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7 Atomic Structure
Contents
7-1 Discovery of the Electron
7-2 Determination of the Charge and Mass of the Electron
7-3 The Nuclear Atom
7-4 Discovery of the Proton and the Neutron
7-5 Traveling Waves
7-6 Electromagnetic Radiation
7-7 The Bohr Model of the Hydrogen Atom
7-8 The Wave Theory of the Electron
7-9 The Heisenberg Uncertainty Principle
7-10 The Schrodinger Equation
7-11 Electron Spin and the Pauli Exclusion Principle
7-12 Pictures of Orbitals
Atomic Structure
• Our goal:
• Understand why some substances behave as they do.
• For example: Why are K and Na reactive metals? Why do H and
Cl combine to make HCl? Why are some compounds molecular
rather than ionic?
• Atom interact through their outer parts, their electrons.
• Electronic structure: The way of electrons in atoms are
arranged around the nucleus.
• Electron structure relates to:
• Number of electrons an atom possess.
• Where they are located.
• What energies they possess.
7-1 Discovery of the Electron
A = alpha
B = gamma
C = beta
J.J. Thomson, measured mass/charge of e(1906 Nobel Prize in Physics)
7-2 Determination of the Charge and Mass of the Electron
Measured mass of e- (1923 Nobel Prize in Physics)
e- charge = -1.60 x 10-19 C; e- mass = 9.10 x 10-28 g
Thomson’s charge/mass of e- = -1.76 x 108 C/g
7-3 The Nuclear Atom
(1908 Nobel Prize in Chemistry)
 particle velocity ~ 1.4 x 107 m/s
(~5% speed of light)
1. atoms positive charge is concentrated in the nucleus
2. proton (p) has opposite (+) charge of electron
3. mass of p is 1840 x mass of e- (1.67 x 10-24 g)
Rutherford’s Model of the Atom
atomic radius ~ 100 pm = 1 x 10-10 m
nuclear radius ~ 5 x 10-3 pm = 5 x 10-15 m
Ruthford pictured the atom as consisting of a small,
dense, positively charged nucleus containing most of the
mass of the atom with the electrons in the space outside
the nucleus.
7-4 Discovery of the Proton and the Neutron
ATOM COMPOSITION
The atom is mostly empty space.
•protons and neutrons in the nucleus.
•the number of electrons is equal to the number of
protons.
•electrons in space around the nucleus.
•extremely small. One teaspoon of water has 3 times as
many atoms as the Atlantic Ocean has teaspoons of water.
ATOMIC COMPOSITION
• Protons
+ electrical charge
mass = 1.672623 x 10-24 g
relative mass = 1.007 atomic mass units (amu)
• Electrons
negative electrical charge
relative mass = 0.0005 amu
• Neutrons
no electrical charge
mass = 1.009 amu
Subatomic Particles
Mass
(g)
Particle
-
-28
Charge
(units)
-19
-1
1.67 x 10-24 +1.6 x 10-19
+1
Electron (e ) 9.1 x 10
Proton (p)
Charge
(Coulombs)
Neutron (n) 1.67 x 10
-24
-1.6 x 10
0
0
mass p = mass n = 1840 x mass e-
_______________ (Z) = number of protons in nucleus
______________(A) = number of protons + number of neutrons
= atomic number (Z) + number of neutrons
___________ are atoms of the same element (X) with different
numbers of neutrons in the nucleus
Mass Number
A
ZX
Atomic Number
1
1H
235
92
2
1H
U
Element Symbol
(D)
238
92
3
1H
U
(T)
Do You Understand Isotopes?
How many protons, neutrons, and electrons are in 146
C?
How many protons, neutrons, and electrons are in 116
C?
7-5 Traveling Waves
The simplest wave motion—traveling wave in a rope
As a result of the up-anddown hand motion (top to
bottom), waves pass along the
long rope from left to right.
This one-dimensional moving
wave is called a traveling wave.
The wavelength of the wave,
λ—the distance between two
successive crests (the length of
one circle) —is identified.
Identifying  and 
The Wave Nature of Light
• Study of light emitted or absorbed by substances has lead
to the understanding of the electronic structure of atoms.
• Characteristics of light:
• All waves have a characteristic wavelength, , and
amplitude, A.
• The frequency, , of a wave is the number of cycles which
pass a point in one second.
• The speed of a wave, c, is given by its frequency
multiplied by its wavelength:
c  
• For light, speed = c.
7-6 Electromagnetic Radiation
Electromagnetic radiation is a form of energy that
consists of perpendicular electric and magnetic fields that
change, at the same time and in phase, with time.
According to a theory proposed by James Clerk
Maxwell (1831-1879) in 1865, electromagnetic radiation—
a propagation of electric and magnetic fields—is produced
by an accelerating electrically charged particle (a charge
particle whose velocity changes). Radio waves, for
example, are a form of electromagnetic radiation produced
by causing fluctuations of the electric current in a specially
designed electrical circuit.
Electromagnetic Radiation
• Modern atomic theory arose out of studies of the
interaction of radiation with matter.
• Electromagnetic radiation moves through a vacuum with
a speed of 2.99792458  108 m/s. (the speed of light)
• Electromagnetic waves have characteristic wavelengths
and frequencies.
• Example: visible radiation has wavelengths between 400
nm (violet) and 750 nm (red).
This sketch of two different electromagnetic waves shows the
propagation of mutually perpendicular oscillating electric and magnetic
fields. For a given wave, the wavelengths, frequencies, and amplitudes of
the electric and magnetic field components are identical. If these view
are of the same instant of time, we would say that (a) has the longer
wavelength and lower frequency, and (b), the shorter wavelength and
higher frequency.
Example
Relating the Frequency and Wavelength of
electromagnetic Radiation. Most of the light from a sodium
vapor lamp has a wavelength of 589 nm. What is the
frequency of this radiation ?
Solution
We can first convert the wavelength of the light from
nanometers to meters and then apply equation (7.1).
－9 m
1
×10
λ = 589 nm ×
1 nm
c = 2.998 × 108 m/s
ν=?
= 5.89 ×10－7 m
Rearrange equation (7.1) to the form ν = c/λ, and solve for ν.
ν = c/λ=
2.998 × 108 m s－1
5.89 ×10－7 m
= 5.09 × 1014 s－1
= 5.09 × 1014 Hz
The Electromagnetic Spectrum
Interference in two overlapping light waves
(a)
In constructive
interference, the troughs
and crests are in step
(in phase), leading to
addition of the two waves.
(b)
In destructive
interference, the troughs
and crests are out of step
(out of phase), leading
to cancellation of the two
waves.
Class Guided Practice Problem
• The yellow light given off by a sodium vapor lamp used for public
lighting has a wavelength of 589 nm. What is the frequency of this
radiation?
c  
Class Practice Problem
• A laser used to weld detached retinas produces radiation with a
frequency of 4.69 x 1014 s-1. What is the wavelength of this
radiation?
The Photoelectric Effect
• Planck’s theory revolutionized
experimental observations.
• Einstein:
• Used Planck’s theory to explain
the photoelectric effect.
• Assumed that light traveled in
energy packets called photons.
• The energy of one photon:
E  h
Quantized Energy and Photons
• Planck: energy can only be absorbed or released from
atoms in certain amounts “chunks” called quanta.
• The relationship between energy and frequency is
E  h
where h is Planck’s constant (6.626  10-34 J.s).
• To understand quantization consider walking up a ramp
versus walking up stairs:
• For the ramp, there is a continuous change in height whereas up
stairs there is a quantized change in height.
Class Guided Practice Problem
• Calculate the energy of a photon of yellow light whose
wavelength is 589 nm.
E  h
Class Practice Problem
• (a)Calculate the smallest increment of energy (a
quantum) that can be emitted or absorbed at a wavelength
of 803 nm. (b) Calculate the energy of a photon of
frequency 7.9 x 1014 s-1. (c) What frequency of radiation
has photons of energy 1.88 x 10-18 J? Now calculate the
wavelength.
7-7 The Bohr Model of the Hydrogen Atom
Line Spectra
• Radiation composed of only one wavelength is called
monochromatic.
• Most common radiation sources that produce radiation
containing many different wavelengths components, a
spectrum.
• This rainbow of colors, containing light of all wavelengths,
is called a continuous spectrum.
• Note that there are no dark spots on the continuous
spectrum that would correspond to different lines.
continuous spectrum
When gases are placed under reduced pressure in a tube
and a high voltage is applied, radiation at different
wavelengths (colors) will be emitted.
Specific Wavelength “Line Spectra”
“Line Spectra” of Hydrogen Atom
•Infrared
•
•/nm 760
Red
H
660
Cyan Blue Violet UV
H
480
H
435
408 400
Line Spectra
• Balmer: discovered that the lines in the visible line
spectrum of hydrogen fit a simple equation.
• Later Rydberg generalized Balmer’s equation to:
 RH

  h
1
 1 1 
 2  2 
 n1 n2 
where RH is the Rydberg constant (1.096776  107 m-1), h
is Planck’s constant (6.626  10-34 J·s), n1 and n2 are
integers (n2 > n1).
This Danish stamp honors Niels Bohr(1885-1962), who made
major contributions to the quantum theory. From 1911 to 1913 he
studied in England, working first with J.J.Thomson at Cambridge
University and then with Ernest Rutherford at the University of
Manchester. He published his quantum theory of the atom in 1914
and was awarded the Noble Prize in physics in 1922.
Bohr Model
• Rutherford assumed the electrons orbited the nucleus
analogous to planets around the sun.
• However, a charged particle moving in a circular path
should lose energy.
• This means that the atom should be unstable according to
Rutherford’s theory.
• Bohr noted the line spectra of certain elements and
assumed the electrons were confined to specific energy
states. These were called orbits.
Line Spectra (Colors)
• Colors from excited gases arise because electrons move
between energy states in the atom.
Line Spectra (Energy)
• Since the energy states are quantized, the light emitted
from excited atoms must be quantized and appear as line
spectra.
• After lots of math, Bohr showed that
18  1 
E   2.18 10 J  2 
n 
where n is the principal quantum number (i.e., n = 1, 2, 3,
… and nothing else).


The existence of the lines had been known for many years, they
were not explained until early in the twentieth century. Building on the
work of Planck and Einstein, Niels Bohr applied quantum theory to
explain the line spectrum of hydrogen in terms of the behavior of the
electron in a hydrogen atom.
The Bohr atom:
1. Only orbitals of certain radii, corresponding to certain definite
energies, are permitted for the electron in a hydrogen atom.
2. An electron in a permitted orbit has a specific energy and is an
“allowed” energy state. An electron in an allowed energy state
will not radiate energy and therefore will not spiral into the nucleus.
3. Energy is emitted or absorbed by the electron only as the electron
changes from one allowed energy state to another. This energy
emitted or absorbed as a photon, E = hν.
Bohr proposed that the electron in a hydrogen atom could circle the
nucleus only in specific orbits designated by a quantum number n. The
quantum number can have integer values, with n = 1 corresponding to
the orbit closest to the nucleus. He showed the relationship between the
value of n and the energy of an electron is
(7.5)
RH is the Rydberg constant (2.18×10–18J). The energy of an
electron is, by convention, a negative number. When an electron
resides in the orbit designated by n = 1, it is said to be in the ground
state. This is the lowest possible energy level in which hydrogen's
electron can exist. If hydrogen's electron is in a higher energy (less
negative) orbit, with n greater than 1, the atom is said to be in an
excited state.
Ground state: the lowest—energy, or most stable state.
Excited state: a higher energy state than the ground state.
Bohr assumed that the electron could "jump" from one allowed
energy state to another by absorbing or emitting photons of radiant
energy of certain frequencies. He described the lines in the hydrogen
spectrum as the energy given off when an electron in an excited state
returns to the ground state. A flame or the application of high voltage
imparts energy to the electron in a hydrogen atom and promotes it to an
orbit of higher n value. When the excited state electron returns to the
ground state, it releases the excess energy in the form of visible light.
The frequency of this emitted radiant energy corresponds exactly to the
energy difference between the two states.
Using his equation for the energy of an electron, Bohr calculated
the energy change and the frequency associated with changing
values of the quantum number n.
(7.6)
Using this relationship, Bohr was able to show that the visible line
spectrum of hydrogen was due to the transitions of electrons in
hydrogen atoms from n = 6 to n = 2, n = 5 to n = 2, n = 4 to n = 2, and
n = 3 to n = 2.
For the transition from n = 5 to n = 2
• Calculate the wavelength in nm of the spectrum of the
hydrogen atom for the electron moves from n=3 to n=2.
• Solution Solve Equations 7.1, 7.3 and 7.6 for frequency
and substitute the value given for n=3, 2.
E  h
1
c  
 1
1 
E  RH  2  2 
n

n
f 
 i
1


-18


1 1 
2.18

10
J
RH 1 1
 2  2 
 2 2
-34
8
hc  ni n j  6.626 10 Js  3.0 10 m / s  3 2 
 6.563 107 m
• The problem asks for the wavelength in nm:
 1nm 
6.563 10 m  9   656.3nm
 10 m 
7
• the wavelength of the red line in the spectrum of the
hydrogen atom.
The visible lines in
the
hydrogen
line
spectrum are known as
the Balmer series, in
honor
of
Johann
Balmer
who
first
developed an equation
by
which
their
frequencies could be
calculated.
Electron
transitions ending in n
= 1 and n = 3 are called
the Lyman and the
Paschen
series,
respectively.
Energy-level
diagram for the
hydrogen atom
Emission and
absorption
spectroscopy
(a)Emission
spectroscopy.
Bright lines are
observed on a
dark background
of
the
photographic
plate.
(b) Absorption
spectroscopy.
Dark lines are
observed on a
bright
background on
the photographic
plate.
Limitations of the Bohr Model
• Can only explain the line spectrum of hydrogen
adequately.
• Electrons are not completely described as small particles.
• Absorb the quantum mechanics, but neglect the duality of
electrons.
New Quantum
Mechanics
Two Ideas
Louis de Broglie—
Wave-Particle Duality
Werner Heisenberg (1901-1976)
—The Uncertainty Principle
7-8 The Wave Theory of the Electron
The Wave Behavior of Matter
• Knowing that light has a particle nature, it seems
reasonable to ask if matter has a wave nature.
• Using Einstein’s and Planck’s equations, de Broglie
showed:
h

m
• The momentum, mv, is a particle property, whereas  is a
wave property.
• de Broglie summarized the concepts of waves and
particles, with noticeable effects if the objects are small.
Wave-Particle Duality
Einstein’s famous equation
E = mc2
Where m is the relativistic mass of the photon and c is the
speed of light. He combined this equation with the Planck
relationship for the energy of a photon E = hν as follows
hν = mc2
hν/c = mc = p
Where p is the momentum of the photon. Using νλ = c, we
have
p = h/λ
In order to use this equation for a material particle, such
as an electron, de Broglie substituted for the momentum, p,
its equivalent—the product of the mass of the particle, m
and its velocity, v. when this is done, we arrive at de
Broglie’s famous relationship.
λ=
h
p
h
=
mv
(7.10)
• What is the wavelength of an electron moving with a
speed of 5.97×106 m/s? The mass of the electron is
9.11×10-31kg.
• Solve: Using the Equation 7.10
 1kgm 2 /s 2  103 g 
h
6.626 1034 Js




28
6 
mv 9.1110  5.97 10 g 
1J
 1kg 
 1.22 10
10
m  0.122nm
demonstrated experimentally
• When X-rays pass through a crystal, an interference
pattern results that is characteristic of the wavelike
properties of electromagnetic radiation.
• This phenomenon is called X-ray diffraction. As
electrons pass through a crystal, they are similarly
diffracted.
• Thus, a stream of moving electrons exhibits the same
kinds of wave behavior as X-rays and all other types of
electromagnetic radiation.
The diffraction fringes of X-rays (or electrons)
7-9 The Heisenberg Uncertainty Principle
The Wave Behavior of Matter
The Uncertainty Principle
• Heisenberg’s Uncertainty Principle: on the mass scale
of atomic particles, we cannot determine exactly the
position, direction of motion, and speed simultaneously.
• For electrons: we cannot determine their momentum and
position simultaneously.
• If x is the uncertainty in position and mv is the
uncertainty in momentum, then
h
x  m 
4
Uncertainty Principle: we cannot measure position and
momentum with great precision simultaneously. If we design an
experiment to locate the position of a particle with great precision,
we cannot measure its momentum precisely, and vice versa.
In simpler terms, if we know precisely where a particle is,
we cannot also know precisely where it has come from or where
it is moving, we cannot also know precisely where it is.
h
x  P 
4
h
x 
4mv
(7.11)
A brief calculation illustrates the dramatic implications
of the uncertainty principle
The electron has a mass of 9.11×10-31 kg and moves at an average
speed of about 5×106 m/s in a hydrogen atom. Let’s assume that we
know the speed to an uncertainty of [that is, an uncertainty of 0.01 ×
5×106 = 5×104 m/s] and that this is the only important source of
uncertainty in the momentum, so that mv  mv . We can use
Equation 7.9 to calculate the uncertainty in the position of the
electron:
Conclusion
• De Broglie’s hypothesis and Heisenberg’s uncertainty
principle set the stage for a new and more broadly
applicable theory of atomic structure.
• In this approach, any attempt to define precisely the
instantaneous location and momentum of the electron is
abandoned.
• The wave nature of the electron is recognized, and its
behavior is described in terms appropriate to waves.
• The result is a model that precisely describes the energy of
the electron while describing its location not precisely but
rather in terms of probabilities.
Electron Density Distribution
Probability of finding an electron in a hydrogen
atom in its ground state.
7-10 The Schrodinger Equation
Quantum Mechanics and Atomic Orbitals
• Schrödinger proposed an equation that contains both wave
and particle terms.
• Solving the equation leads to wave functions.
• The wave function gives the shape of the electronic
orbital.
• The square of the wave function, gives the probability of
finding the electron,
• that is, gives the electron density for the atom.
• In 1926, Schrödinger developed a
mathematical treatment into which
both the wave and particle nature
of matter could be incorporated.
• Schrödinger showed that the wave
functions of a quantum
mechanical system can be
obtained by solving a wave
equation that has since become
known as the Schrödinger
equation.
2
2

d

V 
8  m dx
h
2
2
 E
• Solutions of the Schötdinger‘s equation for the
hydrogen atom give the wave functions for the electron
in the hydrogen atom. These wave functions are called
orbitals to distinguish them from the orbits of the Bohr
theory.
• Wave functions are most easily analyzed in terms of the
three variables required to define a point with respect
to the nucleus.
• The Schrödinger equation is too complicated, requires
advanced calculus, and so we will not be concerned
with its details.
• We can use the result of solution of the Schrödinger
equation even we can not carry out the calculation.
• Schrödinger used his equation to calculate a number of
the properties of the electrons in the hydrogen atom.
The calculated value agree well with the properties
observed by experiment.
The Three Quantum Numbers
1. Schrödinger’s equation requires 3 quantum numbers:
2. Principal Quantum Number, n. This is the same as Bohr’s n.
As n becomes larger, the atom becomes larger and the electron
is further from the nucleus. (n = 1, 2, 3…)
3. Azimuthal Quantum Number, l. This quantum number depends
on the value of n. The values of l begin at 0 and increase to (n 1). We usually use letters for l (s, p, d and f for l = 0, 1, 2, and
3). Usually we refer to the s, p, d and f-orbitals. (l = 0, 1, 2…n1). Defines the shape of the orbitals.
4. Magnetic Quantum Number, ml. This quantum number
depends on l. The magnetic quantum number has integral
values between -l and +l. Magnetic quantum numbers give the
3D orientation of each orbital in space. (m = -l…0…+1)
Assigning Quantum Numbers
1. The principle quantum number
• The principle quantum number, n, can have positive
integral, nonzero values of 1, 2, 3, and so forth. As n
increase, the orbital becomes larger, and the electron
that the electron has a higher energy and is therefore
less tightly bound to the nucleus.
•
n = 1, 2, 3, …..
(7.13)
2. The second quantum number—the
azimuthal quantum number
• The azimuthal quantum number, l—can have integral
values from 0 to n－1 for each value of n, zero or a
positive integer, but not larger than n－1 (where n is the
principal quantum number)
• l = 0, 1, 2, 3, …., n－1
(7.14)
• This quantum number defines the shape of the orbital.
★ The value of l for a particular orbital is generally
designated by the letters s, p, d, and f, corresponding to
l values of 0, 1, 2, and 3, respectively.
Value of l
0
1
2
3
Letter used
s
p
d
f
3 The magnetic quantum number
• The magnetic quantum number, ml, can have integral
values between –l and l, including zero. This quantum
number describes the orientation of the orbital in space.
Orbitals and Quantum Numbers
Class Guided Practice Problem
• (a) For n = 4, what are the possible values of l? (b) For l
= 2. What are the possible values of ml? What are the
representative orbital for the value of l in (a)?
Class Practice Problem
• (c) How many possible values for l and ml are there when
(d) n = 3; (b) n = 5?
Representations of Orbitals
The s-Orbitals
• All s-orbitals are spherical.
• As n increases, the s-orbitals get larger.
• As n increases, the number of nodes increase.
• A node is a region in space where the probability of
finding an electron is zero.
• At a node, 2 = 0
• For an s-orbital, the number of nodes is (n - 1).
The s Orbitals: The electron density
• The representation of the
lowest-energy orbital of the
hydrogen atom is shown in
Fig, the 1s.
• The electron density for the 1s
orbital is that it is spherically
symmetric.
• Recall that the l quantum number for the s orbitals is 0;
therefore, the quantum number must be 0. Thus, for each
value of n, there is only one s orbital.
• All of the other s orbitals (2s, 3s, 4s, and so forth) are
also spherically symmetric and centered on the nucleus.
★So how do s orbitals differ as the value of n changes?
• Look at the radial probability function, also called the
radial probability density.
• is defined as the probability that we will find the
electron at a specific distance from the nucleus.
Radial probability distributions
for the 1s, 2s, and 3s orbitals of hydrogen
★Comparing the radial probability distributions for the 1s,
2s, and 3s orbitals reveals three trends:
1. The number of peaks increases with increasing n, with
the outermost peak being larger than inner ones.
2. The number of nodes increases with increasing n.
3. The electron density becomes more spread out with
increasing n.
Angle probability function
Comparison of the 1s, 2s, and 3s orbitals.
(a) Electron-density distribution of a 1s orbital.
(b) Contour representions of the 1s, 2s, and 3s orbitals. Each
sphere is centered on the atom’s nucleus and encloses the volume in
which there is a 90% probability of finding the electron.
•Value of l = 0.
•Spherical in shape.
•Radius of sphere increases with increasing value of n.
• All the orbitals have the same shape, but they differ in size,
becoming larger as n increases, reflecting the fact that the
electron density becomes more spread out as n increases.
• The most important features of orbitals are shape and
relative size, which are adequately displayed by contour
representations.
The s-Orbitals
The
• Beginning with the
n = 2p-Orbitals
shell, each shell has three p
orbitals.
• The l quantum number for p orbitals is 1, the magnetic
quantum number can have three possible values: -1, 0, and
1.
• Thus, there are three 2p orbitals, three 3p orbitals, and so
forth, corresponding to the three possible values of ml.
• There are three p-orbitals px, py, and pz.
• The three p-orbitals lie along the x-, y- and z- axes of a
Cartesian system.
• The orbitals are dumbbell shaped.
• As n increases, the p-orbitals get larger.
The averaged distribution of the electron density
in a 2p orbital
(a) Electron-density distribution of a 2p orbital.
(b) Contour representations of the three porbitals. The subscript on
the orbital label indicates the axis along which the orbital lies.
• The density is concentrated in two regions on either side
of the nucleus, separated by a node at the nucleus.
• Each set of p orbitals has the dumbbell shapes which has
two lobes.
• The three p orbitals have the same size and shape but differ
from one another in spatial orientation.
• It is convenient to label these as the px, py, and pz orbitals.
The letter subscript indicates the Cartesian axis along
which the orbital is oriented.
• Like s orbitals, p orbitals increase in size as we move from
2p to 3p to 4p, and so forth.
The p-Orbitals
Electron-distribution
of a 2p orbital.
The d and f-Orbitals
• There are five d and seven f-orbitals.
• Three of the d-orbitals lie in a plane bisecting the x-, yand z-axes.
• Two of the d-orbitals lie in a plane aligned along the x-,
y- and z-axes.
• Four of the d-orbitals have four lobes each.
• One d-orbital has two lobes and a collar.
The d Orbitals
Representations of the
five d orbitals
• Value of l is 2.
• Five nd orbitals
• 5 orbitals have different shapes and orientations in space
• 4 of the 5 orbitals have 4 lobes; the other resembles a p
orbital with a doughnut around the center.
• Even though 5 orbitals with different shape, they have
the same energy.
• The representations in Figure are commonly used for
all d orbitals, regardless of principal quantum number.
Orbitals and Quantum Numbers
• Orbitals can be ranked in terms of energy to yield an
Aufbau diagram.
• As n increases, note that the spacing between energy
levels becomes smaller.
• Orbitals of the same energy are said to be degenerate.
7-11 Electron Spin and the Pauli Exclusion Principle
• Line spectra of many electron atoms show each line as a
closely spaced pair of lines.
• Stern and Gerlach designed an experiment to
determine why.
• A beam of atoms was passed through a slit and into a
magnetic field and the atoms were then detected.
• Two spots were found: one with the electrons spinning
in one direction and one with the electrons spinning
in the opposite direction. (ms = +½, －½).