Physics 6C. De Broglie Wavelength Uncertainty Principle. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
|
|
|
- Doreen Cecily Haynes
- 5 years ago
- Views:
Transcription
1 Pyic 6C De Broglie Wavelengt Uncertainty Principle
2 De Broglie Wavelengt Bot ligt and atter ave bot particle and wavelike propertie. We can calculate te wavelengt of eiter wit te ae forula: p v For large object (like a baeball) ti wavelengt will be far too all to eaure, but for tiny particle like electron or neutron, we get wavelengt tat are eaily detectable in te lab.
3 Eaple: Electron are accelerated acro a potential difference of 100 Volt. Find te wavelengt of te electron. Te a of an electron i kg. Copare te energy of tee electron to te energy of poton of equal wavelengt.
4 Eaple: Electron are accelerated acro a potential difference of 100 Volt. Find te wavelengt of te electron. Te a of an electron i kg. Copare te energy of tee electron to te energy of poton of equal wavelengt. Firt ting to realize i tat te electron pick up oe kinetic energy a it accelerate acro te potential difference (1 ev of energy for eac volt). KE electron 100eV J
5 Eaple: Electron are accelerated acro a potential difference of 100 Volt. Find te wavelengt of te electron. Te a of an electron i kg. Copare te energy of tee electron to te energy of poton of equal wavelengt. Firt ting to realize i tat te electron pick up oe kinetic energy a it accelerate acro te potential difference (1 ev of energy for eac volt). KE electron 100eV J Fro ti we can find te peed of te electron v J v Wile very fat, ti i not cloe enoug to te peed of ligt to worry about relativity.
6 Eaple: Electron are accelerated acro a potential difference of 100 Volt. Find te wavelengt of te electron. Te a of an electron i kg. Copare te energy of tee electron to te energy of poton of equal wavelengt. Firt ting to realize i tat te electron pick up oe kinetic energy a it accelerate acro te potential difference (1 ev of energy for eac volt). KE electron 100eV J Fro ti we can find te peed of te electron v J v Wile very fat, ti i not cloe enoug to te peed of ligt to worry about relativity. Now we can jut ue te DeBroglie wavelengt forula: J v 31 6 ( kg)( )
7 Eaple: Electron are accelerated acro a potential difference of 100 Volt. Find te wavelengt of te electron. Te a of an electron i kg. Copare te energy of tee electron to te energy of poton of equal wavelengt. Firt ting to realize i tat te electron pick up oe kinetic energy a it accelerate acro te potential difference (1 ev of energy for eac volt). KE electron 100eV J Fro ti we can find te peed of te electron v J v Wile very fat, ti i not cloe enoug to te peed of ligt to worry about relativity. Now we can jut ue te DeBroglie wavelengt forula: J v 31 6 ( kg)( ) E A poton wit ti wavelengt a energy: c 15 ( ev )( ) 10,100eV Copared to te 100eV electron, ti poton a uc ore energy. Ti i one of te reaon wy electron icrocope are ued to get iage of tiny object a poton bea igt daage te object. 15 J
8 Heienberg Uncertainty Principle Baic Idea you can t get eact eaureent 2 Verion: E p t 2 2
9 Eaple: For te electron in te previou eaple, teir wavelengt wa 0.123n. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed.
10 Eaple: For te electron in te previou eaple, teir wavelengt wa 0.123n. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed. p 2
11 Eaple: For te electron in te previou eaple, teir wavelengt wa 0.123n. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed. p ( v 2 ) 2
12 Eaple: For te electron in te previou eaple, teir wavelengt wa 0.123n. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed. p ( v 2 ) 2 ( ) ( kg v ) J
13 Eaple: For te electron in te previou eaple, teir wavelengt wa 0.123n. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed. p ( v 2 ) 2 ( v ) ( kg v ) J
14 Eaple: For te electron in te previou eaple, teir wavelengt wa 0.123n. Take ti to be te uncertainty in teir poition, and find te correponding uncertainty in teir peed. p ( v 2 ) 2 ( v ) ( kg v ) J Copare ti to te velocity we found in te previou proble. Tat value wa So te uncertainty i alot a uc a te actual velocity!
15 Eaple A certain ato a an energy level 3.50eV above te ground tate. Wen ecited to ti tate, it reain 4.0µ, on average, before eitting a poton and returning to te ground tate. a) Wat i te energy of te poton? Wat i te wavelengt of te poton? b) Wat i te allet poible uncertainty in te energy of te poton?
16 Eaple A certain ato a an energy level 3.50eV above te ground tate. Wen ecited to ti tate, it reain 4.0µ, on average, before eitting a poton and returning to te ground tate. a) Wat i te energy of te poton? Wat i te wavelengt of te poton? b) Wat i te allet poible uncertainty in te energy of te poton? Te poton a energy 3.50 ev. It wavelengt i calculated in te uual way:
17 Eaple A certain ato a an energy level 3.50eV above te ground tate. Wen ecited to ti tate, it reain 4.0µ, on average, before eitting a poton and returning to te ground tate. a) Wat i te energy of te poton? Wat i te wavelengt of te poton? b) Wat i te allet poible uncertainty in te energy of te poton? Te poton a energy 3.50 ev. It wavelengt i calculated in te uual way: E c poton ( ev )( eV 8 ) 355n
18 Eaple A certain ato a an energy level 3.50eV above te ground tate. Wen ecited to ti tate, it reain 4.0µ, on average, before eitting a poton and returning to te ground tate. a) Wat i te energy of te poton? Wat i te wavelengt of te poton? b) Wat i te allet poible uncertainty in te energy of te poton? Te poton a energy 3.50 ev. It wavelengt i calculated in te uual way: E c poton ( ev )( eV 8 ) 355n Ue Heienberg forula to find te iniu uncertainty in te energy:
19 Eaple A certain ato a an energy level 3.50eV above te ground tate. Wen ecited to ti tate, it reain 4.0µ, on average, before eitting a poton and returning to te ground tate. a) Wat i te energy of te poton? Wat i te wavelengt of te poton? b) Wat i te allet poible uncertainty in te energy of te poton? Te poton a energy 3.50 ev. It wavelengt i calculated in te uual way: E c poton ( ev )( eV 8 ) 355n Ue Heienberg forula to find te iniu uncertainty in te energy: E t 2 E (2)( t) E (2)(4 10 ev 6 ) ev Note tat ti i uc aller tan te energy of te poton, o te uncertainty i negligible.
Physics 6C. Heisenberg Uncertainty Principle. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Pyic 6C Heienberg Uncertainty Principle Heienberg Uncertainty Principle Baic Idea you can t get eact meaurement 2 Verion: E p t 2 2 Eample: For te electron in te previou eample, teir wavelengt wa 0.123nm.
Physics Teach Yourself Series Topic 15: Wavelike nature of matter (Unit 4)
Pysics Teac Yourself Series Topic 15: Wavelie nature of atter (Unit 4) A: Level 14, 474 Flinders Street Melbourne VIC 3000 T: 1300 134 518 W: tss.co.au E: info@tss.co.au TSSM 2017 Page 1 of 8 Contents
( ) ( s ) Answers to Practice Test Questions 4 Electrons, Orbitals and Quantum Numbers. Student Number:
Anwer to Practice Tet Quetion 4 Electron, Orbital Quantu Nuber. Heienberg uncertaint principle tate tat te preciion of our knowledge about a particle poition it oentu are inverel related. If we ave ore
Tutorial 2 (Solution) 1. An electron is confined to a one-dimensional, infinitely deep potential energy well of width L = 100 pm.
Seester 007/008 SMS0 Modern Pysics Tutorial Tutorial (). An electron is confined to a one-diensional, infinitely deep potential energy well of widt L 00 p. a) Wat is te least energy te electron can ave?
Homework 1. L φ = mωr 2 = mυr, (1)
Homework 1 1. Problem: Streetman, Sixt Ed., Problem 2.2: Sow tat te tird Bor postulate, Eq. (2-5) (tat is, tat te angular momentum p θ around te polar axis is an integer multiple of te reduced Planck constant,
Assignment Solutions- Dual Nature. September 19
Assignment Solutions- Dual Nature September 9 03 CH 4 DUAL NATURE OF RADIATION & MATTER SOLUTIONS No. Constants used:, = 6.65 x 0-34 Js, e =.6 x 0-9 C, c = 3 x 0 8 m/s Answers Two metals A, B ave work
c hc h c h. Chapter Since E n L 2 in Eq. 39-4, we see that if L is doubled, then E 1 becomes (2.6 ev)(2) 2 = 0.65 ev.
Capter 39 Since n L in q 39-4, we see tat if L is doubled, ten becoes (6 ev)() = 065 ev We first note tat since = 666 0 34 J s and c = 998 0 8 /s, 34 8 c6 66 0 J sc 998 0 / s c 40eV n 9 9 60 0 J / ev 0
A Reconsideration of Matter Waves
A Reconsideration of Matter Waves by Roger Ellman Abstract Matter waves were discovered in te early 20t century from teir wavelengt, predicted by DeBroglie, Planck's constant divided by te particle's momentum,
DUAL NATURE OF RADIATION AND MATTER
DUAL NATURE OF RADIATION AND MATTER Important Points: 1. J.J. Tomson and Sir William Crookes studied te discarge of electricity troug gases. At about.1 mm of Hg and at ig voltage invisible streams called
7. QUANTUM THEORY OF THE ATOM
7. QUANTUM TEORY OF TE ATOM Solutions to Practice Problems Note on significant figures: If te final answer to a solution needs to be rounded off, it is given first wit one nonsignificant figure, and te
Chapter 3. Problem Solutions
Capter. Proble Solutions. A poton and a partile ave te sae wavelengt. Can anyting be said about ow teir linear oenta opare? About ow te poton's energy opares wit te partile's total energy? About ow te
Problem Set 4: Whither, thou turbid wave SOLUTIONS
PH 253 / LeClair Spring 2013 Problem Set 4: Witer, tou turbid wave SOLUTIONS Question zero is probably were te name of te problem set came from: Witer, tou turbid wave? It is from a Longfellow poem, Te
Problem Set 4 Solutions
University of Alabama Department of Pysics and Astronomy PH 253 / LeClair Spring 2010 Problem Set 4 Solutions 1. Group velocity of a wave. For a free relativistic quantum particle moving wit speed v, te
Test on Nuclear Physics
Test on Nuclear Pysics Examination Time - 40 minutes Answer all questions in te spaces provided Tis wole test involves an imaginary element called Bedlum wic as te isotope notation sown below: 47 11 Bd
Physics 41 Homework Set 3 Chapter 17 Serway 7 th Edition
Pyic 41 Homework Set 3 Capter 17 Serway 7 t Edition Q: 1, 4, 5, 6, 9, 1, 14, 15 Quetion *Q17.1 Anwer. Te typically iger denity would by itelf make te peed of ound lower in a olid compared to a ga. Q17.4
Conservation of Energy
Add Iportant Conervation of Energy Page: 340 Note/Cue Here NGSS Standard: HS-PS3- Conervation of Energy MA Curriculu Fraework (006):.,.,.3 AP Phyic Learning Objective: 3.E.., 3.E.., 3.E..3, 3.E..4, 4.C..,
Final exam: Tuesday, May 11, 7:30-9:30am, Coates 143
Final exam: Tuesday, May 11, 7:30-9:30am, Coates 143 Approximately 7 questions/6 problems Approximately 50% material since last test, 50% everyting covered on Exams I-III About 50% of everyting closely
Velocity or 60 km/h. a labelled vector arrow, v 1
11.7 Velocity en you are outide and notice a brik wind blowing, or you are riding in a car at 60 km/, you are imply conidering te peed of motion a calar quantity. ometime, owever, direction i alo important
24P 2, where W (measuring tape weight per meter) = 0.32 N m
Ue of a 1W Laer to Verify the Speed of Light David M Verillion PHYS 375 North Carolina Agricultural and Technical State Univerity February 3, 2018 Abtract The lab wa et up to verify the accepted value
We name Functions f (x) or g(x) etc.
Section 2 1B: Function Notation Bot of te equations y 2x +1 and y 3x 2 are functions. It is common to ave two or more functions in terms of x in te same problem. If I ask you wat is te value for y if x
Lecture 10 - Chapter. 4 Wave & Particles II
Announcement Course webpage ttp://igenergy.pys.ttu.edu/~slee/40/ Textbook PHYS-40 Lecture 0 HW3 will be announced on Tuesday Feb. 9, 05 Outline: Lecture 0 - Capter. 4 Wave & Particles II Matter beaving
AP CHEM WKST KEY: Atomic Structure Unit Review p. 1
AP CHEM WKST KEY: Atoic Structure Unit Review p. 1 1) a) ΔE = 2.178 x 10 18 J 1 2 nf 1 n 2i = 2.178 x 10 18 1 1 J 2 2 6 2 = 4.840 x 10 19 J b) E = λ hc λ = E hc = (6.626 x 10 34 J )(2.9979 x 10 4.840 x
The structure of the atoms
Te structure of te atoms Atomos = indivisible University of Pécs, Medical Scool, Dept. Biopysics All tat exists are atoms and empty space; everyting else is merely tougt to exist. Democritus, 415 B.C.
s s 1 s = m s 2 = 0; Δt = 1.75s; a =? mi hr
Flipping Phyic Lecture Note: Introduction to Acceleration with Priu Brake Slaing Exaple Proble a Δv a Δv v f v i & a t f t i Acceleration: & flip the guy and ultiply! Acceleration, jut like Diplaceent
Notes on wavefunctions II: momentum wavefunctions
Notes on wavefunctions II: momentum wavefunctions and uncertainty Te state of a particle at any time is described by a wavefunction ψ(x). Tese wavefunction must cange wit time, since we know tat particles
Reminder: Exam 3 Friday, July 6. The Compton Effect. General Physics (PHY 2140) Lecture questions. Show your work for credit.
General Pysics (PHY 2140) Lecture 15 Modern Pysics Cater 27 1. Quantum Pysics Te Comton Effect Potons and EM Waves Wave Proerties of Particles Wave Functions Te Uncertainty Princile Reminder: Exam 3 Friday,
3.1 Extreme Values of a Function
.1 Etreme Values of a Function Section.1 Notes Page 1 One application of te derivative is finding minimum and maimum values off a grap. In precalculus we were only able to do tis wit quadratics by find
Exercises for lectures 20 Digital Control
Exercie for lecture 0 Digital Control Micael Šebek Automatic control 06-4- Sampling: and z relationip for complex pole Continuou ignal Laplace tranform wit pole Dicrete ignal z-tranform, t y( t) e in t,
Answer keys. EAS 1600 Lab 1 (Clicker) Math and Science Tune-up. Note: Students can receive partial credit for the graphs/dimensional analysis.
Anwer key EAS 1600 Lab 1 (Clicker) Math and Science Tune-up Note: Student can receive partial credit for the graph/dienional analyi. For quetion 1-7, atch the correct forula (fro the lit A-I below) to
The Features For Dark Matter And Dark Flow Found.
The Feature For Dark Matter And Dark Flow Found. Author: Dan Vier, Alere, the Netherland Date: January 04 Abtract. Fly-By- and GPS-atellite reveal an earth-dark atter-halo i affecting the orbit-velocitie
Analysis: The speed of the proton is much less than light speed, so we can use the
Section 1.3: Wave Proerties of Classical Particles Tutorial 1 Practice, age 634 1. Given: 1.8! 10 "5 kg # m/s; 6.63! 10 "34 J #s Analysis: Use te de Broglie relation, λ. Solution:! 6.63 " 10#34 kg $ m
Lecture: Experimental Solid State Physics Today s Outline
Lecture: Experimental Solid State Pysics Today s Outline Te quantum caracter of particles : Wave-Particles dualism Heisenberg s uncertainty relation Te quantum structure of electrons in atoms Wave-particle
( ) ! = = = = = = = 0. ev nm. h h hc 5-4. (from Equation 5-2) (a) For an electron:! = = 0. % & (b) For a proton: (c) For an alpha particle:
5-3. ( c) 1 ( 140eV nm) (. )(. ) Ek = evo = = V 940 o = = V 5 m mc e 5 11 10 ev 0 04nm 5-4. c = = = mek mc Ek (from Equation 5-) 140eV nm (a) For an electron: = = 0. 0183nm ( )( 0 511 10 )( 4 5 10 3 )
PhyzExamples: Advanced Electrostatics
PyzExaples: Avance Electrostatics Pysical Quantities Sybols Units Brief Definitions Carge or Q coulob [KOO lo]: C A caracteristic of certain funaental particles. Eleentary Carge e 1.6 10 19 C Te uantity
ATOMIC PHYSICS PREVIOUS EAMCET QUESTIONS ENGINEERING
ATOMIC PHYSICS PREVIOUS EAMCET QUESTIONS ENGINEERING 9. Te work function of a certain metal is. J. Ten te maximum kinetic energy of potoelectrons emitted by incident radiation of wavelengt 5 A is: (9 E)
nucleus orbital electron wave 2/27/2008 Quantum ( F.Robilliard) 1
r nucleus orbital electron wave λ /7/008 Quantum ( F.Robilliard) 1 Wat is a Quantum? A quantum is a discrete amount of some quantity. For example, an atom is a mass quantum of a cemical element te mass
ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER /2019
ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS MATH00030 SEMESTER 208/209 DR. ANTHONY BROWN 6. Differential Calculus 6.. Differentiation from First Principles. In tis capter, we will introduce
UNIT-1 MODERN PHYSICS
UNIT- MODERN PHYSICS Introduction to blackbody radiation spectrum: A body wic absorbs all radiation tat is incident on it is called a perfect blackbody. Wen radiation allowed to fall on suc a body, it
Problem Set 3: Solutions
University of Alabama Department of Pysics and Astronomy PH 253 / LeClair Spring 2010 Problem Set 3: Solutions 1. Te energy required to break one OO bond in ozone O 3, OOO) is about 500 kj/mol. Wat is
Lab 6 Derivatives and Mutant Bacteria
Lab 6 Derivatives and Mutant Bacteria Date: September 27, 20 Assignment Due Date: October 4, 20 Goal: In tis lab you will furter explore te concept of a derivative using R. You will use your knowledge
5.1 The derivative or the gradient of a curve. Definition and finding the gradient from first principles
Capter 5: Dierentiation In tis capter, we will study: 51 e derivative or te gradient o a curve Deinition and inding te gradient ro irst principles 5 Forulas or derivatives 5 e equation o te tangent line
Derivative at a point
Roberto s Notes on Differential Calculus Capter : Definition of derivative Section Derivative at a point Wat you need to know already: Te concept of liit and basic etods for coputing liits. Wat you can
The Schrödinger Equation and the Scale Principle
Te Scrödinger Equation and te Scale Princile RODOLFO A. FRINO Jul 014 Electronics Engineer Degree fro te National Universit of Mar del Plata - Argentina rodolfo_frino@aoo.co.ar Earlier tis ear (Ma) I wrote
Exponentials and Logarithms Review Part 2: Exponentials
Eponentials and Logaritms Review Part : Eponentials Notice te difference etween te functions: g( ) and f ( ) In te function g( ), te variale is te ase and te eponent is a constant. Tis is called a power
6.4: THE WAVE BEHAVIOR OF MATTER
6.4: THE WAVE BEHAVIOR OF MATTER SKILLS TO DEVELOP To understand te wave particle duality of matter. Einstein s potons of ligt were individual packets of energy aving many of te caracteristics of particles.
Math 124. Section 2.6: Limits at infinity & Horizontal Asymptotes. 1 x. lim
Mat 4 Section.6: Limits at infinity & Horizontal Asymptotes Tolstoy, Count Lev Nikolgevic (88-90) A man is like a fraction wose numerator is wat e is and wose denominator is wat e tinks of imself. Te larger
The Electromagnetic Spectrum. Today
Today Announcements: HW#7 is due after Spring Break on Wednesday Marc 1 t Exam # is on Tursday after Spring Break Te fourt extra credit project will be a super bonus points project. Tis extra credit can
Pearson Physics Level 30 Unit VII Electromagnetic Radiation: Chapter 14 Solutions
Pearon Pyic Level 30 Unit VII Electromagnetic Radiation: Cater 14 Solution Student Book age 704 Concet Ceck Te colour of te tar are a firt indication of te temerature of teir urface. Te brigt red tar,
Conditions for equilibrium (both translational and rotational): 0 and 0
Leon : Equilibriu, Newton econd law, Rolling, Angular Moentu (Section 8.3- Lat tie we began dicuing rotational dynaic. We howed that the rotational inertia depend on the hape o the object and the location
QUESTIONS ) Of the following the graph which represents the variation of Energy (E) of the photon with the wavelength (λ) is E E 1) 2) 3) 4)
CET II PUC: PHYSICS: ATOMIC PHYSICS INTRODUCTION TO ATOMIC PHYSICS, PHOTOELECTRIC EFFECT DUAL NATURE OF MATTER, BOHR S ATOM MODEL SCATTERING OF LIGHT and LASERS QUESTIONS ) Wic of te following statements
Chapter 10 Light- Reflectiion & Refraction
Capter 0 Ligt- Relectiion & Reraction Intext Questions On Page 68 Question : Deine te principal ocus o a concae irror. Principal ocus o te concae irror: A point on principal axis on wic parallel ligt rays
1watt=1W=1kg m 2 /s 3
Appendix A Matematics Appendix A.1 Units To measure a pysical quantity, you need a standard. Eac pysical quantity as certain units. A unit is just a standard we use to compare, e.g. a ruler. In tis laboratory
These errors are made from replacing an infinite process by finite one.
Introduction :- Tis course examines problems tat can be solved by metods of approximation, tecniques we call numerical metods. We begin by considering some of te matematical and computational topics tat
Solve exponential equations in one variable using a variety of strategies. LEARN ABOUT the Math. What is the half-life of radon?
8.5 Solving Exponential Equations GOAL Solve exponential equations in one variable using a variety of strategies. LEARN ABOUT te Mat All radioactive substances decrease in mass over time. Jamie works in
LAB #3: ELECTROSTATIC FIELD COMPUTATION
ECE 306 Revised: 1-6-00 LAB #3: ELECTROSTATIC FIELD COMPUTATION Purpose During tis lab you will investigate te ways in wic te electrostatic field can be teoretically predicted. Bot analytic and nuerical
Dual Nature of matter and radiation: m v 1 c
Dual Nature of matter and radiation: Potons: Electromagnetic radiation travels in space in te form discrete packets of energy called potons. Tese potons travel in straigt line wit te speed of ligt. Important
Quantum Numbers and Rules
OpenStax-CNX module: m42614 1 Quantum Numbers and Rules OpenStax College Tis work is produced by OpenStax-CNX and licensed under te Creative Commons Attribution License 3.0 Abstract Dene quantum number.
SIMG Solution Set #5
SIMG-303-0033 Solution Set #5. Describe completely te state of polarization of eac of te following waves: (a) E [z,t] =ˆxE 0 cos [k 0 z ω 0 t] ŷe 0 cos [k 0 z ω 0 t] Bot components are traveling down te
Continuity and Differentiability Worksheet
Continuity and Differentiability Workseet (Be sure tat you can also do te grapical eercises from te tet- Tese were not included below! Typical problems are like problems -3, p. 6; -3, p. 7; 33-34, p. 7;
M12/4/PHYSI/HPM/ENG/TZ1/XX. Physics Higher level Paper 1. Thursday 10 May 2012 (afternoon) 1 hour INSTRUCTIONS TO CANDIDATES
M12/4/PHYSI/HPM/ENG/TZ1/XX 22126507 Pysics Higer level Paper 1 Tursday 10 May 2012 (afternoon) 1 our INSTRUCTIONS TO CANDIDATES Do not open tis examination paper until instructed to do so. Answer all te
Physics 107 Problem 2.5 O. A. Pringle h Physics 107 Problem 2.6 O. A. Pringle
Pysis 07 Problem 25 O A Pringle 3 663 0 34 700 = 284 0 9 Joules ote I ad to set te zero tolerane ere e 6 0 9 ev joules onversion ator ev e ev = 776 ev Pysis 07 Problem 26 O A Pringle 663 0 34 3 ev
28 64 Ni is - g/mole Se (D)
EXERCISE-0 CHECK YOUR GRASP SELECT THE CORRECT ALTERNATIVE (ONLY ONE CORRECT ANSWER). Te element aving no neutron in te nucleus of its atom is - (A) ydrogen (B) nitrogen (C) elium (D) boron. Te particles
Rules of Differentiation
LECTURE 2 Rules of Differentiation At te en of Capter 2, we finally arrive at te following efinition of te erivative of a function f f x + f x x := x 0 oing so only after an extene iscussion as wat te
Seat: PHYS 1500 (Fall 2006) Exam #2, V1. After : p y = m 1 v 1y + m 2 v 2y = 20 kg m/s + 2 kg v 2y. v 2x = 1 m/s v 2y = 9 m/s (V 1)
Seat: PHYS 1500 (Fall 006) Exa #, V1 Nae: 5 pt 1. Two object are oving horizontally with no external force on the. The 1 kg object ove to the right with a peed of 1 /. The kg object ove to the left with
PHYSICS 151 Notes for Online Lecture 2.3
PHYSICS 151 Note for Online Lecture.3 riction: The baic fact of acrocopic (everda) friction are: 1) rictional force depend on the two aterial that are liding pat each other. bo liding over a waed floor
The Electron in a Potential
Te Electron in a Potential Edwin F. Taylor July, 2000 1. Stopwatc rotation for an electron in a potential For a poton we found tat te and of te quantum stopwatc rotates wit frequency f given by te equation:
Problem Set 7: Potential Energy and Conservation of Energy AP Physics C Supplementary Problems
Proble Set 7: Potential Energy and Conservation of Energy AP Pysics C Suppleentary Probles 1. Approxiately 5.5 x 10 6 kg of water drops 50 over Niagara Falls every second. (a) Calculate te aount of potential
3.4 Worksheet: Proof of the Chain Rule NAME
Mat 1170 3.4 Workseet: Proof of te Cain Rule NAME Te Cain Rule So far we are able to differentiate all types of functions. For example: polynomials, rational, root, and trigonometric functions. We are
lecture 35: Linear Multistep Mehods: Truncation Error
88 lecture 5: Linear Multistep Meods: Truncation Error 5.5 Linear ultistep etods One-step etods construct an approxiate solution x k+ x(t k+ ) using only one previous approxiation, x k. Tis approac enoys
APPENDIXES. Let the following constants be established for those using the active Mathcad
3 APPENDIXES Let te following constants be establised for tose using te active Matcad form of tis book: m.. e 9.09389700 0 3 kg Electron rest mass. q.. o.6077330 0 9 coul Electron quantum carge. µ... o.5663706
Chemistry. Slide 1 / 63 Slide 2 / 63. Slide 4 / 63. Slide 3 / 63. Slide 6 / 63. Slide 5 / 63. Optional Review Light and Matter.
Slide 1 / 63 Slide 2 / 63 emistry Optional Review Ligt and Matter 2015-10-27 www.njctl.org Slide 3 / 63 Slide 4 / 63 Ligt and Sound Ligt and Sound In 1905 Einstein derived an equation relating mass and
1 Proving the Fundamental Theorem of Statistical Learning
THEORETICAL MACHINE LEARNING COS 5 LECTURE #7 APRIL 5, 6 LECTURER: ELAD HAZAN NAME: FERMI MA ANDDANIEL SUO oving te Fundaental Teore of Statistical Learning In tis section, we prove te following: Teore.
Chemistry I Unit 3 Review Guide: Energy and Electrons
Cheitry I Unit 3 Review Guide: Energy and Electron Practice Quetion and Proble 1. Energy i the capacity to do work. With reference to thi definition, decribe how you would deontrate that each of the following
REVIEW LAB ANSWER KEY
REVIEW LAB ANSWER KEY. Witout using SN, find te derivative of eac of te following (you do not need to simplify your answers): a. f x 3x 3 5x x 6 f x 3 3x 5 x 0 b. g x 4 x x x notice te trick ere! x x g
Derivatives of trigonometric functions
Derivatives of trigonometric functions 2 October 207 Introuction Toay we will ten iscuss te erivates of te si stanar trigonometric functions. Of tese, te most important are sine an cosine; te erivatives
Derivation Of The Schwarzschild Radius Without General Relativity
Derivation Of Te Scwarzscild Radius Witout General Relativity In tis paper I present an alternative metod of deriving te Scwarzscild radius of a black ole. Te metod uses tree of te Planck units formulas:
PHYSICS 211 MIDTERM II 12 May 2004
PHYSIS IDTER II ay 004 Exa i cloed boo, cloed note. Ue only your forula heet. Write all wor and anwer in exa boolet. The bac of page will not be graded unle you o requet on the front of the page. Show
CHAPTER 4 QUANTUM PHYSICS
CHAPTER 4 QUANTUM PHYSICS INTRODUCTION Newton s corpuscular teory of ligt fails to explain te penomena like interference, diffraction, polarization etc. Te wave teory of ligt wic was proposed by Huygen
Addition of Angular Momentum
Addition of Angula Moentu We ve leaned tat angula oentu i ipotant in quantu ecanic Obital angula oentu L Spin angula oentu S Fo ultielecton ato, we need to lean to add angula oentu Multiple electon, eac
4 Conservation of Momentum
hapter 4 oneration of oentu 4 oneration of oentu A coon itake inoling coneration of oentu crop up in the cae of totally inelatic colliion of two object, the kind of colliion in which the two colliding
Preface. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
Preface Here are my online notes for my course tat I teac ere at Lamar University. Despite te fact tat tese are my class notes, tey sould be accessible to anyone wanting to learn or needing a refreser
MAT244 - Ordinary Di erential Equations - Summer 2016 Assignment 2 Due: July 20, 2016
MAT244 - Ordinary Di erential Equations - Summer 206 Assignment 2 Due: July 20, 206 Full Name: Student #: Last First Indicate wic Tutorial Section you attend by filling in te appropriate circle: Tut 0
Math 31A Discussion Notes Week 4 October 20 and October 22, 2015
Mat 3A Discussion Notes Week 4 October 20 and October 22, 205 To prepare for te first midterm, we ll spend tis week working eamples resembling te various problems you ve seen so far tis term. In tese notes
Combining functions: algebraic methods
Combining functions: algebraic metods Functions can be added, subtracted, multiplied, divided, and raised to a power, just like numbers or algebra expressions. If f(x) = x 2 and g(x) = x + 2, clearly f(x)
This appendix derives Equations (16) and (17) from Equations (12) and (13).
Capital growt pat of te neoclaical growt model Online Supporting Information Ti appendix derive Equation (6) and (7) from Equation () and (3). Equation () and (3) owed te evolution of pyical and uman capital
Solution to Theoretical Question 1. A Swing with a Falling Weight. (A1) (b) Relative to O, Q moves on a circle of radius R with angular velocity θ, so
Solution to Theoretical uetion art Swing with a Falling Weight (a Since the length of the tring Hence we have i contant, it rate of change ut be zero 0 ( (b elative to, ove on a circle of radiu with angular
Phy 212: General Physics II 1/31/2008 Chapter 17 Worksheet: Waves II 1
Phy : General Phyic /3/008 Chapter 7 orkheet: ae. Ethanol ha a denity o 659 kg/ 3. the peed o in ethanol i 6 /, what i it adiabatic bulk odulu? 9 N B = ρ = 8.90x0 ethanol ethanol. A phyic tudent eaure
2.3 Formulas. Evaluating Formulas. EXAMPLE 1 Event promotion. Event promoters use the formula. Evaluating Formulas a Solving for a Variable
2.3 Formula Evaluating Formula a Solving for a Variable Many application of matematic involve relationip among two or more quantitie. An equation tat repreent uc a relationip will ue two or more letter
Introduction. Learning Objectives. On completion of this chapter you will be able to:
Introduction Learning Objectives On completion of tis capter you will be able to: 1. Define Compton Effect. 2. Derive te sift in incident ligt wavelengt and Compton wavelengt. 3. Explain ow te Compton
Derivatives of Exponentials
mat 0 more on derivatives: day 0 Derivatives of Eponentials Recall tat DEFINITION... An eponential function as te form f () =a, were te base is a real number a > 0. Te domain of an eponential function
15 N 5 N. Chapter 4 Forces and Newton s Laws of Motion. The net force on an object is the vector sum of all forces acting on that object.
Chapter 4 orce and ewton Law of Motion Goal for Chapter 4 to undertand what i force to tudy and apply ewton irt Law to tudy and apply the concept of a and acceleration a coponent of ewton Second Law to
Work and Energy. Introduction. Work. PHY energy - J. Hedberg
Work and Energy PHY 207 - energy - J. Hedberg - 2017 1. Introduction 2. Work 3. Kinetic Energy 4. Potential Energy 5. Conservation of Mecanical Energy 6. Ex: Te Loop te Loop 7. Conservative and Non-conservative
Exam 1 Review Solutions
Exam Review Solutions Please also review te old quizzes, and be sure tat you understand te omework problems. General notes: () Always give an algebraic reason for your answer (graps are not sufficient),
Lasers & Optical Fibers
Lasers & Optical Fibers 1. Emmission of a poton by an excited atom due to interaction wit passing poton nearby is called A) Spontaneous emission B) Stimulated emission C) induced absorption D) termionic
2.2 WAVE AND PARTICLE DUALITY OF RADIATION
Quantum Mecanics.1 INTRODUCTION Te motion of particles wic can be observed directly or troug microscope can be explained by classical mecanics. But wen te penomena like potoelectric effect, X-rays, ultraviolet
Preview from Notesale.co.uk Page 2 of 42
1 PHYSICAL CHEMISTRY Dalton (1805) Tomson (1896) - Positive and negative carges Ruterford (1909) - Te Nucleus Bor (1913) - Energy levels Atomic Model : Timeline CATHODE RAYS THE DISCOVERY OF ELECTRON Scrödinger
CHAPTER 7 QUANTUM THEORY AND ATOMIC STRUCTURE
CHAPTER 7 QUANTUM THEORY AND ATOMIC STRUCTURE Te value for te speed of ligt will be 3.00x0 8 m/s except wen more significant figures are necessary, in wic cases,.9979x0 8 m/s will be used. TOOLS OF THE
Higher Derivatives. Differentiable Functions
Calculus 1 Lia Vas Higer Derivatives. Differentiable Functions Te second derivative. Te derivative itself can be considered as a function. Te instantaneous rate of cange of tis function is te second derivative.
Contents. Theory Exercise Exercise Exercise Exercise Answer Key 28-29
ATOMIC STRUCTURE Topic Contents Page No. Teory 0-04 Exercise - 05-4 Exercise - 5-9 Exercise - 3 0-3 Exercise - 4 4-7 Answer Key 8-9 Syllabus Bor model, spectrum of ydrogen atom, quantum numbers; Wave-particle
MVT and Rolle s Theorem
AP Calculus CHAPTER 4 WORKSHEET APPLICATIONS OF DIFFERENTIATION MVT and Rolle s Teorem Name Seat # Date UNLESS INDICATED, DO NOT USE YOUR CALCULATOR FOR ANY OF THESE QUESTIONS In problems 1 and, state