PHY 203: Introductory Atomic
Physics, Heat & Optics
(2 Credit Hours)
Atomic Physics
Lecturer: Jerry Opoku-Ansah, Ph.D.
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SOMETHING FOR YOUR MIND
DO WHATEVER HAS TO BE DONE;
DO IT NOW
PROCRATINATION = PRESSURE
= FORCE/AREA
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What is Atomic Physics?
Write down your answer.
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Atomic physics
• field of physics that studies atoms as an isolated
system of electrons and an atomic nucleus. It is
primarily concerned with the arrangement of
electrons around the nucleus and the processes
by which these arrangements change
• branch of physics concerned with the structure of
the atom and the characteristics of subatomic
particles
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The Nature of
the Atom
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The Discovery of the Parts of
the Atom
• Modern scientific usage denotes the atom
as composed of constituent particles: the
electron, the proton and the neutron
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Thomson’s Model
Model suggested in the past:
Also known as the “Plum-Pudding” Model.
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John Joseph Thomson, 1897
Electrons are negatively charged particles that can be “pulled out” of any metal by
a strong electric field (the “thingies” pulled out are all identical and have a charge
to mass ratio about 2,000 times larger than hydrogen ions (which we now know to
be protons)
So atoms cannot be indivisible, if not
indivisible, they must have some
internal structure that is responsible
for the physical and chemical
properties of the atoms of the various
elements
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The Thomson Model
Thomson proposed that the atom is composed of
electrons surrounded by a soup of positive charge to
balance the electrons’ negative charges.
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Thomson’s Atomic Model
◼ Thomson’s “plum-pudding” model of the atom had the positive
charges spread uniformly throughout a sphere the size of the
atom, with electrons embedded in the uniform background.
◼ In Thomson’s view, when the atom was heated, the electrons
could vibrate about their equilibrium positions, thus producing
electromagnetic radiation.
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Other Models suggested in the past:
Thomson’s Model (Previous),
Also known as the “Plum-Pudding” Model.
No nucleus at the centre of an atom.
The positive charge was assumed to spread through-out the atom
forming a kind of Paste or Pudding
The negative electrons were suspended like plums.
This model was discredited by Rutherford’s α-particle experiment
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Rutherford’s Model
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The Rutherford Model
Rutherford confirmed that the atom had a
concentrated center of positive charge and
relatively large mass
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Rutherford’s Model:
An atom: A small positively charged nucleus (radius ≈ 10-15 m)
Surrounded at relatively large distances (radius ≈ 10-10 m) by a
number of electrons.
In the natural state: It is electrically neutral
Nucleus contains a number of protons, each with a charge +e
that equals the number of electrons, each with a charge of –e
This model of the atom:
Most recent, is the Nuclear Atom Model
Also called the “Planetary” Model
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In its natural state, an atom is electrically neutral.
It contains equal numbers of +e and –e
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A Rutherford scattering experiment
α-particles were Directed at a Thin gold foil
If the Plum-Pudding Model was correct:
the α-particles would be expected to pass nearly straight through the foil
as α-particles are relatively massive compared to the small mass of electrons
Screen (ZnS)
flushed
briefly when
struck by an
α-particle
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Rutherford scattering experiment.
Observation:
Not all the α-particles pass through the foil.
Some were deflected at large angles, even backward.
Rutherford said:
“It was almost incredible as if you had fired a 15-inch shell at a piece of tissue
and it came back and hit you”.
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Rutherford scattering experiment.
Conclusion:
The positive charge, instead of being distributed uniformly
throughout the atom was concentrated in a small region
called the nucleus
Concerns:
How could e- in an atom be separated from +vely charged nucleus?
If the electrons are static, they would be pulled inward by
the attractive electric force of the nuclear charge.
HENCE:
The electron MUST be moving around nucleus in some fashion,
like planets revolving around the sun,
hence the “Planetary Model”.
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Difficulties with Planetary Model
An electron moving on a curved path has centripetal acceleration
Therefore radiates em waves.
These waves carry away energy and the electron would spiral
Inward and eventually collapse into the nucleus!
This however does not occur.
Question?
Under what Conditions will an atom emit radiation?
Concept of Spectrum – Line and Continuous
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Spectra of Atoms: Line and Continuous
The hot filament of a bulb emits em waves that have a continuous
range of wavelengths, some are in the visible region.
The sun also gives a continuous spectrum
In contrast
Individual atoms emit only specific wavelength λ, not
continuous range
These λ are characteristic of the atom & give important clues
about its structure.
These can be identified as series of bright fringes, called line
spectrum.
The simplest line spectrum is that of atomic hydrogen
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Under what Conditions isJOA/PHY
the spectrum
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2500
2000
Intensity
1500
1000
500
0
0
200
400
600
800
1000
Pixel
A line spectrum of Hg
Continuous spectrum of the sun
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The individual wavelengths (line spectrum) emitted by Ne and Hg
And
Continuous spectrum of the sun.
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The Line Spectrum of Atomic Hydrogen
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The Line Spectrum of Atomic Hydrogen
Equations for the values of the observed wavelengths:
It gives the short and long wavelength limits of each series
Lyman series
1 1
= R 2 − 2 

1 n 
1
n = 2, 3, 4, 
When an electron makes a transition from ni = 2 to nf = 1
Longest wavelength photon in the Lyman Series is emitted.
Energy change is the smallest possible.
When an electron makes a transition from ni = ∞ to nf = 1
Shortest wavelength photon is emitted.
Energy change is the largest possible.
Lines are increasingly crowded towards the short wavelength limit.
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R:
Rydberg constant
1.097 x 107 m-1
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The Line Spectrum of Atomic Hydrogen
The equations for the values of the observed wavelength are as follows:
It gives the short and long wavelength limits of each series
Balmer series
1
1 1
= R 2 − 2 

2 n 
n = 3, 4, 5, 
Paschen series
1 1
= R 2 − 2 

3 n 
n = 4, 5, 6, 
1
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Wavelengths in the Lyman series (nf = 1) are in the ultraviolet band
Balmer lines (nf = 2) are in the "visible" part of the spectrum
Paschen lines (nf = 3) lie in the infrared band
Brackett series (nf = 4) lie in the infrared region
Pfund series (nf = 5) lie in the infrared region
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Use of The Equations
To Reproduce the wavelengths that hydrogen atoms radiate
But provides No Insight
WHY certain wavelengths are Radiated but others are Not.
Bohr’s Model
Provided that understanding!
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Bohr’s Atomic Model
The Rutherford model had a major drawback, it could not
explain why electrons do not fall into the nucleus by taking a
spiral path
It was in concurrence with the electromagnetic theory that
states "if a charged particle undergoes accelerated
motion, then it must radiate energy (lose)
continuously".
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He depicts the atom as a tiny, spherical body which
consists nucleus at center and negatively charged
particles (electrons) revolving around nucleus in a
certain path known as orbit. He proposed some new
postulate with same basis concepts of Rutherford
theory.
Bohr suggested that electrons in hydrogen could have certain classical motions only when
restricted by a quantum rule.
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The Bohr Model of the Hydrogen Atom
This model of the atom is based on the following assumptions:
An atom is surrounded by electrons moving in circular orbits.
There can only be certain values of the total energy
(electron KE + PE).
These allowed energy levels correspond to different orbits
for the electron as it moves around the nucleus.
The larger orbits being associated with larger total energies.
An electron in an orbit does not radiate em waves.
Hence the orbits are called stationary orbits or stationary states.
A photon is emitted only when the electron changes orbits
from a larger one with a higher energy to a smaller one
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Ei − E f = hf
f is frequency
h is Plank’s constant
A photon is emitted when the electron drops from a larger,
higher-energy orbit to a smaller, lower energy orbit.
This is according to Einstein
Electrons get into the higher energy orbits
By picking up energy when atoms collide (when a gas is heated)
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By acquiring energy whenJOA/PHY
a
high
voltage
is
applied
to
a
gas
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THE ENERGIES AND RADII OF THE BOHR ORBITS
For an electron of mass m and speed v in an orbit of radius r,
Total energy = kinetic energy KE + electric potential energy EPE.
If the nucleus contains Z protons the total energy will be
E = KE + EPE
1 2 kZe 2
= mv −
2
r
k is a Coulomb’s constant
= 8.988 x 109 N.m2/c2
A centripetal force acts on a particle in uniform circular motion
and this is provided by the electrostatic force of attraction
mv 2 kZe 2
=
r
r2
2
kZe
mv 2 =
r
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Substituting into the Total Energy equation
1  kZe 2  kZe 2
kZe 2
E=
−
=−
2 r 
r
2r


The total energy of the atom is negative because the
negative electric potential energy is larger in magnitude than the
positive kinetic energy.
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To calculate E the value of r is obtained as follows:
According to Bohr the orbital angular momentum L is given as
L = I
Where
I = mr2 is the moment of inertia of the electron moving on its circular path
ω = v/r is the angular speed of the electron.
Bohr assumed the angular momentum can assume only certain discrete values
i.e., L is quantized and given as
h
Ln = mvn rn = n
2
n = 1, 2, 3, 
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Solving this equation for vn and substituting the results into the equation
2
kZe
mv 2 =
r
Gives the expression
 h2
 n2

rn =  2
2 
 4 mke  Z
n = 1, 2, 3, 
Substituting the values of the constants
h = 6.626x10-34 Js,
m = 9.109x10-31 kg,
k = 8.988 x 109 Nm2/C2,
e = 1.602 x 10-19 C
Gives the Radii for Bohr Orbits, given by the final equation
(
)
n2
rn = 5.29 10 m
Z
−11
n = 1, 2, 3, 
Radii for Bohr orbits
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Radii for Bohr orbits
(
)
2
n
rn = 5.29 10−11 m
Z
n = 1, 2, 3, 
For the hydrogen atom (Z=1)
the smallest Bohr orbit (n=1)
The radius r1 = 5.29 x 10-11 m.
This particular value is the Bohr radius.
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Substituting the expression for r into the equation
for the total energy gives
 2 2 mk 2e 4  Z 2
 2
En = −
2
h

n
n = 1, 2, 3, 
Substituting values for h, m, k and e yields
the energy in Joules and eV respectively
Energy in Joules
(
)
2
Z
En = − 2.18 10−18 J 2
n
n = 1, 2, 3, 
Energy in eV
Z2
En = −(13.6 eV) 2
n
n = 1, 2, 3, 
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ENERGY LEVEL DIAGRAMS
For the hydrogen atom Z = 1.
The highest energy level corresponds to n = ∞ with energy 0 eV.
For an atom when the electron is completely removed ( r = ∞) from the nucleus
The lowest energy level (Ground state) has n = 1 and value -13.6 eV.
Higher energy levels are called excited states.
From the ground state (n = 1) to the highest possible state (n = ∞)
a Minimum energy of 13.6 eV is required.
This is the Ionization energy and produces a +ve hydrogen ion H+
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ENERGY LEVEL DIAGRAMS
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Spectral Evidence for Quantization Bohr Theory
1.When electron jumps from lower energy level to
higher energy level, it absorbs relevant amount of
energy and this results in the absorption spectrum.
2.When an electron drops to higher level from lower
level, it emits some amount of energy and emission
spectrum is observed.
3.Since there is only one electron in hydrogen atom,
there should be one line in hydrogen spectrum. But
in Bohr theory, there are infinite number of orbits, so
more than one line is observed in spectrum.
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Objection/Limitations of Bohr Model
1.Bohr model could not explain those atoms which have more
than one electron like lithium, helium. This model was
applicable only for those atoms which have one electron.
2.Bohr theory explained only spherical orbits. There was no
explanation for elliptical orbits.
3.This model failed to explain Zeeman Effect and stark effect.
4.Bohr model could not explain the uncertainty principle of
Heisenberg.
5.Bohr model was not related with classification and periodicity
of elements.
6.By using Bohr atomic model, one can’t explain the intensity
of spectrum line.
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THE LINE SPECTRA OF THE HYDROGEN ATOM
SUMMARY
Bohr’s Model shows that the Lyman Series occurs for
Transitions from higher energy levels with
ni = 2, 3, 4, …….∞ to the first energy level nf = 1.
When an electron makes a transition from ni = 2 to nf = 1
Longest wavelength photon in the Lyman Series is emitted
Energy change is the smallest possible.
When an electron makes a transition from the highest level
where ni = ∞ to the lowest level where nf = 1
Shortest wavelength photon is emitted
Energy change is the largest possible.
The higher energy levels are increasingly close together,
Hence lines in the series become more crowded towards short wavelength limit
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THE LINE SPECTRA OF THE HYDROGEN ATOM
For transitions between energy levels
2 2 mk 2 e 4 2  1
1 
=
Z
− 2
3
2



hc
 n f ni 
1
( )
ni , n f = 1, 2, 3, 
ni  n f
nf is the final energy level, ni is the initial energy level
Substituting the values of constants (h, m, k, e, c) gives
R, which is Rydberg’s constant
For the Balmer Series ni = 3, 4, 5, ……. ∞ and nf = 2
For the Paschen Series ni = 4, 5, 6, …..….. ∞ and nf = 3
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Emission lines
Produced when electrons change from
higher to lower energy levels resulting in the
release of photons.
Electrons also make transitions in
reverse directions from lower to higher levels
in a process known as Absorption
An atom absorbs a photon that has exactly
the energy needed to produce the transition.
Thus if photons with a continuous range of wavelengths pass
through a gas and then analyzed, a series of dark absorption lines
appear in the continuous spectrum.
These dark lines indicate the wavelength that have been
removed by the absorption process.
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END OF LECTURE
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