# DO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 DO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS Quantum Mechanics or wave mechanics is the best mathematical theory used today to describe and predict the behaviour of particles and waves. Understanding and applying Quantum Mechanics is crucial in the development of most modern technologies including lasers, semiconductor devices used in mobile phones, display devices, medical imaging machines, etc, etc. For electrons and other particles in atomic and nuclear systems, the Newtonian laws of motion no longer apply and one must use Quantum Mechanics. When a particle is bound such as an electron in an atom, the electron is described by a wave and the concept of particle and trajectory of the particle have no meaning. The laws of Quantum Mechanics were developed in the short period from People such as Planck, Einstein, debroglie, Schrodinger, Heisenberg and Pauli all made significant contributions to the development of this strange theory which has startling consequences. Among physicists, it was a period of great excitement, many of the unexplained facts of physics and chemistry know for more than 5 years seemed suddenly to tumble into place. If electrons do have a wave nature as suggested by debroglie, it should be possible to represent them by a suitable mathematical function known as a wavefunction. In water waves, the physical quantity that varies periodically is the height of the water surface ( h). In sound waves, the variable quantity is the pressure in the medium the waves travel through ( p). In light waves, the variable quantities are the electric and magnetic fields ( E or B). What is it that varies in the case of matter waves? The quantity whose variation constitutes the matter wave of a moving object is known as its wavefunction (psi). Surprisingly, the wavefunction for a matter wave can t be related to anything physical, it is only a mathematical concept. However, when mathematical operations are carried out on the wavefunction, predictions can be made for the probability of locating an electron and the total energy of the electron. The value of the square of the wavefunction is proportional to probability of finding the particle at a certain time and location. For this reason, the quantity is called the probability density function of the particle. A large value of signifies a large probability of finding the particle at a specified time and location and a low value of implies that it is unlikely to find the particle at the specified time and location. Thus, matter waves may be regarded as waves of probability t8_quantum 1

2 A group or packet of matter waves is associated with every moving object. The packet travels with the same velocity as the object does. The waves in the packet have the average debroglie wavelength h/ mv. Even though we can t visualise what is meant by and so can t form a mental image of matter waves, the amazing agreement between measurements and the predictions of Quantum Mechanics means that we have to accept the bizarre concepts of Quantum Mechanics. In ordinary mechanics, a particle can have any energy including zero. But when we describe the particle behaviour using Quantum Mechanics, we find that the particle s energy is always greater than zero and for a bound particle (e.g. electron in an atom) the particle can only have certain discrete values for its energy. Quantum (wave) Mechanics naturally leads to the concept of quantisation. Quantum Mechanics tells us that we can now longer predict exactly where a particle like an electron will travel. For example, when electrons are reflected off a metal crystal a diffraction pattern is formed. We only know the probability of where the electron would be observed. We can t determine the trajectory for the electron. This idea leads to the Uncertainty Principle which is an important consequence of Quantum Mechanics. Heisenberg Uncertainty Principle When we consider the problem of actually measuring the position of a particle, we realise that it presents difficulties. First, there is the difficulty of designing instruments fine enough to measure small structures, such atoms and molecules. There is also the problem of the instrument disturbing the system (as when a large thermometer is used to measure the temperature of a small quantity of liquid). We might expect to correct for such effects, but deeper consideration shows that this is not such a simple matter. For example, to locate the position of an electron in one of its orbits we must look at it - that is, receive a signal from it. If it emits the signal itself, it must change orbit. If it reflects a photon, then the photon must collide with it, thus changing its position. No experiment that we can devise will enable us to look at the electron without some change occurring to the electron. In 197, Werner Heisenberg proposed and demonstrated that we can t know in principle the absolutely precise values that will completely describe a physical system. His uncertainty principle states that attempts to know simultaneously the complementary facts required to describe a system are doomed. Consider a particle travelling along the x-axis and at time t measurements (magnitudes and uncertainties) are made of its position x x and momentum p p. Then, one mathematical version of the Heisenberg Uncertainty Principle is (1) x p h Equation (1) implies that it is impossible to know the exact values of a particles position and momentum simultaneously. The better we know the location of the particle, then the greater must be the uncertainty in the particle s momentum t8_quantum

3 Planck s constant is very small (h = 6.63x1-34 J.s), so for macroscopic objects the uncertainty principle is of no consequence, but that is not the case for atomic sized systems. According to the uncertainty principle, we can never obtain precise knowledge of a physical system, regardless of improvements in experimental techniques. We can only obtain probable values, and this is a characteristic of nature. This principle provided a tremendous support for the methods of Wave Mechanics. It showed that there was an uncertainty inherent in nature, and this was precisely what Wave Mechanics predicted. The theory has been immensely successful in providing correct solutions to many scientific problems, and is one of the corner stones of contemporary physics. There are limits to what we can know. The premise: if we know the present exactly, we can calculate the future" is wrong. Quantum Mechanics Concepts In classical physics, given an initial position and initial velocity for a particle then if one knew the forces acting on the particle, Newton s second law could be solved to accurately predict the position and velocity in the future. This concept is not true, especially in atomic systems. Quantum Mechanics tells us that we can only talk about the probability of certain events occurring. In Quantum Mechanics the starting point is to set up a wave equation describing a particle in some system. This equation is know as the Schrodinger Equation. Solving this equation gives a wavefunction which gives complete knowledge of the particle in the system. For electrons in atoms, four numbers are necessary to specify the wavefunction which is a solution to the wave equation for that system. These four numbers describe the state of the electron. These four numbers are a natural consequence of the wave nature of matter. These four quantum numbers are Principal quantum number n n = 1,, 3, Angular momentum number l l =, 1,,, (n - 1) Magnetic quantum number m l m l = -l, -l+1,,, 1,,, l Spin quantum number m s m s = -1/, +1/ The principal quantum n fulfils the same role as the quantum number n in the Bohr theory of the atom, i.e. the energy levels obtained are given by the value of n. The quantum number l determines the angular momentum of the electron, whereas m l determines the component of the angular momentum along a prescribed direction, for example, the alignment in an external magnetic field. The spin quantum number m s arises from the spin angular momentum of the electron. In one atom, no two electrons can have the same set of four quantum numbers. This is known as the Pauli Exclusion Principle. This principle is the key to understanding the behaviour of the elements in the periodic table t8_quantum 3

4 The principle quantum number n basically determines the shell for the location of the electron and its energy. The angular quantum number l determines the subshell for the location of the electron. The value of l is often replaced by a letter to specify the type of state for the electron l: s, 1 p, d, 3 f, 4 g Using the restrictions on the values of the four quantum numbers, and the Pauli Exclusion Principle it is possible to give the electronic configuration of all the elements in the periodic table for atoms in the ground state where the lowest energy levels are filled first. The total number of states for n is equal to n n = 1 st shell electrons n = nd shell 8 electrons n= 3 rd shell 18 electrons Number of electrons in subshells s-state p-state 6 d-state 1 f-state 14 s subshell electrons p subshell 6 electrons d subshell 1 electrons The electronic configuration is often written in a condensed format, for example, Carbon has six electron 1s s p The electronic configuration of the 1 st twenty elements of the periodic table; 1 H 1s 1 He 1s 1 3 Li 1s s 1 4 Be 1s s 5 B 1s s p 1 6 C 1s s p 7 N 1s s p 3 8 O 1s s p 4 9 F 1s s p 5 1 Ne 1s s p 6 11 Na 1s s p 6 3s 1 1 Mg 1s s p 6 3s 13 Al 1s s p 6 3s 3p 1 14 Si 1s s p 6 3s 3p 15 P 1s s p 6 3s 3p 3 16 S 1s s p 6 3s 3p 4 17 Cl 1s s p 6 3s 3p 5 18 A 1s s p 6 3s 3p 6 19 K 1s s p 6 3s 3p 6 4s 1 Ca 1s s p 6 3s 3p 6 4s Lower energy states can be achieved when the shells and subshells are full. Hence, from the electronic configuration we can easily predict the chemical behaviour of each element and the type of chemical bond it is most likely to form t8_quantum 4

5 The least reactive elements (noble gases) have complete shells and subshells He 1s 1 1 Ne 1s s p 6 18 A 1s s p 6 3s 3p 6 The active metals can easily lose an electron to form positive ions 11 Na 1s s p 6 3s 1 19 K 1s s p 6 3s 3p 6 4s 1 Active non-metals can easily gain an electron to form negative ions 9 F 1s s p 5 17 Cl 1s s p 6 3s 3p 5 Sodium and chlorine will join together in an ionic bond as the sodium atom can easily lose an electron and the chlorine atom can easily gain this electron to give complete shells / subshells. Na e - Na + Cl + e - Cl - Na + Cl - Hydrogen atom The Rutherford-Bohr model of the atom described the electron orbiting around the nucleus in circular orbits. This is a planetary model like the planets orbiting the Sun. However, in terms of Quantum Mechanics the electron has to be regarded as a wave so that experimental observations agree with theoretical predictions. The Schrodinger Wave Equation for a hydrogen atom can be easily solved to give the wavefunction describing the electron and the state of the electron given by the four quantum numbers (n, l, ml, m s ). The ground state of a hydrogen atom (lowest energy level) has the quantum numbers (1,,, 1/). Higher energy states are called excited states. The following diagrams show the electron densities for an electron in the ground state and a number of excited sates. The dimensions (width and height of displayed image) are given in terms of the Bohr radius a = 5.9x1-11 m and the binding energy E B, energy needed to remove the electron (ionization) from the atom are given in electron-volts (ev). The diagrams clearly show the ideas of shells and subshells. s- subshells are spherical while p-subshell have a dumbbell shape. There are regions where there are high probability of finding the electron and other regions where the probability is zero (the electron will never be found at these locations). The electron density patterns are similar to standing wave patterns (regions of nodes and antinodes). Consider the states with n =. Separating regions of high probability are zones of zero probability, hence it is meaningless to think about the electron moving around the nucleus in some type of trajectory. To try and have a three-dimensional view, take the z-axis as pointing to the top of the page and in the plane of the page through the centre of the atom, then rotate each diagram about the z-axis. The higher the principle quantum number n, on average the electron is further from the nucleus and hence its binding energy is lower t8_quantum 5

6 Ground state: n = 1 (s orbital) l = ml = dimensions = a x a EB = 13.6 ev Electron density: n = l = ml = dimensions = 4a x 4a EB = ev 1 Excited state: n = (s orbital) l= m= EB = 3.4 ev Electron density: n = l=1 m= EB = ev Electron density: n = l=1 m=1 EB = ev l = 1 ml = 1 dimensions = 4a x 4a EB = 3.4 ev Excited state: n = (p orbital) 1-1 Excited state: n = (p orbital) l = 1 ml = 1 1 EB = 3.4 ev dimensions = 4a x 4a t8_quantum

7 Electron density: n = 3 3 Dimensions = 6a x 6a EB = 1.56 ev 15 Excited state: n = 3 l = ml = (s orbital) l= m= -15 EB = 1.51 ev Electron density: n = 3 l= 1 m = EB = 1.58 ev 3 l = 1 ml = dimensions = 6a x 6a 1 Excited state: n = 3 EB = 1.51 ev Electron density: n = 3 1 l= m = 3 EB = 1.59 ev 3 Excited state: n = 3 l = ml = dimensions = 6a x 6a 1 EB = 1.51 ev Electron density: n = 4 1 l= 3 m = 1 3 EB =.8494 ev 5 4 Excited state: n = 4 l = 3 ml = 1 3 dimensions = 1a x 1a EB =.85 ev t8_quantum

### Introduction to quantum mechanics

Introduction to quantum mechanics Lecture 3 MTX9100 Nanomaterjalid OUTLINE -What is electron particle or wave? - How large is a potential well? -What happens at nanoscale? What is inside? Matter Molecule

### AP Chemistry A. Allan Chapter 7 Notes - Atomic Structure and Periodicity

AP Chemistry A. Allan Chapter 7 Notes - Atomic Structure and Periodicity 7.1 Electromagnetic Radiation A. Types of EM Radiation (wavelengths in meters) 10-1 10-10 10-8 4 to 7x10-7 10-4 10-1 10 10 4 gamma

### λν = c λ ν Electromagnetic spectrum classification of light based on the values of λ and ν

Quantum Theory and Atomic Structure Nuclear atom small, heavy, positive nucleus surrounded by a negative electron cloud Electronic structure arrangement of the electrons around the nucleus Classical mechanics

### CHAPTER 6: ANSWERS TO ASSIGNED PROBLEMS Hauser- General Chemistry I revised 8/03/08

CHAPTER 6: ANSWERS TO ASSIGNED PROBLEMS Hauser- General Chemistry I revised 8/03/08 6.9 What are the basic SI units for? (a) the wavelength of light meters, although colors are usually reported in 3 digit

### Chapter 7: The Quantum-Mechanical Model of the Atom

C h e m i s t r y 1 A : C h a p t e r 7 P a g e 1 Chapter 7: The Quantum-Mechanical Model of the Atom Homework: Read Chapter 7. Work out sample/practice exercises Suggested Chapter 7 Problems: 37, 39,

### Atomic Structure Ron Robertson

Atomic Structure Ron Robertson r2 n:\files\courses\1110-20\2010 possible slides for web\atomicstructuretrans.doc I. What is Light? Debate in 1600's: Since waves or particles can transfer energy, what is

### Chapter 29: Atomic Structure. What will we learn in this chapter?

Chapter 29: Atomic Structure What will we learn in this chapter? Contents: Electrons in atoms Wave functions Electron spin Pauli exclusion principle Atomic structure Periodic table W. Pauli & N. Bohr Both

### Multi-electron atoms

Multi-electron atoms Today: Using hydrogen as a model. The Periodic Table HWK 13 available online. Please fill out the online participation survey. Worth 10points on HWK 13. Final Exam is Monday, Dec.

### Practice questions for Ch. 7

Name: Class: Date: ID: A Practice questions for Ch. 7 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. When ignited, a uranium compound burns with a green

### AP CHEMISTRY CHAPTER REVIEW CHAPTER 6: ELECTRONIC STRUCTURE AND THE PERIODIC TABLE

AP CHEMISTRY CHAPTER REVIEW CHAPTER 6: ELECTRONIC STRUCTURE AND THE PERIODIC TABLE You should be familiar with the wavelike properties of light: frequency ( ), wavelength ( ), and energy (E) as well as

### Terms H February 12, Atomic Theory H Online.notebook

Match the Theorist to His Idea Discovered the neutron Said the positive charges were in nucleus Discovered the electron First proposed the idea of the atom Proposed that electrons were in energy levels

### Topic 1. Atomic Structure and Periodic Properties

Topic 1 1-1 Atomic Structure and Periodic Properties Atomic Structure 1-2 History Rutherford s experiments Bohr model > Interpretation of hydrogen atom spectra Wave - particle duality Wave mechanics Heisenberg

### Chapter 11 Atoms, Energy and Electron Configurations Objectives

Objectives 1. To review Rutherford s model of the atom 2. To explore the nature of electromagnetic radiation 3. To see how atoms emit light A. Rutherford s Atom.but there is a problem here!! Using Rutherford

### Modern Atomic Theory

Reading: Ch. 9, sections 1-4 Ch. 7, sections 5-6 (lec) Ch. 7, sections 1-3 (lab) Modern Atomic Theory Homework: Chapter 9: 37*, 39*, 41 Chapter 7: 59, 61*, 63, 65 (lec.) Chapter 7: 39, 41, 43, 47 (lab)

### Atomic Structure: Chapter Problems

Atomic Structure: Chapter Problems Bohr Model Class Work 1. Describe the nuclear model of the atom. 2. Explain the problems with the nuclear model of the atom. 3. According to Niels Bohr, what does n stand

### Chapter 10. Modern Atomic Theory and the Periodic Table

Chapter 10 Modern Atomic Theory and the Periodic Table 1 10.1 A brief history 10.1 A brief history atoms proposed by Greek philosopher Dalton s model of atom Thomson s model Rutherford s model there remain

### The Phenomenon of Photoelectric Emission:

The Photoelectric Effect. The Wave particle duality of light Light, like any other E.M.R (electromagnetic radiation) has got a dual nature. That is there are experiments that prove that it is made up of

### 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.

### AP* Atomic Structure & Periodicity Free Response Questions KEY page 1

AP* Atomic Structure & Periodicity ree Response Questions KEY page 1 1980 a) points 1s s p 6 3s 3p 6 4s 3d 10 4p 3 b) points for the two electrons in the 4s: 4, 0, 0, +1/ and 4, 0, 0, - 1/ for the three

### AP Chemistry Chapter 6 Lecture Notes- Electrons! 6.1 The Wave Nature of Light. 6.2 Quantized Energy and Photons. Chapter 6 Homework

AP Chemistry Chapter 6 Lecture Notes- Electrons! Chapter 6 Homework 6.1 The Wave Nature of Light pg 253 #3, 4, 13, 15, 17, 19, 21, 25, 29 The electronic structure of an atom refers to the arrangement of

### Chemistry 417! 1! Fall Chapter 2 Notes

Chemistry 417! 1! Fall 2012 Chapter 2 Notes September 3, 2012! Chapter 2, up to shielding 1. Atomic Structure in broad terms a. nucleus and electron cloud b. nomenclature, so we may communicate c. Carbon-12

### Chem 1A Exam 2 Review Problems

Chem 1A Exam 2 Review Problems 1. At 0.967 atm, the height of mercury in a barometer is 0.735 m. If the mercury were replaced with water, what height of water (in meters) would be supported at this pressure?

### Lecture 12 Quantum Mechanics and Atomic Orbitals

Lecture 12 Quantum Mechanics and Atomic Orbitals Bohr and Einstein demonstrated the particle nature of light.e = hν. De Broglie demonstrated the wavelike properties of particles. λ = h/mv. However, these

### Quantum Mechanics I Physics 325. Importance of Hydrogen Atom

Quantum Mechanics I Physics 35 Atomic spectra and Atom Models Importance of Hydrogen Atom Hydrogen is the simplest atom The quantum numbers used to characterize the allowed states of hydrogen can also

### PSI AP Chemistry Unit 1 MC Homework. Laws of Multiple and Definite Proportions and Conservation of Mass

PSI AP Chemistry Unit 1 MC Homework Name Laws of Multiple and Definite Proportions and Conservation of Mass 1. Dalton's atomic theory explained the observation that the percentage by mass of the elements

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Practice Questions - Chapter 7 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Which one of the following represents an impossible set of

### Elements in the periodic table are indicated by SYMBOLS. To the left of the symbol we find the atomic mass (A) at the upper corner, and the atomic num

. ATOMIC STRUCTURE FUNDAMENTALS LEARNING OBJECTIVES To review the basics concepts of atomic structure that have direct relevance to the fundamental concepts of organic chemistry. This material is essential

### QUANTUM-MECHANICAL MODEL OF THE ATOM. Quantum Mechanics?

QUANTUM-MECHANICAL MODEL OF THE ATOM GENERAL CHEMISTRY by Dr. Istadi 1 Quantum Mechanics? Dual nature of matter and energy The uncertainty principle The wave nature of objects on the atomic scale Quantum

### 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

### Chapter 6 Electromagnetic Radiation and the Electronic Structure of the Atom

Chapter 6 In This Chapter Physical and chemical properties of compounds are influenced by the structure of the molecules that they consist of. Chemical structure depends, in turn, on how electrons are

### CHEMSITRY NOTES Chapter 13. Electrons in Atoms

CHEMSITRY NOTES Chapter 13 Electrons in Atoms Goals : To gain an understanding of : 1. Atoms and their structure. 2. The development of the atomic theory. 3. The quantum mechanical model of the atom. 4.

### Atomic structure The product of frequency and wavelength for all forms of electromagnetic radiation (light) is a constant, the speed of light c.

Chapter 5: Electrons in Atoms Light (Electromagnetic Radiation) Light has the properties of both waves and particles. Light waves carry energy through space. wavelength (λ) meters frequency (ν) Hz (s -1

### TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES. PHYS 3650, Exam 2 Section 1 Version 1 October 31, 2005 Total Weight: 100 points

TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 3650, Exam 2 Section 1 Version 1 October 31, 2005 Total Weight: 100 points 1. Check your examination for completeness prior to starting.

### Electrons in Atoms & Periodic Table Chapter 13 & 14 Assignment & Problem Set

Electrons in Atoms & Periodic Table Name Warm-Ups (Show your work for credit) Date 1. Date 2. Date 3. Date 4. Date 5. Date 6. Date 7. Date 8. Electrons in Atoms & Periodic Table 2 Study Guide: Things You

### Quantum Theory of the Hydrogen Atom

Quantum Theory of the Hydrogen Atom Chemistry 35 Fall 2000 Balmer and the Hydrogen Spectrum 1885: Johann Balmer, a Swiss schoolteacher, empirically deduced a formula which predicted the wavelengths of

### Electromagnetic radiation (Maxwell, 1864) (nature of light) Composed of perpendicular electric field and magnetic field

7 Atomic Structure and Periodicity Electromagnetic radiation (Maxwell, 1864) (nature of light) Composed of perpendicular electric field and magnetic field Electric field (E) (wavelength) t Magnetic field

### Chapter 6 Electronic Structure of Atoms

Chapter 6 Electronic Structure of Atoms 1. Electromagnetic radiation travels through vacuum at a speed of m/s. (a). 6.626 x 26 (b). 4186 (c). 3.00 x 8 (d). It depends on wavelength Explanation: The speed

### The Advanced Placement Examination in Chemistry. Part I Multiple Choice Questions Part II Free Response Questions Selected Questions from1970 to 2010

The Advanced Placement Examination in Chemistry Part I Multiple Choice Questions Part II Free Response Questions Selected Questions from1970 to 2010 Atomic Theory and Periodicity Part I 1984 1. Which of

### 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

### ABC Math Student Copy

Page 1 of 8 Line Spectra Physics Week 15(Sem. 2) Name The Atom Chapter Summary From the last section, we know that all objects emit electromagnetic waves. For a solid object, such as the filament of a

### Chapter 6 Electronic Structure and the Periodic Table

Chapter 6 Electronic Structure and the Periodic Table MULTIPLE CHOICE 1. The Navy uses electromagnetic radiation of extremely long wavelengths to communicate with submerged submarines. The Navy's ELF (Extremely

### Chemistry 2 Chapter 13: Electrons in Atoms Please do not write on the test Use an answer sheet! 1 point/problem 45 points total

Chemistry 2 Chapter 13: Electrons in Atoms Please do not write on the test Use an answer sheet! 1 point/problem 45 points total 1. Calculate the energy in joules of a photon of red light that has a frequency

### Atomic Spectra and Energy Levels. Atomic Spectra

Atomic Spectra and Energy Levels Atomic Spectra Excited atoms emit light (neon signs, etc.) Emission from different elements is different colors. Emission of only certain wavelengths Spectral lines Existence

### 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

### Exam 2 Solutions Chem 6, 9 Section, Spring 2002

1. Dartmouth s FM radio station, WDCR, broadcasts by emitting from its antenna photons of frequency 99.3 MHz (99.3 10 6 Hz). (a) What is the energy of a single WDCR photon? The photon energy is simply

### Wave Function, ψ. Chapter 28 Atomic Physics. The Heisenberg Uncertainty Principle. Line Spectrum

Wave Function, ψ Chapter 28 Atomic Physics The Hydrogen Atom The Bohr Model Electron Waves in the Atom The value of Ψ 2 for a particular object at a certain place and time is proportional to the probability

### 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

### Chapter 3 Atomic Structure and Properties

Chapter 3 Atomic Structure and Properties Introduction The nuclear atom and quantum theory are the accepted theories for the atom. In this chapter, we demonstrate their utility by using them to explain

### Free Electron Fermi Gas (Kittel Ch. 6)

Free Electron Fermi Gas (Kittel Ch. 6) Role of Electrons in Solids Electrons are responsible for binding of crystals -- they are the glue that hold the nuclei together Types of binding (see next slide)

### 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

### Chapter 5. Mendeleev s Periodic Table

Chapter 5 Perodicity and Atomic Structure Mendeleev s Periodic Table In the 1869, Dmitri Mendeleev proposed that the properties of the chemical elements repeat at regular intervals when arranged in order

### Sample Exercise 6.1 Concepts of Wavelength and Frequency

Sample Exercise 6.1 Concepts of Wavelength and Frequency Two electromagnetic waves are represented below. (a) Which wave has the higher frequency? (b) If one wave represents visible light and the other

### Arrangement of Electrons in Atoms

CHAPTER 4 PRE-TEST Arrangement of Electrons in Atoms In the space provided, write the letter of the term that best completes each sentence or best answers each question. 1. Which of the following orbital

### THE NATURE OF THE ATOM

CHAPTER 30 THE NATURE OF THE ATOM CONCEPTUAL QUESTIONS 1. REASONING AND SOLUTION A tube is filled with atomic hydrogen at room temperature. Electromagnetic radiation with a continuous spectrum of wavelengths,

### Chapter 31 Atomic Physics 31.1 Early Model of the Atom 31.2 The Spectrum of Atomic Hydrogen 31.3 Bohr s Model of the Hydrogen Atom 31.

Chapter 31 Atomic Physics 31.1 Early Model of the Atom 31.2 The Spectrum of Atomic Hydrogen 31.3 Bohr s Model of the Hydrogen Atom 31.4 de Broglie Waves and the Bohr Model 31.5 The Quantum Mechanical Hydrogen

### Chapter 7. Electron Structure of the Atom. Chapter 7 Topics

Chapter 7 Electron Structure of the Atom Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Chapter 7 Topics 1. Electromagnetic radiation 2. The Bohr model of

### Electronic Structure and the Periodic Table Learning Outcomes

Electronic Structure and the Periodic Table Learning Outcomes (a) Electronic structure (i) Electromagnetic spectrum and associated calculations Electromagnetic radiation may be described in terms of waves.

### Chapter 7: Electrons in Atoms. Electromagnetic Radiation

Chapter 7: Electrons in Atoms Dr. Chris Kozak Memorial University of Newfoundland, Canada 1 Electromagnetic Radiation Electric and magnetic fields propagate as waves through empty space or through a medium.

### Chapter 8 Molecules. Some molecular bonds involve sharing of electrons between atoms. These are covalent bonds.

Chapter 8 Molecules (We have only three days for chapter 8!) 8.1 The Molecular Bond A molecule is an electrically neutral group of atoms held together strongly enough to behave as a single particle. A

### 13- What is the maximum number of electrons that can occupy the subshell 3d? a) 1 b) 3 c) 5 d) 2

Assignment 06 A 1- What is the energy in joules of an electron undergoing a transition from n = 3 to n = 5 in a Bohr hydrogen atom? a) -3.48 x 10-17 J b) 2.18 x 10-19 J c) 1.55 x 10-19 J d) -2.56 x 10-19

### Quantum Atom: Atomic Structure, Electron Configuration, and Periodicity

Quantum Atom: Atomic Structure, Electron Configuration, and Periodicity Equations: λν = c E = hν E = hν energy of photon difference of energy levels λ = h/p p = mu (momentum and particle wavelength) debroglie

### 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.

### CHAPTER 12 ATOMS ONE MARK QUESTIONS WITH ANSWER. Ans: Electrons were discovered by J.J Thomason in the year 1897.

CHAPTER 12 ATOMS ONE MARK QUESTIONS WITH ANSWER 1. Who discovered electrons? Ans: Electrons were discovered by J.J Thomason in the year 1897. 2. What is the electric charge on an atom? Ans: At atom of

### Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 2 - Cont. 30 January 2014

Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 2 - Cont. 30 January 2014 The Structure of the Atom and the Periodic Table Element Information in the

### The Electronic Structures of Atoms Electromagnetic Radiation

The Electronic Structures of Atoms Electromagnetic Radiation The wavelength of electromagnetic radiation has the symbol λ. Wavelength is the distance from the top (crest) of one wave to the top of the

### A1_Lotukerfið og uppbygging atómanna

Instructor Solutions Manual for Chemistry for Engineering Students, 2 nd Edition 6-1 Lota_2 A1_Lotukerfið og uppbygging atómanna The Electromagnetic Spectrum 6.8 Which of the waves depicted here has the

### Chapter 3 Classification of Elements and Periodicity in Properties

Class XI Chapter 3 Classification of Elements and Periodicity in Properties Chemistry Question 3.1: What is the basic theme of organisation in the periodic table? The basic theme of organisation of elements

### Problem Set 1 Solutions

Chemistry 36 Dr. Jean M. Standard Problem Set Solutions. The first 4 lines in the visible region of atomic line spectrum of hydrogen atom occur at wavelengths of 656., 486., 434.0, and 40. nm (this is

### Atoms. Chemistry 100. Bettelheim, Brown, Campbell & Farrell. Introduction to General, Organic and Biochemistry Chapter 2

Chemistry 100 Bettelheim, Brown, Campbell & Farrell Ninth Edition Introduction to General, Organic and Biochemistry Chapter 2 Atoms Classifications of Matter: Elements An Element is a substance (for example,

### Intermediate Quantum Mechanics Notes for Lecture 1

The Structure of Physics Intermediate Quantum Mechanics Notes for Lecture 1 Structure of Physics, Classical Physics and Quantum Mechanics vs. Classical Physics The two pillars of physics are the Special

### Sample Exercise 6.1 Concepts of Wavelength and Frequency

Sample Exercise 6.1 Concepts of Wavelength and Frequency Two electromagnetic waves are represented in the margin. (a) Which wave has the higher frequency? (b) If one wave represents visible light and the

### Atomic Structure. Atoms and elements

Atomic Structure Atoms and elements Everything in the world is made up from about 100 elements. Every element is made up of very small particles called atoms. An element is a substance in which all the

### Periodic Table & Atomic Structure

St Peter the Apostle High School Chemistry Department Periodic Table & Atomic Structure N4 & N5 Homework Questions Answer questions as directed by your teacher. National 4 level questions are first followed

### 3. What would you predict for the intensity and binding energy for the 3p orbital for that of sulfur?

PSI AP Chemistry Periodic Trends MC Review Name Periodic Law and the Quantum Model Use the PES spectrum of Phosphorus below to answer questions 1-3. 1. Which peak corresponds to the 1s orbital? (A) 1.06

### 7.4. Using the Bohr Theory KNOW? Using the Bohr Theory to Describe Atoms and Ions

7.4 Using the Bohr Theory LEARNING TIP Models such as Figures 1 to 4, on pages 218 and 219, help you visualize scientific explanations. As you examine Figures 1 to 4, look back and forth between the diagrams

### Objectives. PAM1014 Introduction to Radiation Physics. Constituents of Atoms. Atoms. Atoms. Atoms. Basic Atomic Theory

PAM1014 Introduction to Radiation Physics Basic Atomic Theory Objectives Introduce and Molecules The periodic Table Electronic Energy Levels Atomic excitation & de-excitation Ionisation Molecules Constituents

### UNIT TEST Atomic & Molecular Structure. Name: Date:

SCH4U UNIT TEST Atomic & Molecular Structure Name: _ Date: Part A - Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Who postulated that electrons

### Does Quantum Mechanics Make Sense? Size

Does Quantum Mechanics Make Sense? Some relatively simple concepts show why the answer is yes. Size Classical Mechanics Quantum Mechanics Relative Absolute What does relative vs. absolute size mean? Why

### SAMPLE EXAM 2 FALL 2012 SOLUTIONS Chemistry 11, Fall 2007 Exam II November 15, 2007 7:30 PM 9:30 PM

Name: SOLUTIONS III, IV, and V Section (circle): 1 2 3 4 5 SAMPLE EXAM 2 FALL 2012 SOLUTIONS Chemistry 11, Fall 2007 Exam II November 15, 2007 7:30 PM 9:30 PM As always, full credit will not be given unless

### Chapter 3 Atoms and Moles. Section 1 Substances Are Made of Atoms

+ Chapter 3 Atoms and Moles Section 1 Substances Are Made of Atoms + Atomic Theory Atomic Theory explains three separate scientific laws Model on the right is more accurate depiction of an atom + Law of

### 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

### Nanoelectronics. Chapter 2 Classical Particles, Classical Waves, and Quantum Particles. Q.Li@Physics.WHU@2015.3

Nanoelectronics Chapter 2 Classical Particles, Classical Waves, and Quantum Particles Q.Li@Physics.WHU@2015.3 1 Electron Double-Slit Experiment Q.Li@Physics.WHU@2015.3 2 2.1 Comparison of Classical and

### The Periodic Table of the Elements

Chapter 15 The Periodic Table of the Elements In Section 13.4, we saw the example of a square potential well. In that example, there were three bound states. This is the solution for a single electron

### The Evolution of the Atom

The Evolution of the Atom 1808: Dalton s model of the atom was the billiard ball model. He thought the atom was a solid, indivisible sphere. Atoms of each element were identical in mass and their properties.

### CHEM 1411 Chapter 5 Homework Answers

1 CHEM 1411 Chapter 5 Homework Answers 1. Which statement regarding the gold foil experiment is false? (a) It was performed by Rutherford and his research group early in the 20 th century. (b) Most of

### CHAPTER 8 PRACTICE TEST QUESTIONS (END OF CHAPTER 7 TOO)

CHAPTER 8 PRACTICE TEST QUESTIONS (END OF CHAPTER 7 TOO) Information that most likely will be on the front cover of your exam: h i Z 2 ΔE = @ 2.18 x 10 @ 18 f Z 2 f J j @ k n f 2 n i 2 1. Which of the

### Ch 3 Atomic Structure and the Periodic Table. Figure 3.1 size relationship is not to scale, ratio of average diameters atom/nucleus = 10 5

1 Ch 3 Atomic Structure and the Periodic Table Figure 3.1 size relationship is not to scale, ratio of average diameters atom/nucleus = 10 5 2 Atoms are very small and spherical. Radii Range 0.9 x 10-10

### 3 Modern Atomic Theory

CHAPTER 4 3 Modern Atomic Theory SECTION Atoms KEY IDEAS As you read this section, keep these questions in mind: How are electrons organized in an atom? Can the exact location of an electron be determined?

### Chemistry: Atomic Structure

Chemistry: Atomic Structure Organization of the Modern Periodic Table The periodic table is organized by properties. The Atom Today atom = All atoms of the same element are essentially (but not exactly)

### Lecture 18: Quantum Mechanics. Reading: Zumdahl 12.5, 12.6 Outline. Problems (Chapter 12 Zumdahl 5 th Ed.)

Lecture 18: Quantum Mechanics Reading: Zumdahl 1.5, 1.6 Outline Basic concepts of quantum mechanics and molecular structure A model system: particle in a box. Demos how Q.M. actually obtains a wave function.

### Physical Science Test - Final Exam

Physical Science Test: 05-26-10 - Final Exam Name and Nickname: Calculators are allowed. Physical Science Final Exam: Table of Contents I. Metric Prefixes, Defined Units, Derived Units, Conversions, Addition

### Chapter 11 Modern Atomic Theory

Chapter 11 Modern Atomic Theory Rutherford s Atom The concept of a nuclear atom (charged electrons moving around the nucleus) resulted from Ernest Rutherford s experiments. Question left unanswered: how

### Metals and Nonmetals

The Periodic Table and Atomic Properties The periodic table originally came from the observation that when the elements are arranged by atomic mass, properties recur periodically. (Mendeleev) Now we understand

### CHAPTER-3 CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES OF ELEMENTS

CHAPTER-3 CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES OF ELEMENTS Mandeleev s Periodic Law:- The properties of the elements are the periodic function of their atomic masses. Moseley, the English

### Electrons/Periodic Table Review Packet

http://www.carolina.com/teacher-resources/interactive/online-game-cell-structure-cellcraftbiology/tr11062.tr T. Trimpe 2007 http://sciencespot.net/ Part C: Electron Configuration 12. How many electrons

### DEVELOPMENT OF THE PERIODIC TABLE

DEVELOPMENT OF THE PERIODIC TABLE Prior to the 1700s, relatively few element were known, and consisted mostly of metals used for coinage, jewelry and weapons. From early 1700s to mid-1800s, chemists discovered