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Lecture 31
April 12. 2017.
With the assumption of small slit width and large distance x to the screen the expanded
Y
view of the two slits light beams are parallel.
S1
d


S2
Screen
x
sin  
x
x
 n
d
Bright fringes when n=0 or an integer +1,+2, ……. Constructive interference
y
If the screen is far from the slits sin can be approximated by sin   , thus we
x
have bright fringe condition
dy
x
 n  y  n 
d
x

Dark fringes occur when n is an odd integer n = 2m+1 of
y  (2m  1)
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x
d 2
Physics 214 Spring 2016
2
1
Cathode Ray Tube and Thomson's discovery of electrons,  particles
and photons
Cathode Ray Tube and Röntgen’s discovery of X-ray photons
Black Body radiation and Max Planck’s quantum hypothesis: E  h
Photo Electric Effect and its interpretation by Einstein
Discrete Hydrogen Gas Discharge Spectrum and the Balmer – Rydberg
-Ritz formula (1908)
Bohr’s hypothesis of Hydrogen Atom
a.) Electron orbits around proton in Coulomb field
b.) Only certain orbits are permitted
c.) Photons are emitted or absorbed in these transitions
d.) Electrons do not radiate when in the stable orbits
Periodic Table and Rutherford’s Experiment
Nuclear structure and radioactivity
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Physics 214 Spring 2016
2
Improvements of Guericke of Magdeburg’s pump and Volta – Galvani’s battery
resulted in a high vacuum and high voltage cathode ray tube. Upon heating the
cathode, three kind of beams (1897) emerged:
 particles
 particles
 particles
We identified the
 particle with Helium nucleus
 particle with the electron of Benjamin Franklin by Thomson in 1897.
See Fig. 18.7 and 18.8 on page 393.
 particle with high energy photon by Röntgen.
See Fig. 18.10 and 18.11 on page 394.
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Max Planck painted black the inside of a closed cube and drilled a small
hole on one of its side and measured the distribution of  of the emitted
(black body) radiation.
Max Planck could explain the observed spectral distribution of the black body
radiation only if he assumed that the relation between the energy and frequency
of the radiation is
E  h
Using this relation Einstein could explain the Photo Electric Effect
Ee  h 
and obtain the Nobel prize.
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Planck’s relation and its interpretation by Einstein suggests that the spectral lines
with fixed  can be interpreted as an electron transition from one energy level
at r1 to an other energy level with r2 , making Bohr’s hypothesis plausible with
the corollary that electrons do not radiate in stable orbits, only when they are in
transition from r1  r2 .
See Fig. 18.19 on page 401.

But how is the + charge, which attracts the e , is distributed
In 1909-1911 Rutherford used  particles emerging from decaying nuclei and
bombarded an gold foil.
Found the amazing events that  particles scatter backward.
This indicates that a positive charge is concentrated in a small sphere thus the 
particle’s kinetic energy is converted into potential energy
q
mv2
 k nucleus
r
2
and it can recoil like
See graph 3 on page 406.
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Mendeleev’s periodic table can be interpreted as
Z
Atom = Atom
contains Z proton and it is located at
th
the z position and Z electrons orbit around the protons.
Atoms in one columns have equal number of electrons on the
outer orbits.
See Fig. 18.5 on page 390.
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The basic building blocks
•The basic building blocks that make up atoms are •
charge mass
•Proton 1.6 x 10‐19 1.672 x 10‐27kg
•Neutron 0 1.675 x 10‐27kg
•Electron ‐1.6 x 10‐19 9.1 x 10‐31kg
•Photon
0 E = hf p = h/λ
•h = Planck’s constant = 6.626 x 10‐34J.s
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The nucleus
•The nucleus was found by
Rutherford in scattering charged
particles from a gold foil.
•He observed that occasionally the
charged particle was deflected
through a large angle indicating it had
“hit something hard”
The nucleus of any atom is
composed of protons and
neutrons. The protons have
positive electric charge so
repel each other. If they are
close enough the strong force
binds them together and the
nucleus is stable
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Atoms
•Atoms are made up with a central nucleus of protons and neutrons surrounded by
a number of electrons equal to the number of protons.
• The notation we use is 2He4
•2 is the atomic number = number of protons (and electrons)
•4 is the mass number = number of protons + neutrons
•Note atomic mass is the actual mass of the nucleus in atomic mass units with
Carbon set to be 12 units and atomic mass in general is not an integer
•H2O gives the number of atoms required to make a molecule
• water = 2 Hydrogen plus 1 Oxygen
•In a nuclear reaction energy, charge, and atomic mass are conserved.
•Atoms can decay
•Atoms can join together to form new atoms or molecules
•Chemistry is determined by the electrons
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3E-05 Cloud Chamber
As charged particles pass through a
gas electrons are knocked out of the
atom and the ions produced can act
as “seeds” for a super saturated
liquid to condense. This leaves a
visible track of bubbles of liquid.
Cosmic rays are bombarding the
earth continuously and radioactive
decays also produce charged
particles which can be observed in a
cloud chamber. If the chamber is in a
magnetic field the tracks are curved
The first observation of the positron
(anti particle of the electron) was
made in a cloud chamber
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Isotopes
•For a given number of protons there is a nucleus that is most stable for a
particular number of neutrons.
•Isotopes are when for the same number of protons the number of neutrons
is different from the most stable configuration.
•Since the number of electrons is the same the chemical properties are
“identical” but the nucleus can be unstable.
•The larger the difference between ideal and the isotope the more unstable
the nucleus becomes.
•Nuclei have been made artificially that do not exist in nature.
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Lecture 32
April 14. 2017.
Hydrogen Discharge Tube and Emission of Discrete Wavelengths
Description of the discrete Hydrogen Emission Spectrum by the Balmer
(1884) – Rydberg –Ritz formula (1908)
Cathode Ray Tube and Thomson's discovery of electrons,  particles
and photons (1897)
Cathode Ray Tube and Röntgen’s discovery of X-ray photons
Black Body radiation and Max Planck’s quantum hypothesis: E  h
Photo Electric Effect and its interpretation by Einstein
4/7/2016
Physics 214 Spring 2017
1
Bohr’s hypothesis of the Hydrogen Atom
a.) Electron orbits around proton in its Coulomb field like the solar
system
b.) Only certain stable orbits are permitted
c.) Photons are emitted or absorbed in the transitions between these
stable orbits
d.) Electrons do not radiate when move in stable orbits
Periodic Table and Rutherford’s Experiment
Nuclear structure and radioactivity
4/7/2016
Physics 214 Spring 2017
2
Improvements over Guericke's (Mayor of Magdeburg 1654) vacuum
pump and Volta-Galvani’s battery, resulted in Hydrogen gas discharge tube
and in high vacuum and high voltage cathode ray tube.
The Hydrogen discharge tube produced a remarkable four discrete line spectrum:
a red, a blue and two violet lines.
See Fig. 18.17 on page 399.
Balmer (1884) – Rydberg – Ritz (1908) described the above observation by the
equation:
1

 R(
1
1
)

2
2
n m
Where R is called the Rydberg constant and n, m are integers. This
formula was the forerunner of quantum rather then continuum physics.
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Upon heating the cathode of the cathode ray tube (See Fig. 18.6 on page 391)
three kind of beams (1897) emerged:
 particles
 particles
 particles
Which we identify:
 particle with Helium nucleus
 particle with the electron of Benjamin Franklin by Thomson in 1897.
See Fig. 18.7 and 18.8 on page 393.
 particle with high energy photon by Röntgen.
See Fig. 18.10 and 18.11 on page 394.
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Max Planck painted black the inside of a closed cube and drilled a small
hole on one of its side and measured the distribution of  of the emitted
(black body) radiation. (See Fig. 18.18 on page 400)
Max Planck could explain the observed spectral distribution of the black body
radiation only if he assumed that the relation between the energy and frequency
of the radiation is
E  h
Using this relation Einstein could explain the Photo Electric Effect, the emission
of bound electron from metals
Ee  h 
and obtain the Nobel prize.
4/7/2016
Physics 214 Spring 2017
9
4/7/2016
Physics 214 Spring 2017
10
Planck’s relation and its interpretation by Einstein suggests that the discrete
spectral lines of H 2 gas ( See Fig. 18.17 on page 399) with fixed  can be
interpreted as an electron transition from one stable orbit with energy level E1 ( r1 )
with radius r1 to another stable orbit with energy level E2 (r2 ) with radius r2 .
To make Bohr’s hypothesis possible he added the corollary that electrons do not
radiate in stable orbits, only when they are in transition from r1  r2 .
See Fig. 18.19 on page 401.
But how is the + charge, which attracts the e  , is distributed
In 1909-1911 Rutherford used  particles emerging from decaying nuclei and
bombarded a gold foil.
He found amazing events where  particles scatter backward.
This indicates that a positive charge is concentrated in a small sphere thus the 
particle’s kinetic energy is converted into potential energy, stops and recoils.
q
mv2
 k nucleus
r
2
See graph 3 on page 406.
4/7/2016
Physics 214 Spring 2017
11
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Physics 214 Spring 2017
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Mendeleev’s periodic table can be interpreted as
N
Atom
= Atom
z
contains Z proton and N nucleons (protons + neutrons) it is located at
th
the z position in the periodic table and Z electrons orbit around the protons.
Atoms in one columns have equal number of electrons on the outer orbits.
See Fig. 18.5 on page 390.
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The basic building blocks
•The basic building blocks that make up atoms are •
charge mass
•Proton 1.6 x 10‐19 1.672 x 10‐27kg=938.27MeV
•Neutron 0 1.675 x 10‐27kg=939.56MeV
•Electron ‐1.6 x 10‐19 9.1 x 10‐31kg=0.51MeV
•Photon
0 E = hf p = h/λ
•h = Planck’s constant = 6.626 x 10‐34J.s
4/7/2016
Physics 214 Spring 2017
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The nucleus
•The nucleus was found by
Rutherford in scattering charged
particles from a gold foil.
•He observed that occasionally the
charged particle was deflected
through a large angle indicating it had
“hit something hard”
The nucleus of any atom is
composed of protons and
neutrons. The protons have
positive electric charge so
repel each other. If they are
close enough the strong force
binds them together and the
nucleus is stable
4/7/2016
Physics 214 Spring 2017
17
Atoms
•Atoms are made up with a central nucleus of protons and neutrons surrounded by
a number of electrons equal to the number of protons.
• The notation we use is 2He4
•2 is the atomic number = number of protons (and electrons)
•4 is the mass number = number of protons + neutrons
•Note atomic mass is the actual mass of the nucleus in atomic mass units with
Carbon set to be 12 units and atomic mass in general is not an integer
•H2O gives the number of atoms required to make a molecule
• water = 2 Hydrogen plus 1 Oxygen
•In a nuclear reaction energy, charge, and atomic mass are conserved.
•Atoms can decay
•Atoms can join together to form new atoms or molecules
•Chemistry is determined by the electrons
4/7/2016
Physics 214 Spring 2017
18
3E-05 Cloud Chamber
As charged particles pass through a
gas electrons are knocked out of the
atom and the ions produced can act
as “seeds” for a super saturated
liquid to condense. This leaves a
visible track of bubbles of liquid.
Cosmic rays are bombarding the
earth continuously and radioactive
decays also produce charged
particles which can be observed in a
cloud chamber. If the chamber is in a
magnetic field the tracks are curved
The first observation of the positron
(anti particle of the electron) was
made in a cloud chamber
4/7/2016
Physics 214 Spring 2017
19
Isotopes
•For a given number of protons there is a nucleus that is most stable for a
particular number of neutrons.
•Isotopes are when for the same number of protons the number of neutrons
is different from the most stable configuration.
•Since the number of electrons is the same the chemical properties are
“identical” but the nucleus can be unstable.
•The larger the difference between ideal and the isotope the more unstable
the nucleus becomes.
•Nuclei have been made artificially that do not exist in nature.
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Radioactive decay
•The general rule is that if a lower energy configuration exists for the same set of particles then they will try to change into that configuration.
Each radioactive element has a characteristic half life, that is the time for half the sample to decay. Radioactive elements are clocks which tick at a specific rate.
The amount remaining after N half lives is ½ x ½ x ½ ……….. Half lives vary from billions of
years to a fraction of a second.
Those in the range of greater
than thousands of years are
used to date objects on earth
back to it’s formation 4.6
billion years ago
C14 5730 years I129 1.6 million
U238 4.47 billion
http://www.physics.purdue.edu/class/applets/phe/lawdecay.htm
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Types of nuclear decays
A proton can change into a neutron and emit a positron (anti particle of electron) 0
e
1
Atomic number decreases by 1 mass number is the same
A neutron can change into a proton and emit an electron
0
e
‐1
Atomic number increases by 1 mass number is the same
A nucleus can emit an alpha particle which is 2 neutrons and 2 protons (actually a helium nucleus)
4
He
2
Atomic number decreases by 2 mass number decreases by 4
Photons can be emitted
No change in Atomic number or mass number.
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What is the daughter?
•When an element decays it usually changes to a new element.
•The notation we use is 3Li7 where 3 is the number of protons, called the atomic number, and 7 is the number of protons plus neutrons, called the mass number. •Any decay or nuclear reaction conserves charge and mass number.
•
•
4
2He
+ 7N14 = 8O17 + 1H1 nuclear reaction
226 = Rn222 + He4
Ra
nuclear decay
88
86
2
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