3.15 NMR spectroscopy Different types of NMR There are two main types of NMR 1. C 13 NMR 2. H (proton) NMR
|
|
- Donald Stokes
- 6 years ago
- Views:
Transcription
1 .5 NMR spetrosopy Different types of NMR There re two min types of NMR. NMR. (proton) NMR There is only round % in orgni moleules ut modern NMR mhines re sensitive enough to give full spetr for The spetr is simpler spetrum thn the NMR Equivlent ron toms. In NMR spetrum, there is one signl (pek) for eh set of equivlent toms. d d 4 peks peks 4 peks, dinitroenzene, dinitroenzene,4 dinitroenzene N l peks peks N 4 peks peks d peks d e N 5 peks Equivlent ydrogen toms. In n NMR spetrum, there is one signl for eh set of equivlent toms. In ddition the intensity (integrtion vlue) of eh signl is proportionl to the numer of equivlent toms it represents. Ethnol hs groups of different hydrogen toms d d d 4sets of equivlent s: rtio 6::: signl sets of equivlent s: rtio ::9 sets of equivlent s: rtio :: sets of equivlent s: rtio :: Br d 4 sets of equivlent s: rtio ::: N Goly hemrevise.org
2 Solvents Smples re dissolved in solvents without ny toms, e.g. l 4, Dl. This mens tht in the NMR the solvent will not give ny peks The sme solvent is used in NMR nd in this se there will e one pek due to the solvent tht will pper on the spetrum. owever, it is known where this pek is so it n e ignored. In the exm it is likely this pek will not our on the spetr. lirtion nd shift A smll mount of TMS (tetrmethylsilne) is dded to the smple to lirte the spetrum TMS is used euse: its signl is wy from ll the others it only gives one signl it is non-toxi it is inert it hs low oiling point nd so n e removed from smple esily Si tetrmethylsilne The sme lirtion ompound is used for oth nd NMR The spetr re reorded on sle known s the hemil shift (δ), whih is how muh the field hs shifted wy from the field for TMS.. The δ is mesure in prts per million (ppm) is reltive sle of how fr the frequeny of the proton signl hs shifted wy from tht for TMS δ hemil shift (ppm) 0 NMR shift The δ depends on wht other toms/groups re ner the more eletronegtive groups gives greter shift. δ ppm N Goly hemrevise.org δ ppm
3 NMR shift ppm N Goly hemrevise.org
4 Spin-Spin oupling in Nmr In high resolution NMR eh signl in the spetrum n e split into further lines due to inequivlent s on neighouring toms. Nulei in identil hemil environments do not show oupling mongst themselves! Splitting of pek = numer of inequivlent s on neighouring toms + signl singlet doulet triplet qurtet pperne Split numer of peks numer of neighouring inequivlent toms 4 0 reltive size : :: ::: The pek due to group will e triplet s it is next to ( ron with s) The pek due to group will e qurtet s it is next to ( ron with s) The pek due to group will e singlet s it is next to ron with no s) The pek due to group will e triplet s it is next to ron with s Shift Integrtion tre The pek due to group will e singlet s it is next to ron with 0 s Shift.-.6 Integrtion tre The pek due to group will e qurtet s it is next to ron with s Shift.7-4. Integrtion tre ppm ydrogens onded to Nitrogen or xygen usully do not ouple with other protons nd pper s singlets on the NMR spetr The pek due to group will e triplet s it is next to ron with s Shift Integrtion tre The pek due to group will e qurtet s it is next to ron with s Shift.7-4. Integrtion tre Ethnol The pek due to group will e singlet s the ydrogen is onded to n oxygen nd this does not split Shift Integrtion tre N Goly hemrevise.org 4
5 Bringing it ll together. Work out empiril formul Elementl nlysis 66.6%.8%.9%. Using moleulr ion pek m/z vlue from mss spetrum lulte Moleulr formul moleulr ion pek m/z vlue= /.8/.9/6 =5.555 =.8 = =4 =8 = Mr empiril formul 4 8 = 7 If Mr moleulr formul 44 then ompound is 8 6. Use IR spetr to identify min onds/funtionl group 8 6 ould e n ester, roxyli id or omintion of lohol nd ronyl. Look for IR spetr for = nd - onds There is = ut no - sorptions, so must e n ester. - = 4. Use NMR spetr to give detils of ron hin 4 peks only 4 different environments. singlet of re 9 At δ =0.9 Mens groups 9 Pek t δ 4 shows Are suggests Qurtet mens next to Pek t δ. shows = Are suggests Singlet mens djent to with no hydrogens Pek t δ. shows R- Are mens Triplet mens next to 5 4 δ ppm Put ll together to give finl struture N Goly hemrevise.org 5
6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR
6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht
More information6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR
6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht
More informationH 4 H 8 N 2. Example 1 A compound is found to have an accurate relative formula mass of It is thought to be either CH 3.
. Spetrosopy Mss spetrosopy igh resolution mss spetrometry n e used to determine the moleulr formul of ompound from the urte mss of the moleulr ion For exmple, the following moleulr formuls ll hve rough
More informationAnalytical Techniques Chromatography
Anlytil Tehniques hromtogrphy hromtogrphy is n nlytil tehnique tht seprtes omponents in mixture etween moile phse nd sttionry phse. Types of hromtogrphy inlude: thin-lyer hromtogrphy (TL) plte is oted
More information22.Analytical Techniques Chromatography
.Anlytil Tehniques hromtogrphy hromtogrphy is n nlytil tehnique tht seprtes omponents in mixture etween moile phse nd sttionry phse. Types of hromtogrphy inlude: thin-lyer hromtogrphy (TL) plte is oted
More informationC Nuclear Magnetic Resonance
Inherent Difficulties Low bundnce of 13 C (1.1% vs, 99.9% for 1 H) Lower gyromgnetic rtio (1/4 tht of 1 H) - 13 C: 67.28 vs. 1 H 267.53-1/2 1,000,000 nuclei t 60 MHz E ΔE +1/2 1,000,009 nuclei t 60 MHz
More informationNondeterministic Automata vs Deterministic Automata
Nondeterministi Automt vs Deterministi Automt We lerned tht NFA is onvenient model for showing the reltionships mong regulr grmmrs, FA, nd regulr expressions, nd designing them. However, we know tht n
More informationCALCULATING REACTING QUANTITIES
MODULE 2 14 WORKSHEET WORKSHEET For multiple-hoie questions 1 5 irle the letter orresponding to the most orret nswer. 1 The lned eqution for the urning of utnol (C 4 H 9 OH) is given elow: C 4 H 9 OH(l)
More informationCS311 Computational Structures Regular Languages and Regular Grammars. Lecture 6
CS311 Computtionl Strutures Regulr Lnguges nd Regulr Grmmrs Leture 6 1 Wht we know so fr: RLs re losed under produt, union nd * Every RL n e written s RE, nd every RE represents RL Every RL n e reognized
More informationChapter 4rth LIQUIDS AND SOLIDS MCQs
Chpter 4rth LIQUIDS AND SOLIDS MCQs Q.1 Ioni solis re hrterize y () low melting points () goo onutivity in soli stte () high vpour pressure () soluility in polr solvents Q.2 Amorphous solis. () hve shrp
More information1 This question is about mean bond enthalpies and their use in the calculation of enthalpy changes.
1 This question is out men ond enthlpies nd their use in the lultion of enthlpy hnges. Define men ond enthlpy s pplied to hlorine. Explin why the enthlpy of tomistion of hlorine is extly hlf the men ond
More informationTrigonometry Revision Sheet Q5 of Paper 2
Trigonometry Revision Sheet Q of Pper The Bsis - The Trigonometry setion is ll out tringles. We will normlly e given some of the sides or ngles of tringle nd we use formule nd rules to find the others.
More informationScientific notation is a way of expressing really big numbers or really small numbers.
Scientific Nottion (Stndrd form) Scientific nottion is wy of expressing relly big numbers or relly smll numbers. It is most often used in scientific clcultions where the nlysis must be very precise. Scientific
More informationFundamentals of Analytical Chemistry
Homework Fundmentls of nlyticl hemistry hpter 9 0, 1, 5, 7, 9 cids, Bses, nd hpter 9(b) Definitions cid Releses H ions in wter (rrhenius) Proton donor (Bronsted( Lowry) Electron-pir cceptor (Lewis) hrcteristic
More informationSection 1.3 Triangles
Se 1.3 Tringles 21 Setion 1.3 Tringles LELING TRINGLE The line segments tht form tringle re lled the sides of the tringle. Eh pir of sides forms n ngle, lled n interior ngle, nd eh tringle hs three interior
More informationNumbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point
GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply
More informationGeneralization of 2-Corner Frequency Source Models Used in SMSIM
Generliztion o 2-Corner Frequeny Soure Models Used in SMSIM Dvid M. Boore 26 Mrh 213, orreted Figure 1 nd 2 legends on 5 April 213, dditionl smll orretions on 29 My 213 Mny o the soure spetr models ville
More informationElectronic Supporting Information for
Eletroni Supplementry Mteril (ESI) for Polymer Chemistry. This journl is The Royl Soiety of Chemistry 2016 Eletroni Supporting Informtion for BODIPY Bse Hyperbrnhe Conjugte Polymers for Deteting Orgni
More information4-cyanopentanoic acid dithiobenzoate (CPADB) was synthesized as reported by Y.
Eletroni upplementry Mteril (EI) for Journl of Mterils Chemistry B This journl is The Royl oiety of Chemistry 2012 ynthesis of 4-ynopentnoi id dithioenzote (CPADB). 4-ynopentnoi id dithioenzote (CPADB)
More informationSUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
More informationLECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry
LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of
More informationNUCLEAR MAGNETIC RESONANCE SPECTROSCOPY
NMR Spectroscopy 1 NULEAR MAGNETI RESONANE SPETROSOPY Involves interaction of materials with the low-energy radiowave region of the electromagnetic spectrum Origin of Spectra Theory All nuclei possess
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More information( ) Same as above but m = f x = f x - symmetric to y-axis. find where f ( x) Relative: Find where f ( x) x a + lim exists ( lim f exists.
AP Clculus Finl Review Sheet solutions When you see the words This is wht you think of doing Find the zeros Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor Find
More informationImproper Integrals. The First Fundamental Theorem of Calculus, as we ve discussed in class, goes as follows:
Improper Integrls The First Fundmentl Theorem of Clculus, s we ve discussed in clss, goes s follows: If f is continuous on the intervl [, ] nd F is function for which F t = ft, then ftdt = F F. An integrl
More informationContinuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom
Lerning Gols Continuous Rndom Vriles Clss 5, 8.05 Jeremy Orloff nd Jonthn Bloom. Know the definition of continuous rndom vrile. 2. Know the definition of the proility density function (pdf) nd cumultive
More informationProject 6: Minigoals Towards Simplifying and Rewriting Expressions
MAT 51 Wldis Projet 6: Minigols Towrds Simplifying nd Rewriting Expressions The distriutive property nd like terms You hve proly lerned in previous lsses out dding like terms ut one prolem with the wy
More informationPhysics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:
Physics 121 Smple Common Exm 1 NOTE: ANSWERS ARE ON PAGE 8 Nme (Print): 4 Digit ID: Section: Instructions: Answer ll questions. uestions 1 through 16 re multiple choice questions worth 5 points ech. You
More information4. NMR spectra. Interpreting NMR spectra. Low-resolution NMR spectra. There are two kinds: Low-resolution NMR spectra. High-resolution NMR spectra
1 Interpreting NMR spectra There are two kinds: Low-resolution NMR spectra High-resolution NMR spectra In both cases the horizontal scale is labelled in terms of chemical shift, δ, and increases from right
More informationwhere the box contains a finite number of gates from the given collection. Examples of gates that are commonly used are the following: a b
CS 294-2 9/11/04 Quntum Ciruit Model, Solovy-Kitev Theorem, BQP Fll 2004 Leture 4 1 Quntum Ciruit Model 1.1 Clssil Ciruits - Universl Gte Sets A lssil iruit implements multi-output oolen funtion f : {0,1}
More informationLinear Algebra Introduction
Introdution Wht is Liner Alger out? Liner Alger is rnh of mthemtis whih emerged yers k nd ws one of the pioneer rnhes of mthemtis Though, initilly it strted with solving of the simple liner eqution x +
More informationChapter E - Problems
Chpter E - Prolems Blinn College - Physics 2426 - Terry Honn Prolem E.1 A wire with dimeter d feeds current to cpcitor. The chrge on the cpcitor vries with time s QHtL = Q 0 sin w t. Wht re the current
More information1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.
1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the
More informationName Solutions to Test 3 November 8, 2017
Nme Solutions to Test 3 November 8, 07 This test consists of three prts. Plese note tht in prts II nd III, you cn skip one question of those offered. Some possibly useful formuls cn be found below. Brrier
More information15. Quantisation Noise and Nonuniform Quantisation
5. Quntistion Noise nd Nonuniform Quntistion In PCM, n nlogue signl is smpled, quntised, nd coded into sequence of digits. Once we hve quntised the smpled signls, the exct vlues of the smpled signls cn
More informationNuclear Spin States. NMR Phenomenon. NMR Instrumentation. NMR Active Nuclei. Nuclear Magnetic Resonance
Nuclear Magnetic Resonance NMR Phenomenon µ A spinning charged particle generates a magnetic field. A nucleus with a spin angular momentum will generate a magnetic moment (!). E Nuclear Spin States aligned
More informationLecture 6. Notes. Notes. Notes. Representations Z A B and A B R. BTE Electronics Fundamentals August Bern University of Applied Sciences
Lecture 6 epresenttions epresenttions TE52 - Electronics Fundmentls ugust 24 ern University of pplied ciences ev. c2d5c88 6. Integers () sign-nd-mgnitude representtion The set of integers contins the Nturl
More informationCHEM 322 Laboratory Methods in Organic Chemistry. Introduction to NMR Spectroscopy
EM 322 Laboratory Methods in Organic hemistry Introduction to NMR Spectroscopy What structural information does NMR spectroscopy provide? 1) hemical shift (δ) data reveals the molecular (functional group)
More informationTuesday, January 13, NMR Spectroscopy
NMR Spectroscopy NMR Phenomenon Nuclear Magnetic Resonance µ A spinning charged particle generates a magnetic field. A nucleus with a spin angular momentum will generate a magnetic moment (μ). If these
More informationSOLUTIONS TO ASSIGNMENT NO The given nonrecursive signal processing structure is shown as
SOLUTIONS TO ASSIGNMENT NO.1 3. The given nonreursive signl proessing struture is shown s X 1 1 2 3 4 5 Y 1 2 3 4 5 X 2 There re two ritil pths, one from X 1 to Y nd the other from X 2 to Y. The itertion
More informationCHEMISTRY 216 WINTER TERM 2007 END OF TERM EXAM. Time Allowed 2 hours
EMISTRY 216 WITER TERM 2007 ED F TERM EXAM Time Allowed 2 hours ame KEY GSI ame ID umber Lab Section Write legibly. Illegible or messy answers will not be graded. Read these instructions carefully. In
More informationComparing the Pre-image and Image of a Dilation
hpter Summry Key Terms Postultes nd Theorems similr tringles (.1) inluded ngle (.2) inluded side (.2) geometri men (.) indiret mesurement (.6) ngle-ngle Similrity Theorem (.2) Side-Side-Side Similrity
More information332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006
2:221 Principles of Electricl Engineering I Fll 2006 Nme of the student nd ID numer: Hourly Exm 2 Novemer 6, 2006 This is closed-ook closed-notes exm. Do ll your work on these sheets. If more spce is required,
More informationThe Properties of Stars
10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product
More informationChem Homework 11 due Monday, Apr. 28, 2014, 2 PM
Chem 44 - Homework due ondy, pr. 8, 4, P.. . Put this in eq 8.4 terms: E m = m h /m e L for L=d The degenery in the ring system nd the inresed sping per level (4x bigger) mkes the sping between the HOO
More information1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
1 PYTHAGORAS THEOREM 1 1 Pythgors Theorem In this setion we will present geometri proof of the fmous theorem of Pythgors. Given right ngled tringle, the squre of the hypotenuse is equl to the sum of the
More informationCEM143 MWF 8:00 8:50 am. October 5, 2018
CEM43, Fll 208 st Miterm CEM43 MWF 8:00 8:50 m st Miterm toer 5, 208 Nme: Setion: PID: TA: This is lose ook n note exmintion. This exm hs 35 questions. Answer ll questions on the seprte nswer sheet (ule
More informationCEM143 MWF 8:00 8:50 am. October 5, 2018
CEM43, Fll 208 st Miterm CEM43 MWF 8:00 8:50 m st Miterm toer 5, 208 Nme: Setion: PID: TA: This is lose ook n note exmintion. This exm hs 35 questions. Answer ll questions on the seprte nswer sheet (ule
More informationChapter 2. Typology of Polymers
Chpter 2. Typology of Polymers 2.1 Types of bonds in Polymers 1. primry ovlent nd metlli bonds 2. hydrogen bonding 3. dipole intertion 2nd fore 4. dispersion fore (vn der Wls fore) 5. ioni bond e.g.) polyproltone,
More informationVectors. a Write down the vector AB as a column vector ( x y ). A (3, 2) x point C such that BC = 3. . Go to a OA = a
Streth lesson: Vetors Streth ojetives efore you strt this hpter, mrk how onfident you feel out eh of the sttements elow: I n lulte using olumn vetors nd represent the sum nd differene of two vetors grphilly.
More informationIntro to Nuclear and Particle Physics (5110)
Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n-1)/ E/[ n(n-1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41
More information9-1 (a) A weak electrolyte only partially ionizes when dissolved in water. NaHCO 3 is an
Chpter 9 9- ( A ek electrolyte only prtilly ionizes hen dissolved in ter. NC is n exmple of ek electrolyte. (b A Brønsted-ory cid is cule tht dontes proton hen it encounters bse (proton cceptor. By this
More informationAcid-Base Equilibria
Tdeusz Górecki Ionic Equiliri Acid-Bse Equiliri Brønsted-Lory: n cid is proton, se is. Acid Bse ( 3 PO 4, O), ( N 4 ) nd ( PO - 4 ) cn ll ehve s cids. Exmple: 4 N N3 Sustnces hich cn ehve oth s cids nd
More informationChapter 13. R.F.----µ-wave----I.R. (Heat)------Visible------U.V X-Ray------γ-Ray SPECTROSCOPY. Definition: Types to Be Covered:
hamras Glendale ommunity ollege rganic hemistry 105 Exam 4 Materials hapter 13 SPETRSPY Definition: Types to Be overed: A) Infrared Spectroscopy (IR) B) Nuclear Magnetic Resonance Spectroscopy (NMR) )
More informationBOND ORDER (BO): Single bond Þ BO = 1; Double bond Þ BO = 2; Triple bond Þ BO = 3 Bond Order Þ bond strength and bond length
EMISTRY 104 elp Sheet #1 hem 103 Review (Text: h 6, h 7) Do topics pproprite for your lecture Prepred y Dr. Tony Jco http://www.chem.wisc.edu/res/clc (Resource pge) Nuggets: Electronegtivity (6.7), Bond
More informationMAT 403 NOTES 4. f + f =
MAT 403 NOTES 4 1. Fundmentl Theorem o Clulus We will proo more generl version o the FTC thn the textook. But just like the textook, we strt with the ollowing proposition. Let R[, ] e the set o Riemnn
More informationPoly(vinylamine) Microgels: ph-responsive Particles with High Primary Amine Contents
SUPPLEMENTARY INFORMATION Poly(vinylmine) Microgels: ph-responsive Prticles with High Primry Amine Contents Sineent Thioonro, Cory Berkln, Amir H. Milni, Rein Ulijn c n Brin R. Suners, * Polymer Science
More informationChapter 6 Continuous Random Variables and Distributions
Chpter 6 Continuous Rndom Vriles nd Distriutions Mny economic nd usiness mesures such s sles investment consumption nd cost cn hve the continuous numericl vlues so tht they cn not e represented y discrete
More information2.4 Linear Inequalities and Interval Notation
.4 Liner Inequlities nd Intervl Nottion We wnt to solve equtions tht hve n inequlity symol insted of n equl sign. There re four inequlity symols tht we will look t: Less thn , Less thn or
More informationUV-Induced Self-Repairing Polydimethylsiloxane-Polyurethane (PDMS-PUR) Cu- Catalyzed Networks
Eletroni Supplementry Mteril (ESI) for Journl of Mterils Chemistry A. This journl is The Royl Soiety of Chemistry 2014 Supporting Online Mterils UV-Indued Self-Repiring Polydimethylsiloxne-Polyurethne
More informationLogarithms LOGARITHMS.
Logrithms LOGARITHMS www.mthletis.om.u Logrithms LOGARITHMS Logrithms re nother method to lulte nd work with eponents. Answer these questions, efore working through this unit. I used to think: In the
More informationThe final exam will take place on Friday May 11th from 8am 11am in Evans room 60.
Mth 104: finl informtion The finl exm will tke plce on Fridy My 11th from 8m 11m in Evns room 60. The exm will cover ll prts of the course with equl weighting. It will cover Chpters 1 5, 7 15, 17 21, 23
More informationQuantum Mechanics Qualifying Exam - August 2016 Notes and Instructions
Quntum Mechnics Qulifying Exm - August 016 Notes nd Instructions There re 6 problems. Attempt them ll s prtil credit will be given. Write on only one side of the pper for your solutions. Write your lis
More informationInterpreting Integrals and the Fundamental Theorem
Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of
More informationAP CALCULUS Test #6: Unit #6 Basic Integration and Applications
AP CALCULUS Test #6: Unit #6 Bsi Integrtion nd Applitions A GRAPHING CALCULATOR IS REQUIRED FOR SOME PROBLEMS OR PARTS OF PROBLEMS IN THIS PART OF THE EXAMINATION. () The ext numeril vlue of the orret
More informationNon Right Angled Triangles
Non Right ngled Tringles Non Right ngled Tringles urriulum Redy www.mthletis.om Non Right ngled Tringles NON RIGHT NGLED TRINGLES sin i, os i nd tn i re lso useful in non-right ngled tringles. This unit
More informationChapter 0. What is the Lebesgue integral about?
Chpter 0. Wht is the Lebesgue integrl bout? The pln is to hve tutoril sheet ech week, most often on Fridy, (to be done during the clss) where you will try to get used to the ides introduced in the previous
More informationEigenvectors and Eigenvalues
MTB 050 1 ORIGIN 1 Eigenvets n Eigenvlues This wksheet esries the lger use to lulte "prinipl" "hrteristi" iretions lle Eigenvets n the "prinipl" "hrteristi" vlues lle Eigenvlues ssoite with these iretions.
More informationLesson 1.6 Exercises, pages 68 73
Lesson.6 Exercises, pges 68 7 A. Determine whether ech infinite geometric series hs finite sum. How do you know? ) + +.5 + 6.75 +... r is:.5, so the sum is not finite. b) 0.5 0.05 0.005 0.0005... r is:
More informationWeek 10: Line Integrals
Week 10: Line Integrls Introduction In this finl week we return to prmetrised curves nd consider integrtion long such curves. We lredy sw this in Week 2 when we integrted long curve to find its length.
More informationa) Read over steps (1)- (4) below and sketch the path of the cycle on a P V plot on the graph below. Label all appropriate points.
Prole 3: Crnot Cyle of n Idel Gs In this prole, the strting pressure P nd volue of n idel gs in stte, re given he rtio R = / > of the volues of the sttes nd is given Finlly onstnt γ = 5/3 is given You
More informationReading from Young & Freedman: For this topic, read the introduction to chapter 24 and sections 24.1 to 24.5.
PHY1 Electricity Topic 5 (Lectures 7 & 8) pcitors nd Dielectrics In this topic, we will cover: 1) pcitors nd pcitnce ) omintions of pcitors Series nd Prllel 3) The energy stored in cpcitor 4) Dielectrics
More informationConsolidation Worksheet
Cmbridge Essentils Mthemtics Core 8 NConsolidtion Worksheet N Consolidtion Worksheet Work these out. 8 b 7 + 0 c 6 + 7 5 Use the number line to help. 2 Remember + 2 2 +2 2 2 + 2 Adding negtive number is
More informationMathematics 10 Page 1 of 5 Properties of Triangle s and Quadrilaterals. Isosceles Triangle. - 2 sides and 2 corresponding.
Mthemtis 10 Pge 1 of 5 Properties of s Pthgoren Theorem 2 2 2 used to find the length of sides of right tringle Tpe of s nd Some s Theorems ngles s Slene Isoseles Equilterl ute - ll ngles re less thn 90
More informationInfinite Geometric Series
Infinite Geometric Series Finite Geometric Series ( finite SUM) Let 0 < r < 1, nd let n be positive integer. Consider the finite sum It turns out there is simple lgebric expression tht is equivlent to
More informationLCM AND HCF. Type - I. Type - III. Type - II
LCM AND HCF Type - I. The HCF nd LCM of two numbers re nd 9 respectively. Then the number of such pirs () 0 () () (SSC CGL Tier-I Exm. 0 Second Sitting). The product of two numbers 08 nd their HCF. The
More informationKey for Chem 130 Second Exam
Nme Key for Chem 130 Second Exm On the following pges you will find questions tht cover the structure of molecules, ions, nd solids, nd the different models we use to explin the nture of chemicl bonding.
More informationFormal languages, automata, and theory of computation
Mälrdlen University TEN1 DVA337 2015 School of Innovtion, Design nd Engineering Forml lnguges, utomt, nd theory of computtion Thursdy, Novemer 5, 14:10-18:30 Techer: Dniel Hedin, phone 021-107052 The exm
More informationGM1 Consolidation Worksheet
Cmridge Essentils Mthemtis Core 8 GM1 Consolidtion Worksheet GM1 Consolidtion Worksheet 1 Clulte the size of eh ngle mrked y letter. Give resons for your nswers. or exmple, ngles on stright line dd up
More information3.1 Review of Sine, Cosine and Tangent for Right Angles
Foundtions of Mth 11 Section 3.1 Review of Sine, osine nd Tngent for Right Tringles 125 3.1 Review of Sine, osine nd Tngent for Right ngles The word trigonometry is derived from the Greek words trigon,
More informationSupporting Information
tom-thik Interlyer Mde of VD-Grown Grphene Film on Seprtor for dvned thium-sulfur tteries Zhenzhen Du 1, hengkun Guo 2, njun Wng 3, jun Hu 1, Song Jin 1, Timing Zhng 1, Honghng Jin 1, Zhiki Qi 1, Sen Xin
More informationI 3 2 = I I 4 = 2A
ECE 210 Eletril Ciruit Anlysis University of llinois t Chigo 2.13 We re ske to use KCL to fin urrents 1 4. The key point in pplying KCL in this prolem is to strt with noe where only one of the urrents
More informationProblem 22: Buffer solutions 1. The equilibrium, which governs the concentration of H + within the solution is HCOOH! HCOO + H + + Hence K
Problem : Buffer solutions. The equilibrium, hich governs the concentrtion of H ithin the solution is HCOOH! HCOO H [HCOO ] 4 Hence. [HCOOH] nd since [HCOOH] 0.00 M nd [HCOO ] 0.50 M -4 0.00 4..8 M 0.50
More informationChapter 1: Fundamentals
Chpter 1: Fundmentls 1.1 Rel Numbers Types of Rel Numbers: Nturl Numbers: {1, 2, 3,...}; These re the counting numbers. Integers: {... 3, 2, 1, 0, 1, 2, 3,...}; These re ll the nturl numbers, their negtives,
More informationLecture 3. In this lecture, we will discuss algorithms for solving systems of linear equations.
Lecture 3 3 Solving liner equtions In this lecture we will discuss lgorithms for solving systems of liner equtions Multiplictive identity Let us restrict ourselves to considering squre mtrices since one
More informationCS 373, Spring Solutions to Mock midterm 1 (Based on first midterm in CS 273, Fall 2008.)
CS 373, Spring 29. Solutions to Mock midterm (sed on first midterm in CS 273, Fll 28.) Prolem : Short nswer (8 points) The nswers to these prolems should e short nd not complicted. () If n NF M ccepts
More informationProject 3: Using Identities to Rewrite Expressions
MAT 5 Projet 3: Usig Idetities to Rewrite Expressios Wldis I lger, equtios tht desrie properties or ptters re ofte lled idetities. Idetities desrie expressio e repled with equl or equivlet expressio tht
More informationNuclear spin and the splitting of energy levels in a magnetic field
Nuclear spin and the splitting of energy levels in a magnetic field Top 3 list for 13 C NMR Interpretation 1. Symmetry 2. Chemical Shifts 3. Multiplicity 13 C NMR of C 3 O 1 NMR of C 3 O 13 C NMR of C
More informationReview of Gaussian Quadrature method
Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge
More informationChemActivity L4: Proton ( 1 H) NMR
hemactivity L: Proton ( ) NMR (What can a NMR spectrum tell you aout the structure of a molecule?) This activity is designed to e completed in a ½ hour laoratory session or two classroom sessions. Model
More informationSpacetime and the Quantum World Questions Fall 2010
Spetime nd the Quntum World Questions Fll 2010 1. Cliker Questions from Clss: (1) In toss of two die, wht is the proility tht the sum of the outomes is 6? () P (x 1 + x 2 = 6) = 1 36 - out 3% () P (x 1
More informationCHAPTER 20: Second Law of Thermodynamics
CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het
More informationg i fφdx dx = x i i=1 is a Hilbert space. We shall, henceforth, abuse notation and write g i f(x) = f
1. Appliction of functionl nlysis to PEs 1.1. Introduction. In this section we give little introduction to prtil differentil equtions. In prticulr we consider the problem u(x) = f(x) x, u(x) = x (1) where
More informationSomething found at a salad bar
Nme PP Something found t sld r 4.7 Notes RIGHT TRINGLE hs extly one right ngle. To solve right tringle, you n use things like SOH-H-TO nd the Pythgoren Theorem. n OLIQUE TRINGLE hs no right ngles. To solve
More informationAP Calculus AB Unit 4 Assessment
Clss: Dte: 0-04 AP Clulus AB Unit 4 Assessment Multiple Choie Identify the hoie tht best ompletes the sttement or nswers the question. A lultor my NOT be used on this prt of the exm. (6 minutes). The slope
More informationHints for Exercise 1 on: Current and Resistance
Hints for Exercise 1 on: Current nd Resistnce Review the concepts of: electric current, conventionl current flow direction, current density, crrier drift velocity, crrier numer density, Ohm s lw, electric
More informationPhysics 2135 Exam 1 February 14, 2017
Exm Totl / 200 Physics 215 Exm 1 Ferury 14, 2017 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the est or most nerly correct nswer. 1. Two chrges 1 nd 2 re seprted
More informationNOT TO SCALE. We can make use of the small angle approximations: if θ á 1 (and is expressed in RADIANS), then
3. Stellr Prllx y terrestril stndrds, the strs re extremely distnt: the nerest, Proxim Centuri, is 4.24 light yers (~ 10 13 km) wy. This mens tht their prllx is extremely smll. Prllx is the pprent shifting
More informationChapter 13: Nuclear Magnetic Resonance (NMR) Spectroscopy direct observation of the H s and C s of a molecules
hapter 13: Nuclear Magnetic Resonance (NMR) Spectroscopy direct observation of the s and s of a molecules Nuclei are positively charged and spin on an axis; they create a tiny magnetic field + + Not all
More informationInstructions. An 8.5 x 11 Cheat Sheet may also be used as an aid for this test. MUST be original handwriting.
ID: B CSE 2021 Computer Orgniztion Midterm Test (Fll 2009) Instrutions This is losed ook, 80 minutes exm. The MIPS referene sheet my e used s n id for this test. An 8.5 x 11 Chet Sheet my lso e used s
More information