals?
What are energies of orbitals?
3d
Total Energy
3p
3s
2p
2s
1s
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Implications of QM for chemistry
Electron configuration in atoms:
How do the electrons fit into the available orbitals?
What are energies of orbitals?
Filling orbitals … lowest to highest energy, 2 e’s per orbital
3d
3p
Total Energy
H
He
Li
Be
B
C
N
O
Oxygen = 1s2 2s2 2p4
3s
2p e e e
2s e e
1s e e
e
Shell not full reactive
Shell full stable
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Schrodinger predicts wave functions and energies
l=1
l=0
4p
Energy
4s
3s
2s
1s
3p
l=2
3d
m=-2,-1,0,1,2
Li
Na
2p
m=-1,0,1
Why would the behavior of Li be similar to Na?
a. because shape of outer most electron is similar.
b. because energy of outer most electron is similar.
c. both a and b
d. some other reason
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Schrodinger predicts wave functions and energies
l=1
l=0
4p
Energy
4s
3s
2s
1s
3p
l=2
3d
m=-2,-1,0,1,2
Li
Na
2p
m=-1,0,1
Why would the behavior of Li be similar to Na?
a. because shape of outer most electron is similar.
b. because energy of outer most electron is similar.
✔ c. both a and b
d. some other reason
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PHYS272: Gauss’ Law
Electric field is determined by the charge
enclosed in the Gaussian sphere
22
A multielectron atom and “screening”
•
The figure on the right is a
sketch of a lithium atom, which
has 3 electrons. The allowed
electron states are naturally
arranged in shells of different
size centered on the nucleus.
The n = 1 states make up the K
shell, the n = 2 states make up
the L shell, and so on.
•
Due to the Pauli exclusion
principle, the 1s subshell of the
K shell (n = 1, l = 0, ml = 0) can
accommodate only two
electrons (one with ms = + 1/2,
one with ms = –1/2). Hence the
third electron goes into the 2s
subshell of the L shell (n = 2,
l = 0, ml = 0).
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Ground-state electron configurations
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Ground-state electron configurations (Zoom in)
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The Periodic Table and Quantum Mechanics
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The periodic table and Quantum Mechanics
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The Periodic Table and Quantum Mechanics
The outer electrons (“valence electrons”)
determine the chemical properties of elements
e.g. Na 1s22s22p63s (outer electron loosely bound valence
+1); Cl 1s22s22p63s23p5 (missing one electron valence -1)
Individually dangerous elements but you can eat NaCl.
e.g. He, Ne, Ar are noble gases; all electron
states are filled.
Real bumper sticker sold by the
American Chemical Society.
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What element is this ? What is its electron configuration ?
l=0
4p
l=1
m=-1,0,1
l=2
m=-2,-1,0,1,2
3d
Energy
4s
3s
3p
2p
2s
What is the electron
configuration for an atom with
20 electrons ? (Write it out !)
a. 1s2, 2s2, 2p6, 3s2, 3p4
b. 1s2, 2s2, 2p6, 3s2, 3p6, 3d2
c. 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d6
d. 1s2, 2s2, 2p6, 3s2, 3p6, 4s2
e. none of the above
1s
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What element is this ? What is its electron configuration ?
l=0
4p
l=1
m=-1,0,1
l=2
m=-2,-1,0,1,2
3d
Energy
4s
3s
3p
2p
2s
1s
What is the electron
configuration for an atom with
20 electrons ? (Write it out !)
a. 1s2, 2s2, 2p6, 3s2, 3p4
b. 1s2, 2s2, 2p6, 3s2, 3p6, 3d2
c. 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d6
d. 1s2, 2s2, 2p6, 3s2, 3p6, 4s2
e. none of the above
Answer is d! Calcium: Fills lowest energy levels first.
Which orbitals are occupied determines
chemical behavior (bonding, reactivity, “alkaline earth”)
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More on calcium
l=0
l=1
l=2
m=-1,0,1
m=-2,-1,0,1,2
4p
3d
N.B. 3d is above 4s level
4th Shell Calcium has 3 complete shells.
Energy
4s
3p
3s
3rd Shell
Incomplete shell:
Chemical behavior & bonding
determined by electrons in outer
most shell (furthest from the
nucleus).
4
2p
2s
2st Shell
2
1
3
1s
1st Shell
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Mystery of calcium energy levels
l=0
l=1
l=2
m=-1,0,1
m=-2,-1,0,1,2
4p
3d
N.B. 3d level is above 4s level
4th Shell
Energy
4s
3p
3s
3rd Shell
2p
2s
1s
2st Shell
1st Shell
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Screening in multi-electron atoms
• An atom of atomic number Z has a nucleus of charge +Ze and Z
electrons of charge –e each. Electrons in outer shells “see” a
nucleus of charge +Zeffe, where Zeff < Z, because the nuclear
charge is partially “screened” by electrons in the inner shells.
This equation works
when one electron is
screened from the
nucleus by other
electrons.
Warning: Eqn 41.43 is
wrong except for hydrogen.
Screening is important.
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Clicker question on charge screening
Potassium has 19 electrons. It is relatively easy to
remove one electron but substantially more difficult to
then remove a second electron. Why is this?
A. The second electron feels a stronger attraction to the other
electrons than did the first electron that was removed.
B. When the first electron is removed, the other electrons readjust
their orbits so that they are closer to the nucleus.
C. The first electron to be removed was screened from more of the
charge on the nucleus than is the second electron.
D. all of the above
E. none of the above
34
Clicker question on charge screening
Potassium has 19 electrons. It is relatively easy to
remove one electron but substantially more difficult to
then remove a second electron. Why is this?
A. The second electron feels a stronger attraction to the
other electrons than did the first electron that was removed.
B. When the first electron is removed, the other electrons
readjust their orbits so that they are closer to the nucleus.
C. The first electron to be removed was screened from more
of the charge on the nucleus than is the second electron.
D. all of the above
E. none of the above
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For next time
• Moving on to QM of Molecules
 Read material in advance
 Concepts require wrestling with material
•Homework #9 due tonight (Apr. 5)
–Chap 41 in its entirety
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