Module 1 – Introduction to Atomic Structure
Evolution of Atomic Theory
1. First clear concept of Atom starts with the Jain School of Thought in 6th Century BC in
India. The Jains considered that matter is made of atoms or “paramanus”. The Jain School also developed an elaborate set of theories on how atoms could combine, move, vibrate, etc.
2. In Western School, the concept of Atom starts in 5th Century BC through Ionian
Philosopher Democritus. The concept of atom was similar to Jain School in the sense that atoms were considered to be fundamental particles that can not be cut or
broken into parts. The word “atom” was coined by him from the Greek adjective “atomos” meaning uncuttable.
3. Atomistic philosophy in Islam was developed around 11th century AD by Imam
Ghazali synthesizing the Jain and Greek Schools of thoughts about Atom. His atomic theory was more in tune with the Jain School rather than of the Greek School.
4. Towards late 18th century scientific developments started renewed philosophical
Dalton’s Atomic Theory
1. Elements are made of extremely small particles
called atoms.
2. Atoms of a given element are identical in size,
mass, and other properties; atoms of different
elements differ in size, mass, and other
properties.
3. Atoms cannot be subdivided, created, or
destroyed.
4. Atoms of different elements combine in simple
whole-number
ratios
to
form
chemical
compounds.
5. In chemical reactions, atoms are combined,
separated, or rearranged.
Thomson’s Plum Pudding Model
1. The model was proposed by Thomson in 1904 before the discovery of nucleus.
2. Electrons or “corpuscles” are floating in a soup of positive charge to balance the negative charges. 3. The positive charge was assumed to be like a
“pudding”, and the negatively charged electrons as “plums” and hence the terminology Plum Pudding Model taken from a British dessert.
4. Rutherford-Geiger-Marsden gold foil experiment in 1909 disproved the Plum Pudding Model and showed that instead of a soup of positive charge, an atom consisted of a small nucleus of strong positive charge paving the way to Rutherford’s Atomic Model.
Rutherford-Geiger-Marsden Experiment
Rutherford’s Atomic Model
Limitations of Rutherford’s Model
Black Body Radiation
A black body is an ideal body which
allows the whole of the incident
radiation to pass into itself ( without
reflecting the energy ) and absorbs
within itself this whole incident
radiation (without passing on the
energy). This propety is valid for
radiation
corresponding
to
all
wavelengths and to all angels of
incidence. Therefore, the black body is
an ideal absorber of incident radaition.
Basic Laws of Radiation:
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder
objects (per unit area). The amount of energy
radiated is proportional to the temperature of the
object.
Ultraviolet (UV) Catastrophe
The Rayleigh-Jeans Law:
* It agrees with experimental
measurements
for
long
wavelengths.
* It predicts an energy output that
diverges
towards
infinity
as
wavelengths grow smaller.
* The failure has become known as
the ultraviolet catastrophe.
4
2
)
,
(
T
ckT
Planck’s Law of Black Body Radiation
The Planck’s Law of Black Body Radiation states in terms of
wavelength:
1
1
5
2
2
)
,
(
kT
hc
e
hc
T
I
•
The above equation related intensity of
emission with Temperature and wavelength.
•
It fits well with experimental observation of
black body radiation.
•
As opposed to classical model of continuous
energy distribution, energy is emitted in forms of
quantized packets, where h is Planck’s constant
:
c
/
h
(
m)
1000 100 10 1 0.1 0.01
Earth Sun
Hotter objects emit at
shorter wavelengths.
max= 3000/T
Hotter objects emit more energy than colder objects
Applications of Black Body Radiation
•
Roughly we can say that the stars radiate like
blackbody radiators. This is important because it
means that we can use the theory for blackbody
radiators to infer things about stars like its
effective temperature.
•
Interesting applications include designing
Planck-Einstein Relationship
hc
/
h
E
h = Planck’s Constant = 6.626 x 10
-34joule seconds (J s)
Energy could be gained or lost in individual units or
Bohr’s Postulates
Bohr’s Atomic Model
1.
In an atom, the electrons revolve around the
nucleus in certain definite circular paths
called orbits, or shells.
2.
Each shell or orbit corresponds to a definite
energy. Therefore, these circular orbits are
also known as energy levels or energy shells.
3.
Electrons in an atom can have only certain
permissible energies .
Rydberg’s Formula and Bohr’s Theory
Rydberg’s formula is used to explain spectral lines of hydrogen like chemical elements.
Utilizing Bohr’s Postulates, it can be deduced that the energy of a photon emitted by a hydrogen atom is given by the difference of two hydrogen energy levels :
Now in terms of wave-length we have:
Where R is Rydberg’s constant, such that:
R =
Bohr-Sommerfeld Model
Bohr-Sommerfield Model
•
Bohr’s model failed in case of
heavier elements where the
spectral lines observed did not
corroborate with the applied
magnetic field. It was found that
spectral lines are not
homogenous but consists of
several convenient lines.
•
Sommerfield proposed that not
only do electrons travel in certain
orbits but the orbits have
different shapes and the orbits
could tilt in the presence of a
magnetic field. This explained
well the splitting of spectral lines
observed for heavier elements
Advantages and Disadvantages of Bohr-Sommerfield Model
• Sommerfield’s Model predicted the splits in the spectrum. The electrons moving on the two orbits of the same n number but of different shape have a bit different energies which explained the splitting of spectral lines or very closely spaced spectral lines.
• Sommerfield’s Model also showed that
orbits don’t have to lie on the same plane and could tilt in the presence of a magnetic field.
• The fundamental flaw was that
Hydrogen Spectral Series
The Hydrogen Spectral Series can be explained through Rydberg’s formula:
Balmer Spectral Series
•
The Balmer series is particularly useful in astronomy
because the Balmer lines appear in numerous stellar
objects due to the abundance of hydrogen in the universe,
and therefore are commonly seen and relatively strong
compared to lines from other elements.
•
The familiar red H-alpha spectral line of hydrogen gas in
Particles act like Waves!
p
h
/
De- Broglie’s Matter waves was a brilliant idea.
It proposed:
If light (which is a wave) is quantized (like
Heisenberg’s Uncertainity Principle
•
It is impossible to know
both
the position and momentum
exactly, i.e.,
D
x
=0 and
D
p
=0
•
These uncertainties are inherent in the physical world and
have nothing to do with the skill of the observer
•
Because
h
is so small, these uncertainties are not
observable in normal everyday situations
4
/
.
p
h
x
D
Another Consequence of
Heisenberg’s Uncertainty Principle
•
A quantum particle can never be in a state of rest,
as this would mean we know both its position and
momentum precisely
•
The more accurately we know the energy of a body,
31
Orbitals
Orbitals are regions in space where an electron
is likely to be found:
–
90% of the time the electron is within the
boundaries described by the electron density map
–
The exact path of an electron in a given orbital is
32
Describing Orbitals
Use quantum numbers to describe orbitals.
A given orbital can be described by a set of 3
quantum numbers:
1. Principal quantum number (n)
33
Principal Quantum Number (n)
(
n) describes the size and energy of the orbital:
–
Possible values: whole number integer
•
1, 2, 3, …
–
As “n” increases so does the size and energy of
34
Angular momentum quantum number (
l)
(l) is related to the shape of the orbital:
–
Possible values: (
l)
is an integer between 0 and
n-1
35
Angular momentum quantum number (
l)
(
l)
Value
Letter Designation
0
s
1
p
2
d
n
Possible
l
values
Designation
1
0
1s
2
0
1
2s
2p
37
Magnetic quantum number (m
l
)
(m
l) is related to the orientation of the orbital
in 3-D space:
38
Magnetic quantum number (m
l
)
Consider the p orbital…it has an l value of 1
and thus the possible m
lvalues are -1, 0, +1
39
M
l
and Orbitals
l
m
l# orbitals
0 (s)
0
1
1 (p)
-1, 0, 1
3
2 (d)
-2, -1, 0, 1, 2
5
40
Quantum Number Summary
–
A set of 3 quantum numbers describes a specific
orbital
•
Energy and size - n
•
Shape -
l
41
4
th
Quantum Number!
A 4
thquantum number was added to describe
the spin on a given electron.
–
Called the electron spin quantum number - m
s42
More on electron spin
•
Each orbital can hold a maximum of 2
electrons of opposite spin.
•
Pauli exclusion principle states that no two
Summary
•
Three quantum numbers describe a specific
orbital
–
Energy and size, shape, and orientation
•
Four quantum numbers describe a specific
electron in an atom
Stern-Gerlach Experiment
The Stern–Gerlach experiment involves sending a beam of particles through an inhomogeneous magnetic field and observing their deflection. The results show that particles possess an intrinsic angular momentum that is most closely
Aufbau Principle
The
Aufbau principle
from the German
Aufbau
meaning
"building up, construction":
Pauli’s Exclusion Principle
Hund’s Rule
Schrodinger’s Equation
Schrodinger Equation gives the understanding of Quantum
Mechanics Model:
What did this equation do for knowing more about atomic structure?
1. Schroëdinger's equation eliminated the illogical quantum jump of
electrons from one orbit to another as seen in Bohr’s Model, replacing it with a transitional process in which the wave pattern gradually fades out, while the new wave pattern fades in, during which time radiation is being emitted.
Particle in a 1-D Box
An electron in a chemical bond is a real time example of a Particle in a 1-D box
How is it so?
Imagine an electron in a C-C single bond. Since carbon atoms are roughly 24000 times more massive than an electron, thinking classically for a moment, this would be like a ball-bearing between two wrecking balls, which would certainly seem like two infinitely high walls. The box length for a C-C single bond would be roughly 1.5 Å giving a defined confined space.
Uses:
1. Particle in a 1-D box model can be used to predict the wavelength of maximum absorbance for highly conjugated organic molecules.
Applications of Particle in a 1-D Box in Nanotechnology
A Quantum Harmonic Oscillator
Representing a ball on a spring in a classical
harmonic oscillator, a quantum harmonic
oscillator is applicable for vibrational
motion of a diatomic molecule where, two
atoms are assumed to be attached to a
spring representing the chemical bond.
The energy solution is given by:
The energy of a system described by a harmonic oscillator potential cannot have zero energy . Thus, physical systems such as atoms in a solid lattice or in
