Chapter 6: Electronic Structure of Atoms

1
Chapter 6 Electronic Structure of Atoms
Light is a form of electromagnetic radiation
(EMR)

• an oscillating charge, such as an electron,
  gives rise to electromagnetic radiation

Electric Field
Magnetic Field
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Chapter 6 Electronic Structure of Atoms

• Both the Electric and the Magnetic field
  propagate through
• space

• In vacuum, both move at the speed of light (3 x
  108 m/s)

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Chapter 6 Electronic Structure of Atoms

• Electromagnetic radiation is characterized by
• wavelength (?), or frequency (?) and
• amplitude (A)

l
A intensity
l
l
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Chapter 6 Electronic Structure of Atoms
Frequency (n) measures how many wavelengths pass
a point per second
1 s
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Chapter 6 Electronic Structure of Atoms
Electromagnetic radiation travels at the speed of
light c 3 x 108 m s-1
Relation between wavelength, frequency, and
amplitude c l n
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Chapter 6 Electronic Structure of Atoms
400 nm
750 nm
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Chapter 6 Electronic Structure of Atoms
Red Orange Yellow Green Blue Ultraviolet
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Chapter 6 Electronic Structure of Atoms
What is the wavelength, in m, of radiowaves
transmitted by the local radio station WHQR 91.3
MHz?
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Chapter 6 Electronic Structure of Atoms
A certain type of laser emits green light of 532
nm. What frequency does this wavelength
correspond to?
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Chapter 6 Electronic Structure of Atoms
Classically, electromagnetic radiation (EMR) was
thought to have only wave-like properties.
Two experimental observations challenged this
view
Blackbody radiation
Photoelectric Effect
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Chapter 6 Electronic Structure of Atoms
Blackbody radiation

• Hot objects emit light

• The higher T, the higher
• the emitted frequency

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Chapter 6 Electronic Structure of Atoms
Blackbody radiation
prediction of classical theory
there would be NO DARKNESS
Brightness
ultraviolet catastrophe
T2
T1
wavelength (l)
visible region
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Chapter 6 Electronic Structure of Atoms
Blackbody radiation
Max Planck (1858 - 1947)

• light is emitted by oscillators

• high energy oscillators require a minimum amount
  of energy to be excited
• E h ?
• energy is not provided by temperature in black
  body

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Chapter 6 Electronic Structure of Atoms
Blackbody radiation
frequency of oscillator
E h ?
Plancks constant 6.63 x 10-34 J s
Energy of radiation is related to frequency, not
intensity
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Chapter 6 Electronic Structure of Atoms
What is the energy of a photon of electromagnetic
radiation that has a frequency of 400 kHz?
2.65 x 10-28 J
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Chapter 6 Electronic Structure of Atoms
Photoelectric Effect
Albert Einstein (1879-1955)
e-
e-
e-
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Chapter 6 Electronic Structure of Atoms
Photoelectric Effect
Albert Einstein (1879-1955)
e-
e-
e-
e-

• Light of a certain minimum frequency is required
  to dislodge electrons from metals

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Chapter 6 Electronic Structure of Atoms
Photoelectric Effect

• Ability of light to dislodge electrons from
  metals is related to its frequency, not intensity

E h ?

• This means that light comes in units of h?

• Intensity is related only to the number of
  units

• The h? unit is called a quantum of energy

• A quantum of light (EMR) energy photon

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Chapter 6 Electronic Structure of Atoms
Relationship between Energy, Wavelength, and
Frequency
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Chapter 6 Electronic Structure of Atoms
What is the energy of a photon of light of 532
nm?
3.74 x 10-19 J
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Chapter 6 Electronic Structure of Atoms
Electromagnetic Radiation
stream of particles (photons)
or
wave
E h n
Whether light behaves as a wave or as a stream of
photons depends on the method used to investigate
it !
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Chapter 6 Electronic Structure of Atoms
Understanding light in terms of photons helped
understand atomic structure
many light sources produce a continuous spectrum
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Chapter 6 Electronic Structure of Atoms
Thermally excited atoms in the gas phase emit
line spectra
continuous spectrum (all wavelengths together
white light)
line spectrum (only some wavelengths emission
will have a color)
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Chapter 6 Electronic Structure of Atoms
Photograph of the H2 line spectrum (Balmer
series) in the visible region
(1825-1898)
Johann Balmer (1825-1898)
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Chapter 6 Electronic Structure of Atoms
Niels Bohr was the first to offer an explanation
for line spectra
Bohr Model of the Hydrogen Atom

• Only orbits of defined energy and radii are
  permitted in the hydrogen atom

• An electron in a permitted orbit has a specific
  energy and will not radiate energy and will not
  spiral into the nucleus

• Energy is absorbed or emitted by the electron as
  the electron moves from one allowed orbit into
  another. Energy is absorbed or emitted as a
  photon of E hn

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Chapter 6 Electronic Structure of Atoms
Niels Bohr was the first to offer an explanation
for line spectra
electron orbits
n 1 n 2 n 3 n 4 n 5 n 6
nucleus
Bohrs Model of the Hydrogen Atom
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Chapter 6 Electronic Structure of Atoms
Bohrs Model of the Hydrogen Atom
Energy
absorption of a photon
e
Ground State
nucleus
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Chapter 6 Electronic Structure of Atoms
Bohrs Model of the Hydrogen Atom
Energy
e
Ground State
nucleus
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Chapter 6 Electronic Structure of Atoms
Bohrs Model of the Hydrogen Atom
Energy
e
excited state
Ground State
nucleus
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Chapter 6 Electronic Structure of Atoms
Bohrs Model of the Hydrogen Atom
Energy
e
Ground State
nucleus
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Chapter 6 Electronic Structure of Atoms
Bohrs Model of the Hydrogen Atom
Energy
e
Ground State
emission of a photon
nucleus
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Chapter 6 Electronic Structure of Atoms
Which of these transitions represents an
absorption process?
(a)
(b)
(c)
Energy
Which of these transitions involves the largest
change in energy?
Which of these transitions leads to the emission
of the longest wavelength photon?
Ground State
Does this wavelength correspond to a high or low
frequency?
nucleus
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Chapter 6 Electronic Structure of Atoms
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Chapter 6 Electronic Structure of Atoms
n Principal Quantum Number (main energy levels)
hPlancks constant, cspeed of light, RH
Rydberg constant
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Chapter 6 Electronic Structure of Atoms
For an electron moving from n 4 to n 2
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Chapter 6 Electronic Structure of Atoms
For an electron moving from n 4 to n 2
DE - 4.09 x 10-19 J
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Chapter 6 Electronic Structure of Atoms
The energy of the photon emitted is
E 4.09 x 10-19 J
What wavelength (in nm) does this energy
correspond to?
l 486 x 10-9 m
486 nm
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Chapter 6 Electronic Structure of Atoms
Balmer Series
l 486 nm
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Chapter 6 Electronic Structure of Atoms
The Wave Behavior of Matter
If light can behave like a stream of particles
(photons)
then (small) particles should be able to behave
like waves, too
For a particle of mass m, moving at a velocity v
De Broglie Wavelength
e.g electrons have a wavelength (electron
microscope!)
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Chapter 6 Electronic Structure of Atoms
The Uncertainty Principle
Werner Heisenberg (1901-1976)
and Niels Bohr
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Chapter 6 Electronic Structure of Atoms
The Uncertainty Principle
It is impossible to know both the exact position
and the exact momentum of a subatomic particle
uncertainty in momentum, mv
uncertainty in position, x
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Chapter 6 Electronic Structure of Atoms
Quantum Mechanics and Atomic Orbitals
Erwin Schrödinger (1887-1961)
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Chapter 6 Electronic Structure of Atoms
Quantum Mechanics and Atomic Orbitals

• Schrödinger proposed wave mechanical model of
  the atom

• Electrons are described by a wave function, ?

• The square of the wave function, ?2, provides
  information on
• the location of an electron (probability density
  or electron density)

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Chapter 6 Electronic Structure of Atoms
Quantum Mechanics and Atomic Orbitals

• the denser the stippling, the
• higher the probability of finding
• the electron

• shape of electron density
• regions depends on energy of
• electron

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Chapter 6 Electronic Structure of Atoms
Bohrs model
n 1
orbit
electron circles around nucleus
Schrödingers model
orbital
n 1
or
electron is somewhere within that spherical region
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Chapter 6 Electronic Structure of Atoms
Bohrs model

• requires only a single quantum number (n) to
  describe an orbit

Schrödingers model

• requires three quantum numbers (n, l, and m) to
  describe an orbital

n principal quantum number l second or
azimuthal quantum number ml magnetic quantum
number
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Chapter 6 Electronic Structure of Atoms
Schrödingers model
(1) n principal quantum number (analogous to
Bohr model)
- the higher n, the higher the energy of the
electron
- is always a positive integer 1, 2, 3, 4 .
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Chapter 6 Electronic Structure of Atoms
Schrödingers model
(2) l azimuthal quantum number
- takes integral values from 0 to n-1
n 3
e.g.
- l defines the shape of an electron orbital
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Chapter 6 Electronic Structure of Atoms
Schrödingers model
z
y
x
s-orbital
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Chapter 6 Electronic Structure of Atoms
Schrödingers model
(3) ml magnetic quantum number
- takes integral values from -l to l, including 0
e.g.
l 2
- ml describes the orientation of an electron
orbital in space
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Chapter 6 Electronic Structure of Atoms
Shells

• are sets of orbitals with the same quantum
  number, n

• a shell of quantum number n has n subshells

Subshells

• are orbitals of one type within the same shell

• total number of orbitals in a shell is n2

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Chapter 6 Electronic Structure of Atoms
n
1
2
4
3
l
0
0, 1
0, 1, 2
0, 1, 2, 3
1s
2s, 2p
3s, 3p, 3d
4s, 4p, 4d, 4f
ml
0
0, -1,0,1
0 -1,0,1 -2,-1,0,1,2
0 -1,0,1 -2,-1,0,1,2 -3,-2,-1,0,1,2,3
orbitals in subshell
1
1
3
1
3
5
1
3
5
7
Total of orbitals in shell
1
4
9
16
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Chapter 6 Electronic Structure of Atoms
3s-room
3p-room
3deluxe-room
3rd floor
2s-room
2promotion-room
2nd floor
standard-room
1st floor
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Chapter 6 Electronic Structure of Atoms
Orbital energy levels in the Hydrogen Atom
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Chapter 6 Electronic Structure of Atoms
What is the designation for the n3, l2 subshell
?
How many orbitals are in this subshell ?
What are the possible values for ml for each of
these orbitals ?
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Chapter 6 Electronic Structure of Atoms
Which of the following combinations of quantum
numbers is possible?
n1, l1, ml -1
n3, l0, ml -1
n3, l2, ml 1
n2, l1, ml -2
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Chapter 6 Electronic Structure of Atoms
Representation of Orbitals
1s
2s
3s
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Chapter 6 Electronic Structure of Atoms
Representation of Orbitals
2p orbitals
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Chapter 6 Electronic Structure of Atoms
Representation of Orbitals
all three p orbitals
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Chapter 6 Electronic Structure of Atoms
Representation of Orbitals
3d orbitals
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Chapter 6 Electronic Structure of Atoms
Which combination of quantum numbers is possible
for the orbital shown below?
(a) n1, l0, ml 0
(c) n3, l3, ml -2
(b) n2, l-1, ml 1
(d) n3, l2, ml -1
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Chapter 6 Electronic Structure of Atoms
There is a fourth quantum number that
characterizes electrons spin magnetic quantum
number, ms
ms can only take two values, 1/2 or -1/2
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Chapter 6 Electronic Structure of Atoms
Wolfgang Pauli (1900-1958)
A. Einstein W. Pauli
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Chapter 6 Electronic Structure of Atoms
Paulis Exclusion Principle
No two electrons in an atom can have the same set
of 4 quantum numbers, n, l, ml, and ms
For a given orbital, e.g. 2s, n, l, ml are fixed
n2, l0, ml 0
gt an orbital can only contain two electron if
they differ in ms
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Chapter 6 Electronic Structure of Atoms
A maximum of 2 electron can occupy one orbital,
IF these two electrons have opposite spin
n2, l0, ml 0, ms 1/2 n2, l0, ml 0, ms
-1/2
2s
2p
arrows pointing up/down indicate electron spin
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Chapter 6 Electronic Structure of Atoms
Energy levels in the hydrogen atom
all subshells of a given shell have the same
energy
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Chapter 6 Electronic Structure of Atoms
Energy levels in many-electron atoms

• In many-electron atoms, the energy of an orbital
  increases with l, for a given n

• In many-electron atoms, the lower energy
  orbitals get filled first

• orbitals with the same energy are said to be
  degenerate

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Chapter 6 Electronic Structure of Atoms
Electron Configurations
Line Notation
1H
1s1
2He
1s2
1s22s1
3Li
1s22s2
4Be
1s22s22p2
6C
1s22s22p3
7N
10Ne
1s22s22p6
11Na
1s22s22p63s1
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Chapter 6 Electronic Structure of Atoms
Electron Configurations
Hunds Rule For degenerate orbitals, the energy
is minimized when the number of electrons with
the same spin is maximized
gt degenerate orbitals (p, d, etc) get filled
with one electron each first (same spin).
1s22s22p3
7N
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Chapter 6 Electronic Structure of Atoms
the Aufbau Principle helps you to remember the
order in which orbitals get filled
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
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Chapter 6 Electronic Structure of Atoms
1s22s22p63s23p2
Line notation
14Si
Ne
3s23p2
Condensed line notation
orbital diagram (no energy info)
3
d
2
p
1
core electrons
s
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Chapter 6 Electronic Structure of Atoms
1s22s22p63s23p2
Line notation
14Si
Ne
3s23p2
Condensed line notation
orbital diagram (no energy info)
3
d
2
p
1
s
Valence electrons take part in bonding
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Chapter 6 Electronic Structure of Atoms
What is the electronic structure of Cl?
3s23p5
Ne
17Cl
valence electrons (7)
3
d
2
p
1
core electrons electron configuration of the
preceding noble gas
s
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Chapter 6 Electronic Structure of Atoms
What is the electronic structure of Ca?
Ar
4s2
20Cl
(4s orbital is filled before 3d !)
4
f
3
d
2
p
1
s
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Chapter 6 Electronic Structure of Atoms
What is the electronic structure of Br?
Ar
3d104s24p5
35Br
(4s orbital is filled before 3d !)
valence electrons (7)
4
f
3
For main group elements, electrons in a filled
d-shell (or f-shell) are not valence electrons
d
2
p
1
s
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Chapter 6 Electronic Structure of Atoms
Does it matter in which order the electron
configuration is written ?
1s22s22p63s23p63d104s24p5
ordered by orbital number
35Br
or
1s22s22p63s23p64s23d104p5
ordered by energy
4
f
3
d
2
p
1
NO, both are correct!
s
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Chapter 6 Electronic Structure of Atoms
What is the electron configuration of vanadium
(V)?
Ar
3d34s2
23V
(4s orbital is filled before 3d !)
4
f
3
d
2
valence electrons (5)
p
1
core electrons electron configuration of the
preceding noble gas
s
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Chapter 6 Electronic Structure of Atoms
What is the electron configuration of chromium
(Cr)?
Ar
3d54s1
24Cr
4
f
3
d
2
p
1
s
A half-filled or completely filled d-shell is a
preferred configuration
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Chapter 6 Electronic Structure of Atoms
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Chapter 6 Electronic Structure of Atoms
What is the electronic structure of the Ca ion?
Ar
4s2
20Ca
Ar
20Ca2
4
f
3
d
2
p
1
s
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Chapter 6 Electronic Structure of Atoms

• Metals tend to lose electrons to form cations
• Nonmetals tend to gain electrons to form anions

• Atoms tend to gain or lose the number of
  electrons
• needed to achieve the
• electron configuration of the closest noble gas

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Chapter 6 Electronic Structure of Atoms
What is the electronic structure of the ion
formed by Se?
Ar
3d104s24p4
34Se
Ar
3d104s24p6
Kr
34Se2-
4
f
3
d
2
p
1
s
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Chapter 6 Electronic Structure of Atoms
What is the electronic structure of the ion
formed by Br?
Ar
3d104s24p5
35Br
Ar
3d104s24p6
Kr
35Br-
4
f
3
d
2
p
1
s
84
Chapter 6 Electronic Structure of Atoms
What is the electronic structure of the ion
formed by Rb?
Kr
5s1
37Rb
Kr
37Rb
5
4
f
3
d
2
p
1
s
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Chapter 6 Electronic Structure of Atoms
37Rb
Ar
3d104s24p6
Kr
35Br-
Ar
3d104s24p6
Kr
34Se2-
Ar
3d104s24p6
Kr
they are isoelectronic
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Chapter 6 Electronic Structure of Atoms
Which of the four orbital diagrams written below
for nitrogen violates the Pauli Exclusion
Principle?
violates Hunds rule (all spins must point in the
same direction)
violates Hunds rule (degenerate orbitals get one
electron each, first)
doesnt violate anything
violates Paulis Exclusion Principle there are
two same spin electrons in one orbital, i.e. all
4 quantum numbers are the same which is
impossible
1s
2s
2p
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Chapter 6 Electronic Structure of Atoms
What is the total number of orbitals in the
fourth shell (n4) ? a. 16 b. 12 c.
4 d. 3
what is the total number of different s,p, d and
f orbitals?
n4
l 0 1 2 3
s p d f
0
-1,0,1
-3,-2,-1,0,1,2,3
ml
-2,-1,0,1,2
one s three p five d 7 f
orbitals
16 orbitals
(n2)
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Chapter 6 Electronic Structure of Atoms
What is the number of subshells in the third
shell (n3) ? a. 18 b. 9 c. 3 d. 1
How many different types of orbitals are there?
n3
l 0 1 2
s p d
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Chapter 6 Electronic Structure of Atoms
What is the electron configuration of the sodium
cation, Na ? a. 1s22s22p63s1 b.
1s22s22p6 c. 1s22s22p63s2 d. 1s22s22p7
11Na
11 electrons -1 10 electrons
1s2
2s2
2p6