# of transitions from the upper energy level to the lower one per unit time caused by a spontaneous emission of radiation with the frequency ω = (E E

Save this PDF as:

Size: px
Start display at page:

Download "of transitions from the upper energy level to the lower one per unit time caused by a spontaneous emission of radiation with the frequency ω = (E E"

## Transcription

2 Planck constant. The number of transitions from the energy level E to the energy level E per unit time caused by a stimulated emission of radiation may be written in the form where i = B B =σ π B hω, () 3 B = hω / ( π c )(exp( hω / kt) ) () is a blackbody emissivity (Planck s function), σ is the stimulated emission cross-section, T is the temperature, k is the Boltzmann constant, c is the speed of light, and width. is the line The number of transitions from the lower level to the upper one per unit time may be written in the form where σ is the absorption cross-section. σ π B. (3) ω = BB = h Here A, B and B are the coefficients introduced by Einstein [6], the coefficients B and B being modified to account for the line width. We denote as and the number of atoms occupying the energy levels E and E, respectively. The levels E and E are suggested for simplicity to be non-degenerated. In the equilibrium state the full number of transitions from the lower level to the upper one is equal to the number of reverse transitions : = B B = = ( A + B B ). (4) The line width is suggested to be equal to the natural line width [7]: = A + B B. (5) state. It is assumed that the lower level has a zero energy width, i.e. this level is a ground It follows from the last equation that = A / ( B B ). (6) Substituting this expression in the equation (4), we obtain / = B B = σ π B h ω. (7)

3 In the limit of high temperatures T, corresponding to the range of frequencies hω <kt, the function B ( T) is given by the Rayleigh-Jeans formula B = kt / c, (8) where is the frequency of radiation, = ω / π. Since B when T, it follows from the equation (6) that the coefficient B is depending on the temperature T in such a manner that when T. It is clear that. The ratio of frequencies of transitions caused by spontaneous and induced emission of radiation is given by the expression B B < B B s / i = A /( B B ) = ( B B)/( B B). (9) This ratio is approaching zero when T, since B B. It means that in the range of frequencies hω <kt thermal radiation is produced by the stimulated emission, whereas the contribution of a spontaneous emission may be neglected. the ratio It follows from equations (7) and (8) that in the Rayleigh-Jeans range of frequencies is given by the formula / / =σ ωkt/(πh c ). (0) An analysis of observational data on thermal radio emission from various astrophysical objects suggests that the absorption cross-section does not depend on a wavelength of radiation and has an order of magnitude of an atomic cross-section, 5 σ 0 cm [,5]. Only this assumption is consistent with the observed spectra of thermal radio emission from major planets, the spectral indices of radio emission from galactic and extragalactic sources, and the wavelength dependence of radio source size. form If the absorption cross-section is constant then the energy distribution of atoms has a / = const( E E ) kt. () For all real values of the temperature and wavelength of radiation the ratio () is much smaller than unit. For example, at λ=m the ratio () is less than, if T<0 8 K. It implies that, where is the total number of atoms. This relation was used in [5] to obtain the condition for emission. There are no reasons to expect that the Boltzmann distribution is still valid for an ensemble of atoms interacting with thermal radiation. form From the relation B B κ we obtain the stimulated emission cross-section in the 3

4 σ h ω /( πb ) = λl T /( π), () where λ is the wavelength, and l = πh c / ( kt ) T. Thus, Einstein s relation B B =, equivalent to σ = σ, is not valid in the Rayleigh-Jeans region. Consider now the Wien region hω >kt. There are strong theoretical and observational indications of the stimulated character of thermal blackbody radiation in the whole range of spectrum [8]. First, the spectral energy density of thermal blackbody radiation is described by a single Planck s function at all frequencies. Second, there are clear observational indications of the existence of thermal harmonics in stellar spectra and of laser type sources. The latter are connected with the induced origin of thermal radiation, similarly to well known maser sources. In particular, a possible non-saturated X-ray laser source emitting in the Fe J [9]. K α line at 6.49 kev was recently discovered in the radio-loud quasar MG Assuming the stimulated origin of thermal blackbody radiation, i.e. < s i, from Eq.(8) one can obtain the relation BB = σ πb /( hω), and then the stimulated emission cross-section in the form the ratio σ ( λ / π) exp( hω / kt ). (3) The absorption cross-section is likely to be constant in the whole range of spectrum, so, according to Eq.(6), is given by the formula / / ( σ ω / πc ) exp( h ω / kt), (4) which is somewhat similar to the Boltzmann law. The exact formula for the ratio can be obtained from Eq.(6) : / / =σ ω / ( πc )(exp( h ω / kt) ). (5) The function (5) has a maximum at ω =.6kT. It means that, in the field of thermal blackbody radiation, the excited levels with E E kt are the most populated. 5 umerically, ( / ) = T, so the ratio / is less than, if only T<3*0 max 7 K. For the temperatures T>4*0 7 K the population of the levels corresponding to the maximum of the function (5) is inverse. It suggests that laser type sources are more easily realized in X-ray and gamma-ray range of spectrum than in the optical region. The well known example is a possible gamma-laser in the Galactic Center emitting in the line 0.5 MeV [0]. The author is grateful to A.V.Postnikov for useful discussions. 4

5 [].M.agar, A.S.Wilson, and H.Falcke. Astrophys. J., 559, L87 (00). J.S.Ulvestad, and L.C.Ho. Astrophys. J., 56, L33 (00). [] F.V.Prigara, astro-ph/00399 (00). [3] S.R.Pottasch, Planetary ebulae (D.Reidel, Dordrecht, 984). [4].Siodmiak, and R.Tylenda. Astron. Astrophys., 373, 03 (00). [5] F.V.Prigara, astro-ph/00483 (00). [6] J.R.Singer, Masers (Wiley, ew York, 959). M.Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, ew York, 967). [7] L.D.Landau, and E.M.Lifshitz, Quantum Mechanics, on-relativistic Theory (Addison- Wesley, Reading, MA, 958). V.B.Berestetskii, E.M.Lifshitz, and L.P.Pitaevskii, Quantum Electrodynamics (auka, Moscow, 989). [8] F.V.Prigara, astro-ph/007 (00). [9] G.Chartas et al., astro-ph/0 (00). [0] R.E.Lingenfelter, and R.Ramaty, in AIP Proc. 83: The Galactic Center, edited by G.Riegler, and R.Blandford (AIP, ew York, 98). 5

### Rate Equations and Detailed Balance

Rate Equations and Detailed Balance Initial question: Last time we mentioned astrophysical masers. Why can they exist spontaneously? Could there be astrophysical lasers, i.e., ones that emit in the optical?

Blackbody radiation derivation of Planck s radiation low 1 Classical theories of Lorentz and Debye: Lorentz (oscillator model): Electrons and ions of matter were treated as a simple harmonic oscillators

### COLLEGE PHYSICS. Chapter 29 INTRODUCTION TO QUANTUM PHYSICS

COLLEGE PHYSICS Chapter 29 INTRODUCTION TO QUANTUM PHYSICS Quantization: Planck s Hypothesis An ideal blackbody absorbs all incoming radiation and re-emits it in a spectrum that depends only on temperature.

### - the total energy of the system is found by summing up (integrating) over all particles n(ε) at different energies ε

Average Particle Energy in an Ideal Gas - the total energy of the system is found by summing up (integrating) over all particles n(ε) at different energies ε - with the integral - we find - note: - the

### Molecular Spectroscopy: Applications

Chapter 6. Molecular Spectroscopy: Applications Notes: Most of the material presented in this chapter is adapted from Stahler and Palla (24), Chap. 6, and Appendices B and C. 6.1 Carbon Monoxyde (CO) Since

### The Nature of Electromagnetic Radiation

II The Nature of Electromagnetic Radiation The Sun s energy has traveled across space as electromagnetic radiation, and that is the form in which it arrives on Earth. It is this radiation that determines

### - thus, the total number of atoms per second that absorb a photon is

Stimulated Emission of Radiation - stimulated emission is referring to the emission of radiation (a photon) from one quantum system at its transition frequency induced by the presence of other photons

### The Early History of Quantum Mechanics

Chapter 2 The Early History of Quantum Mechanics In the early years of the twentieth century, Max Planck, Albert Einstein, Louis de Broglie, Neils Bohr, Werner Heisenberg, Erwin Schrödinger, Max Born,

### The Experimental Basis of Quantum Theory

The Experimental Basis of Quantum Theory Preliminary Remarks New theories do not appear from nowhere, they are usually based on (unexplained) experimental results. People have to be ready for it, e.g.

Blackbody Radiation References 1) R.A. Serway, R.J. Beichner: Physics for Scientists and Engineers with Modern Physics, 5 th Edition, Vol. 2, Ch.40, Saunders College Publishing (A Division of Harcourt

### Lecture 1: Microscopic Theory of Radiation

253a: QFT Fall 2009 Matthew Schwartz Lecture : Microscopic Theory of Radiation Blackbody Radiation Quantum Mechanics began on October 9, 900 with Max Planck s explanation of the blackbody radiation spectrum.

### From lowest energy to highest energy, which of the following correctly orders the different categories of electromagnetic radiation?

From lowest energy to highest energy, which of the following correctly orders the different categories of electromagnetic radiation? From lowest energy to highest energy, which of the following correctly

### The Role of Electric Polarization in Nonlinear optics

The Role of Electric Polarization in Nonlinear optics Sumith Doluweera Department of Physics University of Cincinnati Cincinnati, Ohio 45221 Abstract Nonlinear optics became a very active field of research

### Concept 2. A. Description of light-matter interaction B. Quantitatities in spectroscopy

Concept 2 A. Description of light-matter interaction B. Quantitatities in spectroscopy Dipole approximation Rabi oscillations Einstein kinetics in two-level system B. Absorption: quantitative description

### Solar Energy. Outline. Solar radiation. What is light?-- Electromagnetic Radiation. Light - Electromagnetic wave spectrum. Electromagnetic Radiation

Outline MAE 493R/593V- Renewable Energy Devices Solar Energy Electromagnetic wave Solar spectrum Solar global radiation Solar thermal energy Solar thermal collectors Solar thermal power plants Photovoltaics

### Spectroscopic Notation

Spectroscopic Notation Most of the information we have about the universe comes to us via emission lines. However, before we can begin to understand how emission lines are formed and what they tell us,

Activity 17 Electromagnetic Radiation Why? Electromagnetic radiation, which also is called light, is an amazing phenomenon. It carries energy and has characteristics of both particles and waves. We can

### We consider a hydrogen atom in the ground state in the uniform electric field

Lecture 13 Page 1 Lectures 13-14 Hydrogen atom in electric field. Quadratic Stark effect. Atomic polarizability. Emission and Absorption of Electromagnetic Radiation by Atoms Transition probabilities and

### 5.111 Principles of Chemical Science

MIT OpenCourseWare http://ocw.mit.edu 5.111 Principles of Chemical Science Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.111 Lecture Summary

### Ay 122 - Fall 2004 Electromagnetic Radiation And Its Interactions With Matter

Ay 122 - Fall 2004 Electromagnetic Radiation And Its Interactions With Matter (This version has many of the figures missing, in order to keep the pdf file reasonably small) Radiation Processes: An Overview

### Energy conservation. = h(ν- ν 0 ) Recombination: electron gives up energy = ½ mv f. Net energy that goes into heating: ½ mv i.

Thermal Equilibrium Energy conservation equation Heating by photoionization Cooling by recombination Cooling by brehmsstralung Cooling by collisionally excited lines Collisional de-excitation Detailed

### Blackbody radiation. Main Laws. Brightness temperature. 1. Concepts of a blackbody and thermodynamical equilibrium.

Lecture 4 lackbody radiation. Main Laws. rightness temperature. Objectives: 1. Concepts of a blackbody, thermodynamical equilibrium, and local thermodynamical equilibrium.. Main laws: lackbody emission:

### Astronomy 421. Lecture 8: Stellar Spectra

Astronomy 421 Lecture 8: Stellar Spectra 1 Key concepts: Stellar Spectra The Maxwell-Boltzmann Distribution The Boltzmann Equation The Saha Equation 2 UVBRI system Filter name Effective wavelength (nm)

### THE MEANING OF THE FINE STRUCTURE CONSTANT

THE MEANING OF THE FINE STRUCTURE CONSTANT Robert L. Oldershaw Amherst College Amherst, MA 01002 USA rloldershaw@amherst.edu Abstract: A possible explanation is offered for the longstanding mystery surrounding

### 2. Molecular stucture/basic

2. Molecular stucture/basic spectroscopy The electromagnetic spectrum Spectral region for atomic and molecular spectroscopy E. Hecht (2nd Ed.) Optics, Addison-Wesley Publishing Company,1987 Spectral regions

### History of the Atomic Model. Bohr s Model of the Atom

Bohr s Model of the Atom Niels Bohr (93) was the first to propose that the periodicity in the properties of the elements might be explained by the electronic structure of the atom Democritus (400 B.C.)

### THE CURRENT-VOLTAGE CHARACTERISTICS OF AN LED AND A MEASUREMENT OF PLANCK S CONSTANT Physics 258/259

DSH 2004 THE CURRENT-VOLTAGE CHARACTERISTICS OF AN LED AND A MEASUREMENT OF PLANCK S CONSTANT Physics 258/259 I. INTRODUCTION Max Planck (1858-1947) was an early pioneer in the field of quantum physics.

### Radiation Bookkeeping: a guide to astronomical molecular spectroscopy and radiative transfer problems with an emphasis

Radiation Bookkeeping: a guide to astronomical molecular spectroscopy and radiative transfer problems with an emphasis on RADEX Huib Jan van Langevelde & Floris van der Tak Original HJvL (Leiden 1994),

### PRACTICE EXAM IV P202 SPRING 2004

PRACTICE EXAM IV P202 SPRING 2004 1. In two separate double slit experiments, an interference pattern is observed on a screen. In the first experiment, violet light (λ = 754 nm) is used and a second-order

### Widths of spectral lines

Widths of spectral lines Real spectral lines are broadened because: Energy levels are not infinitely sharp. Atoms are moving relative to observer. 3 mechanisms determine profile φ(ν) Quantum mechanical

### Radiation Transfer in Environmental Science

Radiation Transfer in Environmental Science with emphasis on aquatic and vegetation canopy media Autumn 2008 Prof. Emmanuel Boss, Dr. Eyal Rotenberg Introduction Radiation in Environmental sciences Most

### CHAPTER 4 Structure of the Atom

CHAPTER 4 Structure of the Atom 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

### Name Date Class ELECTRONS IN ATOMS. Standard Curriculum Core content Extension topics

13 ELECTRONS IN ATOMS Conceptual Curriculum Concrete concepts More abstract concepts or math/problem-solving Standard Curriculum Core content Extension topics Honors Curriculum Core honors content Options

### Review of the isotope effect in the hydrogen spectrum

Review of the isotope effect in the hydrogen spectrum 1 Balmer and Rydberg Formulas By the middle of the 19th century it was well established that atoms emitted light at discrete wavelengths. This is in

### 8.1 Radio Emission from Solar System objects

8.1 Radio Emission from Solar System objects 8.1.1 Moon and Terrestrial planets At visible wavelengths all the emission seen from these objects is due to light reflected from the sun. However at radio

### Chemistry 102 Summary June 24 th. Properties of Light

Chemistry 102 Summary June 24 th Properties of Light - Energy travels through space in the form of electromagnetic radiation (EMR). - Examples of types of EMR: radio waves, x-rays, microwaves, visible

### How Matter Emits Light: 1. the Blackbody Radiation

How Matter Emits Light: 1. the Blackbody Radiation Announcements n Quiz # 3 will take place on Thursday, October 20 th ; more infos in the link `quizzes of the website: Please, remember to bring a pencil.

### nm cm meters VISIBLE UVB UVA Near IR 200 300 400 500 600 700 800 900 nm

Unit 5 Chapter 13 Electrons in the Atom Electrons in the Atom (Chapter 13) & The Periodic Table/Trends (Chapter 14) Niels Bohr s Model Recall the Evolution of the Atom He had a question: Why don t the

### Principle of Thermal Imaging

Section 8 All materials, which are above 0 degrees Kelvin (-273 degrees C), emit infrared energy. The infrared energy emitted from the measured object is converted into an electrical signal by the imaging

### Basic Nuclear Concepts

Section 7: In this section, we present a basic description of atomic nuclei, the stored energy contained within them, their occurrence and stability Basic Nuclear Concepts EARLY DISCOVERIES [see also Section

### Raman Scattering Theory David W. Hahn Department of Mechanical and Aerospace Engineering University of Florida (dwhahn@ufl.edu)

Introduction Raman Scattering Theory David W. Hahn Department of Mechanical and Aerospace Engineering University of Florida (dwhahn@ufl.edu) The scattering of light may be thought of as the redirection

### The use of infrared radiation in measurement and non-destructive testing.

The use of infrared radiation in measurement and non-destructive testing. M. Hain, J. Bartl, V. Jacko Institute of Measurement Science Slovak Academy of Sciences, Bratislava, Slovakia e-mail: Miroslav.Hain@savba.sk

### Today. Kirchoff s Laws. Emission and Absorption. Stellar Spectra & Composition

Today Kirchoff s Laws Emission and Absorption Stellar Spectra & Composition 1 Three basic types of spectra Continuous Spectrum Intensity Emission Line Spectrum Absorption Line Spectrum Wavelength Spectra

### Welcome to Quantum Mechanics

Welcome to Quantum Mechanics The most important fundamental laws and facts have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence

### Chapter 5. Second Edition ( 2001 McGraw-Hill) 5.6 Doped GaAs. Solution

Chapter 5 5.6 Doped GaAs Consider the GaAs crystal at 300 K. a. Calculate the intrinsic conductivity and resistivity. Second Edition ( 2001 McGraw-Hill) b. In a sample containing only 10 15 cm -3 ionized

### A Theory for the Cosmological Constant and its Explanation of the Gravitational Constant

A Theory for the Cosmological Constant and its Explanation of the Gravitational Constant H.M.Mok Radiation Health Unit, 3/F., Saiwanho Health Centre, Hong Kong SAR Govt, 8 Tai Hong St., Saiwanho, Hong

### PTYS/ASTR 206 Section 2 Spring 2007 Homework #2 (Page 1/5) NAME: KEY

PTYS/ASTR 206 Section 2 Spring 2007 Homework #2 (Page 1/5) NAME: KEY Due Date: start of class 2/6/2007 5 pts extra credit if turned in before 9:00AM (early!) (To get the extra credit, the assignment must

### Main properties of atoms and nucleus

Main properties of atoms and nucleus. Atom Structure.... Structure of Nuclei... 3. Definition of Isotopes... 4. Energy Characteristics of Nuclei... 5. Laws of Radioactive Nuclei Transformation... 3. Atom

Journal of Theoretics Journal Home Page MASS BOOM VERSUS BIG BANG: THE ROLE OF PLANCK S CONSTANT by Antonio Alfonso-Faus E.U.I.T. Aeronáutica Plaza Cardenal Cisneros s/n 8040 Madrid, SPAIN e-mail: aalfonso@euita.upm.es

### Emission Temperature of Planets

Emission Temperature of Planets The emission temperature of a planet, T e, is the temperature with which it needs to emit in order to achieve energy balance (assuming the average temperature is not decreasing

### Lecture 3: Optical Properties of Bulk and Nano. 5 nm

Lecture 3: Optical Properties of Bulk and Nano 5 nm The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model) 0 e - n( ) n' n '' n ' = 1 + Nucleus

### 6.1 Electromagnetic Waves

6.1 Electromagnetic Waves electromagnetic radiation can be described as a harmonic wave in either time or distance waves are characterized by their period, frequency, wavelength and wave number Planck's

Investigating electromagnetic radiation Announcements: First midterm is 7:30pm on 2/17/09 Problem solving sessions M3-5 and T3-4,5-6. Homework due at 12:50pm on Wednesday. We are covering Chapter 4 this

### 6-2. A quantum system has the following energy level diagram. Notice that the temperature is indicated

Chapter 6 Concept Tests 6-1. In a gas of hydrogen atoms at room temperature, what is the ratio of atoms in the 1 st excited energy state (n=2) to atoms in the ground state(n=1). (Actually H forms H 2 molecules,

### Light is a type of electromagnetic (EM) radiation, and light has energy. Many kinds of light exist. Ultraviolet (UV) light causes skin to tan or burn.

Light and radiation Light is a type of electromagnetic (EM) radiation, and light has energy. Many kinds of light exist. Ultraviolet (UV) light causes skin to tan or burn. Infrared (IR) light is used in

### AMPLIFICATION OF ATOMIC WAVES BY STIMULATED EMISSION OF ATOMS. Christian J. Borde

AMPLIFIATION OF ATOMI WAVES BY STIMULATED EMISSION OF ATOMS hristian J. Borde Laboratoire de Physique des Lasers, NRS/URA 8, Universite Paris-Nord, Villetaneuse, France. INTRODUTION: The recent development

### D.S. Boyd School of Earth Sciences and Geography, Kingston University, U.K.

PHYSICAL BASIS OF REMOTE SENSING D.S. Boyd School of Earth Sciences and Geography, Kingston University, U.K. Keywords: Remote sensing, electromagnetic radiation, wavelengths, target, atmosphere, sensor,

### Experimental Determination of Planck s Constant

Experimental Determination of Planck s Constant Ryan Eagan The Pennsylvania State University University Park, Pennsylvania 16802 Email: ree5047@psu.edu July 25, 2011 Abstract Experimental determination

### Further Modification of JB s criticism of the FM Paper in E & E

Further Modification of JB s criticism of the FM Paper in E & E This is a shortened and updated version of my criticism of FM s paper [THE STABLE STATIONARY VALUE OF THE EARTH S GLOBAL AVERAGE ATMOSPHERIC

### Lecture 2: Radiation/Heat in the atmosphere

Lecture 2: Radiation/Heat in the atmosphere TEMPERATURE is a measure of the internal heat energy of a substance. The molecules that make up all matter are in constant motion. By internal heat energy, we

### THE DOUBLE SLIT INTERFERENCE OF THE PHOTON-SOLITONS

Bulg. J. Phys. 29 (2002 97 108 THE DOUBLE SLIT INTERFERENCE OF THE PHOTON-SOLITONS P. KAMENOV, B. SLAVOV Faculty of Physics, University of Sofia, 1126 Sofia, Bulgaria Abstract. It is shown that a solitary

### Astro Lecture 15. Light and Matter (Cont d) 23/02/09 Habbal_Astro Lecture 15

Astro110-01 Lecture 15 Light and Matter (Cont d) 1 What have we learned? Three basic types of spectra continuous spectrum emission line spectrum absorption line spectrum Light tells us what things are

### Our Galaxy, the Milky Way

Our Galaxy, the Milky Way In the night sky, the Milky Way appears as a faint band of light. Dusty gas clouds obscure our view because they absorb visible light. This is the interstellar medium that makes

### Today. Electromagnetic Radiation. Light & beyond. Thermal Radiation. Wien & Stefan-Boltzmann Laws

Today Electromagnetic Radiation Light & beyond Thermal Radiation Wien & Stefan-Boltzmann Laws 1 Electromagnetic Radiation aka Light Properties of Light are simultaneously wave-like AND particle-like Sometimes

### 3. Electronic Spectroscopy of Molecules I - Absorption Spectroscopy

3. Electronic Spectroscopy of Molecules I - Absorption Spectroscopy 3.1. Vibrational coarse structure of electronic spectra. The Born Oppenheimer Approximation introduced in the last chapter can be extended

### Chapter 9 Statistical Mechanics

Chapter 9 Statistical Mechanics 9. Statistical Distributions This first section is just an overview. Statistical mechanics deals with the behavior of systems of a large number of particles. It does this

### Introduction to Spectroscopy.

Introduction to Spectroscopy. ARCHIMEJ TECHNOLOGY The SPECTROSCOPY 2.0 Company To understand what the core of our project is about, you need to grasp some basic notions of optical spectroscopy. This lesson

### Simple Laser-Induced Fluorescence Setup to Explore Molecular Spectroscopy. Abstract

Simple Laser-Induced Fluorescence Setup to Explore Molecular Spectroscopy S. B. Bayram and M.D. Freamat Miami University, Department of Physics, Oxford, OH 45056 (Dated: July 23, 2012) Abstract We will

### The Physics of Energy sources Stellar fusion

The Physics of Energy sources Stellar fusion B. Maffei Bruno.maffei@manchester.ac.uk Stellar Fusion Introduction! Many sources of renewable energy rely on the Sun! From radiation directly Solar cells Solar

### Group Theory and Chemistry

Group Theory and Chemistry Outline: Raman and infra-red spectroscopy Symmetry operations Point Groups and Schoenflies symbols Function space and matrix representation Reducible and irreducible representation

### Solutions for the Homework 7

Statistical Physics: November 7, 212 Solutions for the Homework 7 Problem 7.39: Change variables in equation 7.83 to λ = /ǫ, and thus derive a formula for the photon spectrum as a function of wavelength.

### Molecular Spectroscopy

Molecular Spectroscopy 1 I. OPTICAL TRANSITIONS IN MOLECULES: INTRODUCTION The origin of spectral lines in molecular spectroscopy is the absorption, emission, and scattering of a proton when the energy

### Phys 234H Practice Final Exam (Note: this practice exam contains more questions than will the final, which will have 25 multiple-choice questions.

Phys 234H Practice Final Exam (Note: this practice exam contains more questions than will the final, which will have 25 multiple-choice questions. MULTIPLE CHOICE. Choose the one alternative that best

### People s Physics book

The Big Idea Quantum Mechanics, discovered early in the 20th century, completely shook the way physicists think. Quantum Mechanics is the description of how the universe works on the very small scale.

### (b) Explain how the principle of conservation of momentum is a natural consequence of Newton s laws of motion. [3]

Physics A Unit: G484: The Newtonian World 1(a) State Newton s second law of motion. The resultant force on an object is proportional to the rate of change of momentum of the object In part (a) the candidate

### Chapter 18: The Structure of the Atom

Chapter 18: The Structure of the Atom 1. For most elements, an atom has A. no neutrons in the nucleus. B. more protons than electrons. C. less neutrons than electrons. D. just as many electrons as protons.

### Nuclear Magnetic Resonance (NMR) Spectroscopy cont... Recommended Reading:

Applied Spectroscopy Nuclear Magnetic Resonance (NMR) Spectroscopy cont... Recommended Reading: Banwell and McCash Chapter 7 Skoog, Holler Nieman Chapter 19 Atkins, Chapter 18 Relaxation processes We need

### arxiv:astro-ph/0110525 v4 4 Feb 2002

arxiv:astro-ph/0110525 v4 4 Feb 2002 The difficult discrimination of Impulse Stimulated Raman Scattering redshift against Doppler redshift J. Moret-Bailly February 4, 2002 Pacs 42.65.Dr Stimulated Raman

Nuclear Physics and Radioactivity 1. The number of electrons in an atom of atomic number Z and mass number A is 1) A 2) Z 3) A+Z 4) A-Z 2. The repulsive force between the positively charged protons does

### Absorption and Addition of Opacities

Absorption and Addition of Opacities Initial questions: Why does the spectrum of the Sun show dark lines? Are there circumstances in which the spectrum of something should be a featureless continuum? What

### HW to be handed in: Extra (do not hand in):

CHEM344 HW#5 Due: Fri, Feb 28@2pm BEFORE CLASS! HW to be handed in: Atkins(9 th ed.) Chapter 7: Exercises: 7.6(b), 7.8(b), 7.10(b), 7.13(b) (moved to HW6), 7.15(b), 7.17(b), Problems: 7.2, 7.6, 7.10, 7.18,

### Concerning an Heuristic Point of View Toward the Emission and Transformation of Light

A. Einstein, Ann. Phys. 17, 132 1905 Concerning an Heuristic Point of View Toward the Emission and Transformation of Light A. Einstein Bern, 17 March 1905 (Received March 18, 1905) Translation into English

### 1. Basics of LASER Physics

1. Basics of LASER Physics Dr. Sebastian Domsch (Dipl.-Phys.) Computer Assisted Clinical Medicine Medical Faculty Mannheim Heidelberg University Theodor-Kutzer-Ufer 1-3 D-68167 Mannheim, Germany sebastian.domsch@medma.uni-heidelberg.de

### Chapter 15. The Chandrasekhar Limit, Iron-56 and Core Collapse Supernovae

Chapter 15. The Chandrasekhar Limit, Iron-56 and Core Collapse Supernovae 1. The Equation of State: Pressure of an Ideal Gas Before discussing results of stellar structure and stellar evolution models

### Chapter 9. Gamma Decay

Chapter 9 Gamma Decay As we have seen γ-decay is often observed in conjunction with α- or β-decay when the daughter nucleus is formed in an excited state and then makes one or more transitions to its ground

### Calculation of Blackbody Radiance. What is a Blackbody?

Calculation of Blackbody Radiance What is a Blackbody? A blackbody is a hypothetical object that absorbs all incident electromagnetic radiation while maintaining thermal equilibrium. No light is reflected

### PUMPED Nd:YAG LASER. Last Revision: August 21, 2007

PUMPED Nd:YAG LASER Last Revision: August 21, 2007 QUESTION TO BE INVESTIGATED: How can an efficient atomic transition laser be constructed and characterized? INTRODUCTION: This lab exercise will allow

### Cosmic Dust in an Expanding Universe?

Planck energy - E - ev Cosmic Dust in an Expanding Universe? QED Radiations, Discovery Bay, Hong Kong, China nanoqed@gmail.com Copyright 2016 Horizon Research Publishing All rights reserved. Abstract Dust

Lecture 8: Radiation Spectrum The information contained in the light we receive is unaffected by distance The information remains intact so long as the light doesn t run into something along the way Since

### EQUATION OF STATE. e (E µ)/kt ± 1 h 3 dp,

EQUATION OF STATE Consider elementary cell in a phase space with a volume x y z p x p y p z = h 3, (st.1) where h = 6.63 1 7 erg s is the Planck constant, x y z is volume in ordinary space measured in

### Introduction to the QuanX

Introduction to the QuanX Energy-Dispersive X-ray Fluorescence Spectrometry Theory Introduction Overview: Theory Presentation EDS overview Basic overview History of X-ray spectrometry Atomic Structure

### 5. The Nature of Light. Does Light Travel Infinitely Fast? EMR Travels At Finite Speed. EMR: Electric & Magnetic Waves

5. The Nature of Light Light travels in vacuum at 3.0. 10 8 m/s Light is one form of electromagnetic radiation Continuous radiation: Based on temperature Wien s Law & the Stefan-Boltzmann Law Light has

### The coherence length of black-body radiation

Eur. J. Phys. 19 (1998) 245 249. Printed in the UK PII: S143-87(98)86653-1 The coherence length of black-body radiation Axel Donges Fachhochschule und Berufskollegs NTA Prof. Dr Grübler, Seidenstrasse

### Atomic Theory and the Periodic Table

Atomic Theory and the Periodic Table Petrucci, Harwood and Herring: Chapters 9 and 10 Aims: To examine the Quantum Theory, to understand the electronic structure of elements, To explain the periodic table

### The Greenhouse Effect

The Greenhouse Effect The Greenhouse Effect Solar and terrestrial radiation occupy different ranges of the electromagnetic spectrum, that we have been referring to as shortwave and longwave. The Greenhouse

### Chapter 7. Quantum Theory and Atomic Structure

Chapter 7. Quantum Theory and Atomic Structure A problem arose in Rutherford s nuclear model. A nucleus and electron attract each other; to remain apart the electron must move. The energy of the electron

### 8 Radiative Cooling and Heating

8 Radiative Cooling and Heating Reading: Katz et al. 1996, ApJ Supp, 105, 19, section 3 Thoul & Weinberg, 1995, ApJ, 442, 480 Optional reading: Thoul & Weinberg, 1996, ApJ, 465, 608 Weinberg et al., 1997,