4.1 The Atomic Models of Thomson and Rutherford
4.2 Rutherford Scattering
4.3 The Classic Atomic Model
4.4 The Bohr Model of the Hydrogen Atom
4.5 Successes and Failures of the Bohr Model
4.6 Characteristic X-Ray Spectra and Atomic Number
4.7 Atomic Excitation by Electrons
GROUP THEORY
CONSTRUCTING CHARACTER TABLE IS FOLLOWED BY 4 STEPS through orthogonality rule
STEP 1 : FIND THE NUMBER OF IRRs
Number of IRs = Number of classes.- In C3v
there is 3 classes so Г1,Г2 Г3
STEP 2: FIND OUT THE DIMENSIONS
Sum of the squares of the dimensions of IRRs = Order of the Group
We have to identify a set of 3 positive integers (I1 I2 I3 dimensions of IRRs) which satisfy this condition
The only value of I which satisfy this condition are 1,1,2 so that I12 = I22
SO 3 IRRs of C3v ,two are 1-D and one is 2-D
STEP 3 : FIND character of two 1-D IRRs
In every point group is 1-D IRR who characters are equal to 1 .this IRRs is called totally symmetric IRR
Thus we have
Which satisfy the rule sum of the square of the characters of all operations in any IRR is equal to the order of the group
FIND characters of another 1-D IRRsConditions
All the characters of this IRRs equal to +1 or -1
Also IRR must be Orthogonal to Г1
Г1 has six +1 as characters of the sym operations 1 for E ; 2 (1) for C3 ; 3 (1) for σv
The characters of Г2 is Orthogonal to Г1 so it has three +1 and three -1
For E in 1-D is +1 ; for 2 C3 in 1-D is +1 ; FOR 3 σV is -1
GROUP THEORY
CONSTRUCTING CHARACTER TABLE IS FOLLOWED BY 4 STEPS through orthogonality rule
STEP 1 : FIND THE NUMBER OF IRRs
Number of IRs = Number of classes.- In C3v
there is 3 classes so Г1,Г2 Г3
STEP 2: FIND OUT THE DIMENSIONS
Sum of the squares of the dimensions of IRRs = Order of the Group
We have to identify a set of 3 positive integers (I1 I2 I3 dimensions of IRRs) which satisfy this condition
The only value of I which satisfy this condition are 1,1,2 so that I12 = I22
SO 3 IRRs of C3v ,two are 1-D and one is 2-D
STEP 3 : FIND character of two 1-D IRRs
In every point group is 1-D IRR who characters are equal to 1 .this IRRs is called totally symmetric IRR
Thus we have
Which satisfy the rule sum of the square of the characters of all operations in any IRR is equal to the order of the group
FIND characters of another 1-D IRRsConditions
All the characters of this IRRs equal to +1 or -1
Also IRR must be Orthogonal to Г1
Г1 has six +1 as characters of the sym operations 1 for E ; 2 (1) for C3 ; 3 (1) for σv
The characters of Г2 is Orthogonal to Г1 so it has three +1 and three -1
For E in 1-D is +1 ; for 2 C3 in 1-D is +1 ; FOR 3 σV is -1
A brief introduction to lanthanide elements is given.
Order .ppts like this at <https://www.fiverr.com/anikmal/teamup-with-you-to-prepare-the-best-presentation>
Along with their physical and chemical properties are also shown. Helpful for quick understanding on lanthanide series.
Nature of coordination compounds, coordination sphere, coordination number, oxidation state of central metal atom, lewis acids, types of ligands, types of complex(cationic and anionic), Valance bond theory, crystal field theory, werner theory of coordination compounds, Nomenclature of coordination compounds.Eg and t2g ,CFSE, Degeneracy, Application of coordination compounds, Charge of the coordination sphere.
Spatial arrangements, inner and outer orbital complexes, low and high spin complex, spin pair and spin free complexes, isomerism, types of isomerism.
3.1 Discovery of the X Ray and the Electron
3.2 Determination of Electron Charge
3.3 Line Spectra
3.4 Quantization
3.5 Blackbody Radiation
3.6 Photoelectric Effect
3.7 X-Ray Production
3.8 Compton Effect
3.9 Pair Production and Annihilation
A brief introduction to lanthanide elements is given.
Order .ppts like this at <https://www.fiverr.com/anikmal/teamup-with-you-to-prepare-the-best-presentation>
Along with their physical and chemical properties are also shown. Helpful for quick understanding on lanthanide series.
Nature of coordination compounds, coordination sphere, coordination number, oxidation state of central metal atom, lewis acids, types of ligands, types of complex(cationic and anionic), Valance bond theory, crystal field theory, werner theory of coordination compounds, Nomenclature of coordination compounds.Eg and t2g ,CFSE, Degeneracy, Application of coordination compounds, Charge of the coordination sphere.
Spatial arrangements, inner and outer orbital complexes, low and high spin complex, spin pair and spin free complexes, isomerism, types of isomerism.
3.1 Discovery of the X Ray and the Electron
3.2 Determination of Electron Charge
3.3 Line Spectra
3.4 Quantization
3.5 Blackbody Radiation
3.6 Photoelectric Effect
3.7 X-Ray Production
3.8 Compton Effect
3.9 Pair Production and Annihilation
CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I
5.1 X-Ray Scattering (review and some more material)
5.2 De Broglie Waves
5.3 Electron Scattering / Transmission electron microscopy
5.4 Wave Motion
5.5 Waves or Particles?
5.6 Uncertainty Principle
5.7 Probability, Wave Functions, and the Copenhagen Interpretation
5.8 Particle in a Box
CHAPTER 10 Molecules and Solids
10.1 Molecular Bonding and Spectra
10.2 Stimulated Emission and Lasers
10.3 Structural Properties of Solids
10.4 Thermal and Magnetic Properties of Solids
10.5 Superconductivity
10.6 Applications of Superconductivity
7.1 Application of the Schrödinger Equation to the Hydrogen Atom
7.2 Solution of the Schrödinger Equation for Hydrogen
7.3 Quantum Numbers
7.4 Magnetic Effects on Atomic Spectra – The Normal Zeeman Effect
7.5 Intrinsic Spin
7.6 Energy Levels and Electron Probabilities
CHAPTER 6 Quantum Mechanics II
6.0 Partial differentials
6.1 The Schrödinger Wave Equation
6.2 Expectation Values
6.3 Infinite Square-Well Potential
6.4 Finite Square-Well Potential
6.5 Three-Dimensional Infinite-Potential Well
6.6 Simple Harmonic Oscillator
6.7 Barriers and Tunneling in some books an extra chapter due to its technical importance
A presentation on atomic structure and chemical bond. Here you can find the full details of atomic structure and 5 types of chemical bond. This is for the course of Inorganic Pharmacy, Course code is PHAR-1103. This can be also used for Biochemistry students and other.
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#be like boss
This would enable students to explain the emission spectrum of hydrogen using the Bohr model of the hydrogen atom; calculate the energy, wavelength, and frequencies involved in the electron transitions in the hydrogen atom; relate the emission spectra to common occurrences like fireworks and neon lights; and describe the Bohr model of the atom and the inadequacies of the Bohr model.
Quantum Mechanics: Electrons, Transistors, & LASERS. Paul H. Carr
Quantum Mechanics, QM, has enabled new technologies that impact our daily lives. Yet, there have been at least 14 different QM interpretations in the last century. “If you think you understand QM, you don’t,” said Richard Feynman. Our macroscopic language is inadequate to describe the wave-particle duality of microscopic QM particles. Mathematics works better. This talk illuminated the production of the play Copenhagen, in which German physicist Werner Heisenberg, who directed the German attempt to make an atom bomb, visited Niels Bohr in Denmark during WWII.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
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ESC Beyond Borders _From EU to You_ InfoPack general.pdf
CHAPTER 4Structure of the Atom
1. 4.1 The Atomic Models of Thomson and Rutherford
4.2 Rutherford Scattering
4.3 The Classic Atomic Model
4.4 The Bohr Model of the Hydrogen Atom
4.5 Successes and Failures of the Bohr Model
4.6 Characteristic X-Ray Spectra and Atomic Number
4.7 Atomic Excitation by Electrons
CHAPTER 4
Structure of the AtomStructure of the Atom
In the present first part of the paper the mechanism of the binding of
electrons by a positive nucleus is discussed in relation to Planck’s
theory. It will be shown that it is possible from the point of view taken to
account in a simple way for the law of the line spectrum of hydrogen.
- Niels Bohr, 1913
2. Structure of the Atom
Pieces of evidence that scientists had in 1900 to indicate that
the atom was not a fundamental unit:
1) There seemed to be too many kinds of atoms, each
belonging to a distinct chemical element.
2) Atoms and electromagnetic phenomena were intimately
related.
3) The problem of valence. Certain elements combine with
some elements but not with others, a characteristic that
hinted at an internal atomic structure.
4) The discoveries of radioactivity, of x rays, and of the
electron.
3. 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.
Thomson’s Atomic Model
4. Experiments of Geiger and Marsden
Rutherford, Geiger, and Marsden
conceived a new technique for
investigating the structure of matter
by scattering α particles from atoms.
Geiger showed that many α particles
were scattered from thin gold-leaf
targets at backward angles greater
than 90°.
5. Example 4.1
The maximum scattering angle corresponding to the maximum momentum
change.
Maximum momentum change of the α particle is
or
Determine θ by letting Δpmax be perpendicular to the direction of motion.
6. If an α particle were scattered by many electrons and N electrons
results in .
The number of atoms across the thin gold layer of 6 × 10−7
m:
Assume the distance between atoms is
and there are .
That gives .
Multiple Scattering from Electrons
7. even if the α particle scattered from all 79 electrons in
each atom of gold.
The experimental results were not consistent with Thomson’s
atomic model.
Rutherford proposed that an atom has a positively charged core
(nucleus) surrounded by the negative electrons.
Rutherford’s Atomic Model
8. Scattering experiments help us study matter too small to be
observed directly.
There is a relationship between the impact parameter b and the
scattering angle θ.
When b is small,
r gets small.
Coulomb force gets large.
θ can be large and the particle can be repelled backward.
4.2: Rutherford Scattering
9. Any particle inside the circle of area πb0
2
will be similarly scattered.
The cross section σ = πb2
is related to the probability for a particle being
scattered by a nucleus.
The fraction of incident particles scattered is
The number of scattering nuclei per unit area .
Rutherford Scattering
10. In actual experiment a detector is positioned from θ to θ + dθ that
corresponds to incident particles between b and b + db.
The number of particles scattered per unit area is
Rutherford Scattering Equation
11. 4.3: The Classical Atomic Model
Let’s consider atoms as a planetary model.
The force of attraction on the electron by the nucleus and Newton’s
2nd law give
where v is the tangential velocity of the electron.
The total energy is
12. The Planetary Model is Doomed
From classical E&M theory, an accelerated electric charge
radiates energy (electromagnetic radiation) which means total
energy must decrease. Radius r must decrease!!
Electron crashes into the nucleus!?
Physics had reached a turning point in 1900 with Planck’s
hypothesis of the quantum behavior of radiation.
13. 4.4: The Bohr Model of the Hydrogen Atom
Bohr’s general assumptions:
1) “Stationary states” (orbiting electrons do not radiate energy) exist
in atoms.
2) E = E1 − E2 = hf
3) Classical laws of physics do not apply to transitions between
stationary states.
4) The mean kinetic energy of the electron-nucleus system is
K = nhforb/2, where forb is the frequency of rotation.
14. Bohr Radius
The diameter of the hydrogen atom for stationary states is
Where the Bohr radius is given by
The smallest diameter of the hydrogen atom is
n = 1 gives its lowest energy state (called the “ground” state)
15. The Hydrogen Atom
The energies of the stationary states
where E0 = 13.6 eV.
Emission of light occurs when the atom is
in an excited state and decays to a lower
energy state (nu → nℓ).
where f is the frequency of a photon.
R∞ is the Rydberg constant.
16. Transitions in the Hydrogen Atom
Lyman series
The atom will remain in the
excited state for a short time
before emitting a photon and
returning to a lower stationary
state. All hydrogen atoms exist
in n = 1 (invisible).
Balmer series
When sunlight passes through
the atmosphere, hydrogen
atoms in water vapor absorb
the wavelengths (visible).
17. Fine Structure Constant
The electron’s velocity in the Bohr model:
On the ground state,
v1 = 2.2 × 106
m/s ~ less than 1% of the speed of light.
The ratio of v1 to c is the fine structure constant.
18. The Correspondence Principle
Need a principle to relate the new modern results with classical
ones.
Classical electrodynamics Bohr’s atomic model
Determine the properties
of radiation
Bohr’s correspondence
principle
In the limits where classical and quantum
theories should agree, the quantum
theory must reduce the classical result.
+
19. The Correspondence Principle
The frequency of the radiation emitted fclassical is equal to the orbital frequency
forb of the electron around the nucleus.
The frequency of the transition from n + 1 to n is
For large n,
Substitute E0:
20. 4.5: Successes and Failures of the Bohr Model
The electron and hydrogen nucleus actually revolved about their
mutual center of mass.
The electron mass is replaced by its reduced mass.
The Rydberg constant for infinite nuclear mass is replaced by R.
21. Limitations of the Bohr Model
The Bohr model was a great step of the new quantum theory,
but it had its limitations.
1) Works only to single-electron atoms.
2) Could not account for the intensities or the fine structure
of the spectral lines.
3) Could not explain the binding of atoms into molecules.
22. 4.6: Characteristic X-Ray Spectra and
Atomic Number
Shells have letter names:
K shell for n = 1
L shell for n = 2
The atom is most stable in its ground state.
When it occurs in a heavy atom, the radiation emitted is an x ray.
It has the energy E (x ray) = Eu − Eℓ.
An electron from higher shells will fill the inner-
shell vacancy at lower energy.
23. Atomic Number
L shell to K shell Kα x ray
M shell to K shell Kβ x ray
Atomic number Z = number of protons in the nucleus.
Moseley found a relationship between the frequencies of the
characteristic x ray and Z.
This holds for the Kα x ray.
24. Moseley’s Empirical Results
The x ray is produced from n = 2 to n = 1 transition.
In general, the K series of x ray wavelengths are
Moseley’s research clarified the importance of the electron shells
for all the elements, not just for hydrogen.
25. 4.7: Atomic Excitation by Electrons
Franck and Hertz studied the phenomenon of ionization.
Accelerating voltage is below 5 V.
electrons did not lose energy.
Accelerating voltage is above 5 V.
sudden drop in the current.
26. Atomic Excitation by Electrons
Ground state has E0 to be zero.
First excited state has E1.
The energy difference E1 − 0 = E1 is the excitation energy.
Hg has an excitation energy of
4.88 eV in the first excited state
No energy can be transferred to
Hg below 4.88 eV because not
enough energy is available to
excite an electron to the next
energy level
Above 4.88 eV, the current drops because scattered electrons no longer
reach the collector until the accelerating voltage reaches 9.8 eV and so on.