Lecture 18 Title : Fine Structure : multi-electron atoms

Size: px
Start display at page:

Download "Lecture 18 Title : Fine Structure : multi-electron atoms"

Transcription

1 Lecture 8 Title : Fine Structure : multi-electrn atms Page-0 In this lecture we will cncentrate n the fine structure f the multielectrn atms. As discussed in the previus lecture that the fine structure arises due t spin rbit cupling. Here we will discuss abut the spin rbit cupling in case f mre than ne electrn and their effect n terms transitins.

2 Page- The Hamiltnian fr the multielectrn atms * H = H + H + HSpin Orbit where H where N N * = i + me i= i= U ( ri ) = + N Ze r ( ) U r N i i= i i< j i e r ij J and H N e = r N i< j ij i< j e r H = A l. s Spin Orbit i i ij Nn-Spherical part nly L The Spin-rbit interactin cuples the ttal spin and ttal rbital angular mmentum (L) t frm the ttal angular mmentum J. S The figure-8. represents the vectr diagram and accrdingly we write l s l J = L + S (fr ne electrn atms). s Because f this cupling, the ne electrn wavefunctins Lm Sm which are the eigenfunctins f l s H CentralField are n mre the eigenfunctins f the ttal Hamiltnian H. + i, j e r ij e H = HCF + + AL. S r i, j l m s m Lm Jm l s L J l m s m Figure 8. l s s ij Sm

3 Page- The eigenfunctins f the H will be Jm J which are the cupled wavefunctins and can be derived frm the uncupled wavefunctins Lml Sm s, as described in previus lectures. Accrding t the cupling f angular mmentum the value f J = J = L+ S,... L S and the ntatin is S + L where L= 0,,,,...are SPF,,, respectively. S the perturbatin energy E = Jm A LS. Jm J J Nw, J = L + S J = L + S + LS. LS. = J L S J And thus, the energy crrectin due t the spin-rbit interactin is A E = JmJ ALS. JmJ = [ J( J+ ) L( L+ ) S( S+ ) ] (8.)

4 Page- S + is the knwn as multiplicity. Indicates the degeneracy f the level due t spin. If S = 0 => multiplicity is : singlet term. If S = / => multiplicity is : dublet term. If S = => multiplicity is : triplet term and s n. In the fllwing we will discuss the effect f spin-rbit interactin n terms t terms transitins. Singlet levels S = 0; J = L+ S = L A E = J( J + ) L( L+ ) = 0 P P S S 0 Selectin Rules : l =±, L= 0, ±, S = 0, J = 0, ±

5 Page- ublet levels Transitin frm t P Fr L=, S =, J = 5, Using equatin-8. ( ) ( ) ( ) A E = = A ( ) ( ) ( ) A E = = A Fr P L=, S =, J =, ( ) ( ) ( ) A A E P = = ( ) ( ) ( ) A E P = = A S the cnstructin f energy levels 0 A A 5 P A A P P

6 Page-5 It is imprtant t knw the degeneracy lifted by this spin-rbit interactin. The degeneracy fr level is 0 (L+ )(S+ ) = (. + )(. + ) = 0 When this level splits int 5 and, then the degeneracy is 6 because J = 5, m 5,,,,, 5 J =. All m J levels will 5 be degenerate. The m J degeneracy will nt be lifted until the external magnetic field is applied. Similarly, the degeneracy is because J =, m,,, J =. The degeneracy fr P level is 6 (L+ )(S + ) = (. + )(. + ) = 6 When this level splits int P and P P the degeneracy is because J =, m,,, J =. All m J levels will be degenerate. The m J degeneracy will nt be lifted until the external magnetic field is applied. Similarly, P the degeneracy is because J =, m, J =. We will discuss the later the effect f magnetic field n these levels. Transitins : as shwn in the adjacent figure-8. A Fr transitin = 0 + A Fr transitin = 0 A + A A Fr transitin = 0 A 0 Figure 8. In general A > A s transitin pattern will be > >.

7 Page-6 P transitin Fr term S = L = J =,, S,,, Fr P term S = L = J =,, 0 p, p, p0 Nw, let us calculate the perturbatin energies fr these levels using equatin-8.. We take the spin-rbit cnstants A and A fr and P respectively. A E ( ) = [ 6 ] = A, E ( ) ( ) A E = 6 = A A E ( P) = [ 6 ] = A, E ( P) A ( ) [ ] E P = 0 = A A = 6 6 = A A = = A Transitin energies are = + A A 0 = A A 0 = A + A 0 = A A 0 = A + A 5 0 P P P = A + A 6 0 P 0

8 Page- The Observed transitin f Calcium is given in this figure belw. 5 6 Figure-8. Observed transitins Observed transitins (nm) Observed transitins (cm - ) Calculated transitins (cm - ) = + A A = A A = A + A = A A = A + A = A + A

9 Page-8 Frm transitins and E0 A A =.6 E0 A + A = 5. A = 5..6 = 05. A = 5.85 cm Frm transitins and E0 A A = 8.6 E0 A A =.6 A = A = =.65 cm And 0 = 6.8 cm The ther transitins calculated frm these values are given in the table.

10 Page- Let us take anther example, the transitins f Cpper [d sp] F [d s5s] Fr term S = L = S, J =, 5,,, 5,, Fr F term S = L = J =,, 5, F, F, F5, F Fr F A 5 EJ ( = ) =... A = A 6 6 EJ= = = E ( ) [ ] 0 5 A 5 6 A 8 ( J = ) = [ ] =. = A A 5 6 A 8 E( J = ) = [ ] =. = 6A Fr A 6 A E ( J = ) = [ ] =. = A 5 E J = ) = A 5 [ ] = A. = A ( A 5 A E( J = ) = [ ] =. = A E A A 6 ( J = ) = [ ] =. = A

11 Page-0 The cnstructed energy level diagram is shwn in this figure belw. F F F F 5 F 0 5 Selectin rules: derived frm Wigner-Eckart therem discussed earlier l =±, S = 0, J = 0, ±. The J = 0 J = 0is frbidden. The transitin energies are () v(f ) = A + A () v(f ) = A A () v(f 5 ) = + () v(f5 ) = A A

12 Page- A (5) v(f5 5 ) = A+ (6) v(f5 ) = A+ A A () v(f 5 ) = 6A+ (8) v(f ) = 6A+ A () v(f ) = 6A+ A The experimental set up fr recrding the cpper F spectrum. Cu electrdes Cu arc Fiber ptic cupled spectrmeter High vltage pwer supply The cpper F spectrum. Intensity (arb. units) Cpper (F -> ) Wavelength (nm)

13 Page- Assigning the bserved three transitins as fllws. Transitins Observed wavelength (nm) Observed transitin energy (cm - ) F F 65.. F S we have three equatins belw t slve fr btaining three parameters. A + A =. A = 50.8 A + =. Frm these abve equatins, we get A + =. A = 50.8 A = X 5. A = = cm = *5. = A = =..* A 5. = = cm

14 Page- Transitins Transitin energy Calculated transitin energy (cm - ) Calculated transitins (nm) bserved transitins (nm) F A + A F A A F F 5 A A A F5 5 A F 5 A + A A F 5 6A F 6A + A F 6A + A

15 Page- Summary f Atmic Energy levels Grss structure f the atmic energy levels: It cvers largest interactins within the atm: (a) Kinetic energy f electrns in their rbits. (b) Attractive electrstatic ptential between psitive nucleus and negative electrns (c) Repulsive electrstatic interactin between electrns in a multi-electrn atm. These interactins give energies in the -0 ev range and upwards. It determine the spectrum range whether a phtn is IR, visible, UV r X-ray. Fine structure: Spectral lines ften cme as multiplets. E.g., Hα line. This smaller interactins within atm, called spin-rbit interactin. The rigin f this interactin is Electrns in rbit abut nucleus give rise t magnetic mment which interacts with spin f the electrns. This intrduces splitting f the energy levels and prduces small shift in energy. Hund s rule : () Of the terms given by equivalent electrns, thse with greatest multiplicity lie deepest, and f these the lwest is that with the greatest L () Multiplets frmed equivalent electrns are regular when less than half the shell is ccupied, but inverted when mre than half shell is ccupied.

16 Page-5 Recap In this lecture we have seen the effect f spin rbit cupling n the fine structure f the multielectrn atms. We have discussed the transitins between the varius spin multiplicity energy levels, smetime called as multiplets. We have als gne thrugh the experiments in the cpper transitins and als learnt hw t assign the transitins. We als learnt hw t evaluate the spin-rbit cnstant term fr a level frm the bserved transitins.

Sodium D-line doublet. Lectures 5-6: Magnetic dipole moments. Orbital magnetic dipole moments. Orbital magnetic dipole moments

Sodium D-line doublet. Lectures 5-6: Magnetic dipole moments. Orbital magnetic dipole moments. Orbital magnetic dipole moments Lectures 5-6: Magnetic diple mments Sdium D-line dublet Orbital diple mments. Orbital precessin. Grtrian diagram fr dublet states f neutral sdium shwing permitted transitins, including Na D-line transitin

More information

1 The limitations of Hartree Fock approximation

1 The limitations of Hartree Fock approximation Chapter: Pst-Hartree Fck Methds - I The limitatins f Hartree Fck apprximatin The n electrn single determinant Hartree Fck wave functin is the variatinal best amng all pssible n electrn single determinants

More information

Lecture 13: Electrochemical Equilibria

Lecture 13: Electrochemical Equilibria 3.012 Fundamentals f Materials Science Fall 2005 Lecture 13: 10.21.05 Electrchemical Equilibria Tday: LAST TIME...2 An example calculatin...3 THE ELECTROCHEMICAL POTENTIAL...4 Electrstatic energy cntributins

More information

11. DUAL NATURE OF RADIATION AND MATTER

11. DUAL NATURE OF RADIATION AND MATTER 11. DUAL NATURE OF RADIATION AND MATTER Very shrt answer and shrt answer questins 1. Define wrk functin f a metal? The minimum energy required fr an electrn t escape frm the metal surface is called the

More information

Regents Chemistry Period Unit 3: Atomic Structure. Unit 3 Vocabulary..Due: Test Day

Regents Chemistry Period Unit 3: Atomic Structure. Unit 3 Vocabulary..Due: Test Day Name Skills: 1. Interpreting Mdels f the Atm 2. Determining the number f subatmic particles 3. Determine P, e-, n fr ins 4. Distinguish istpes frm ther atms/ins Regents Chemistry Perid Unit 3: Atmic Structure

More information

Chapter 9: Quantization of Light

Chapter 9: Quantization of Light Chapter 9: Quantizatin Light 9.1 Planck s Quantum Thery 9.1.1 Distinguish between Planck s quantum thery and classical thery energy The undatin the Planck s quantum thery is a thery black bdy radiatin.

More information

Name: Period: Date: ATOMIC STRUCTURE NOTES ADVANCED CHEMISTRY

Name: Period: Date: ATOMIC STRUCTURE NOTES ADVANCED CHEMISTRY Name: Perid: Date: ATOMIC STRUCTURE NOTES ADVANCED CHEMISTRY Directins: This packet will serve as yur ntes fr this chapter. Fllw alng with the PwerPint presentatin and fill in the missing infrmatin. Imprtant

More information

**DO NOT ONLY RELY ON THIS STUDY GUIDE!!!**

**DO NOT ONLY RELY ON THIS STUDY GUIDE!!!** Tpics lists: UV-Vis Absrbance Spectrscpy Lab & ChemActivity 3-6 (nly thrugh 4) I. UV-Vis Absrbance Spectrscpy Lab Beer s law Relates cncentratin f a chemical species in a slutin and the absrbance f that

More information

Interference is when two (or more) sets of waves meet and combine to produce a new pattern.

Interference is when two (or more) sets of waves meet and combine to produce a new pattern. Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme

More information

Physical Nature of the Covalent Bond Appendix H + H > H 2 ( ) ( )

Physical Nature of the Covalent Bond Appendix H + H > H 2 ( ) ( ) Physical Nature f the Cvalent Bn Appeni his stuy f the nature f the H cvalent bn frms a mlecular rbital as a linear cmbinatin f scale hyrgenic rbitals, LCAO-MO. he quantum mechanical integrals necessary

More information

Phy 213: General Physics III 6/14/2007 Chapter 28 Worksheet 1

Phy 213: General Physics III 6/14/2007 Chapter 28 Worksheet 1 Ph 13: General Phsics III 6/14/007 Chapter 8 Wrksheet 1 Magnetic Fields & Frce 1. A pint charge, q= 510 C and m=110-3 m kg, travels with a velcit f: v = 30 ˆ s i then enters a magnetic field: = 110 T ˆj.

More information

s of the two electrons are strongly coupled together to give a l couple together to give a resultant APPENDIX I

s of the two electrons are strongly coupled together to give a l couple together to give a resultant APPENDIX I APPENDIX I Cupling Schemes and Ntatin An extensive treatment f cupling schemes and ntatin is given by White r Kuhn. A brief review is given here t allw ne t read this manual with sme insight. The mtins

More information

Q1. In figure 1, Q = 60 µc, q = 20 µc, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q due to the other 2 charges.

Q1. In figure 1, Q = 60 µc, q = 20 µc, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q due to the other 2 charges. Phys10 Secnd Majr-08 Zer Versin Crdinatr: Dr. I. M. Nasser Saturday, May 3, 009 Page: 1 Q1. In figure 1, Q = 60 µc, q = 0 µc, a = 3.0 m, and b = 4.0 m. Calculate the ttal electric frce n q due t the ther

More information

Differentiation Applications 1: Related Rates

Differentiation Applications 1: Related Rates Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm

More information

LCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical).

LCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical). Principles f Organic Chemistry lecture 5, page LCAO APPROIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (catin, anin r radical).. Draw mlecule and set up determinant. 2 3 0 3 C C 2 = 0 C 2 3 0 = -

More information

Module 4: General Formulation of Electric Circuit Theory

Module 4: General Formulation of Electric Circuit Theory Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated

More information

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes.

More information

MANIPAL INSTITUTE OF TECHNOLOGY

MANIPAL INSTITUTE OF TECHNOLOGY MANIPAL INSTITUTE OF TECHNOLOGY MANIPAL UNIVERSITY, MANIPAL SECOND SEMESTER B.Tech. END-SEMESTER EXAMINATION - MAY 013 SUBJECT: ENGINEERING PHYSICS (PHY101/10) Time: 3 Hrs. Max. Marks: 50 Nte: Answer any

More information

Name Honors Chemistry / /

Name Honors Chemistry / / Name Hnrs Chemistry / / Beynd Lewis Structures Exceptins t the Octet Rule Mdel Hydrgen is an exceptin t the ctet rule because it fills its uter energy level with nly 2 electrns. The secnd rw elements B

More information

Thermodynamics and Equilibrium

Thermodynamics and Equilibrium Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,

More information

d sinθ = mλ Interference and diffraction double slit or diffraction grating d sinθ = mλ d sinθ is the path difference x (small angle approximation)

d sinθ = mλ Interference and diffraction double slit or diffraction grating d sinθ = mλ d sinθ is the path difference x (small angle approximation) Wave Optics Wave prperties f light The clrs in a rainbw are ROY G. BIV (Red, range, yellw, green, blue, indig, vilet). White light is a cmbinatin f all clrs Black is the absence f light Wavelength determines

More information

GAUSS' LAW E. A. surface

GAUSS' LAW E. A. surface Prf. Dr. I. M. A. Nasser GAUSS' LAW 08.11.017 GAUSS' LAW Intrductin: The electric field f a given charge distributin can in principle be calculated using Culmb's law. The examples discussed in electric

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins

More information

Chapter 5: Force and Motion I-a

Chapter 5: Force and Motion I-a Chapter 5: rce and Mtin I-a rce is the interactin between bjects is a vectr causes acceleratin Net frce: vectr sum f all the frces n an bject. v v N v v v v v ttal net = i = + + 3 + 4 i= Envirnment respnse

More information

NMR Shifts. III computing Knight shifts and chemical shifts:

NMR Shifts. III computing Knight shifts and chemical shifts: NMR Shifts. III cmputing Knight shifts and chemical shifts: ) Shift mechanisms, hyperfine fields, Susceptibility: While K and d are frmally identical, typically K refers t shifts in metals r due t cnductin

More information

Complex Reactions and Mechanisms (continued)

Complex Reactions and Mechanisms (continued) 5.60 Spring 2005 Lecture #29 page 1 Cmplex Reactins and Mechanisms (cntinued) Sme cmments abut analyzing kinetic data A) Reactins with ne reactant: A prducts a) Plt r analyze [A vs. t ln[a vs. t 1/[A vs.

More information

In the half reaction I 2 2 I the iodine is (a) reduced (b) oxidized (c) neither of the above

In the half reaction I 2 2 I the iodine is (a) reduced (b) oxidized (c) neither of the above 6.3-110 In the half reactin I 2 2 I the idine is (a) reduced (b) xidized (c) neither f the abve 6.3-120 Vitamin C is an "antixidant". This is because it (a) xidizes readily (b) is an xidizing agent (c)

More information

Prof. Dr. I. Nasser Phys530, T142 3-Oct-17 Fermi_gases. 0 f e. and fall off exponentially like Maxwell-Boltzmaan distribution.

Prof. Dr. I. Nasser Phys530, T142 3-Oct-17 Fermi_gases. 0 f e. and fall off exponentially like Maxwell-Boltzmaan distribution. Pr. Dr. I. Nasser Phys, -Oct-7 FERMI_DIRAC GASSES Fermins: Are particles hal-integer spin that bey Fermi-Dirac statistics. Fermins bey the Pauli exclusin principle, which prhibits the ccupancy an available

More information

SCIENCE 10: CHEMISTRY,

SCIENCE 10: CHEMISTRY, , 1 Atmic Thery and Bnding The Nucleus - The particles that make up an atm are called subatmic particles - The three subatmic particles are prtns, neutrns and electrns. - Prtns, which have a +1 (psitive)

More information

NUMBERS, MATHEMATICS AND EQUATIONS

NUMBERS, MATHEMATICS AND EQUATIONS AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t

More information

Electric Current and Resistance

Electric Current and Resistance Electric Current and Resistance Electric Current Electric current is the rate f flw f charge thrugh sme regin f space The SI unit f current is the ampere (A) 1 A = 1 C / s The symbl fr electric current

More information

Kinematic transformation of mechanical behavior Neville Hogan

Kinematic transformation of mechanical behavior Neville Hogan inematic transfrmatin f mechanical behavir Neville Hgan Generalized crdinates are fundamental If we assume that a linkage may accurately be described as a cllectin f linked rigid bdies, their generalized

More information

Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN

Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Prfessr and Chair Mechanical Engineering Department Christian Brthers University 650 East Parkway Suth Memphis, TN 38104 Office: (901) 321-3424 Rm: N-110 Fax : (901) 321-3402

More information

Introduction to Smith Charts

Introduction to Smith Charts Intrductin t Smith Charts Dr. Russell P. Jedlicka Klipsch Schl f Electrical and Cmputer Engineering New Mexic State University as Cruces, NM 88003 September 2002 EE521 ecture 3 08/22/02 Smith Chart Summary

More information

Finding the Earth s magnetic field

Finding the Earth s magnetic field Labratry #6 Name: Phys 1402 - Dr. Cristian Bahrim Finding the Earth s magnetic field The thery accepted tday fr the rigin f the Earth s magnetic field is based n the mtin f the plasma (a miture f electrns

More information

Solution to HW14 Fall-2002

Solution to HW14 Fall-2002 Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges

More information

Phys. 344 Ch 7 Lecture 8 Fri., April. 10 th,

Phys. 344 Ch 7 Lecture 8 Fri., April. 10 th, Phys. 344 Ch 7 Lecture 8 Fri., April. 0 th, 009 Fri. 4/0 8. Ising Mdel f Ferrmagnets HW30 66, 74 Mn. 4/3 Review Sat. 4/8 3pm Exam 3 HW Mnday: Review fr est 3. See n-line practice test lecture-prep is t

More information

Chem 163 Section: Team Number: ALE 24. Voltaic Cells and Standard Cell Potentials. (Reference: 21.2 and 21.3 Silberberg 5 th edition)

Chem 163 Section: Team Number: ALE 24. Voltaic Cells and Standard Cell Potentials. (Reference: 21.2 and 21.3 Silberberg 5 th edition) Name Chem 163 Sectin: Team Number: ALE 24. Vltaic Cells and Standard Cell Ptentials (Reference: 21.2 and 21.3 Silberberg 5 th editin) What des a vltmeter reading tell us? The Mdel: Standard Reductin and

More information

Electrochemistry. Reduction: the gaining of electrons. Reducing agent (reductant): species that donates electrons to reduce another reagent.

Electrochemistry. Reduction: the gaining of electrons. Reducing agent (reductant): species that donates electrons to reduce another reagent. Electrchemistry Review: Reductin: the gaining f electrns Oxidatin: the lss f electrns Reducing agent (reductant): species that dnates electrns t reduce anther reagent. Oxidizing agent (xidant): species

More information

The special theory of relativity

The special theory of relativity The special thery f relatiity The preliminaries f special thery f relatiity The Galilean thery f relatiity states that it is impssible t find the abslute reference system with mechanical eperiments. In

More information

(2) Even if such a value of k was possible, the neutrons multiply

(2) Even if such a value of k was possible, the neutrons multiply CHANGE OF REACTOR Nuclear Thery - Curse 227 POWER WTH REACTVTY CHANGE n this lessn, we will cnsider hw neutrn density, neutrn flux and reactr pwer change when the multiplicatin factr, k, r the reactivity,

More information

Plan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations

Plan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations STAPLE Physics 201 Name Final Exam May 14, 2013 This is a clsed bk examinatin but during the exam yu may refer t a 5 x7 nte card with wrds f wisdm yu have written n it. There is extra scratch paper available.

More information

TOPPER SAMPLE PAPER 2 Class XII- Physics

TOPPER SAMPLE PAPER 2 Class XII- Physics TOPPER SAMPLE PAPER 2 Class XII- Physics Time: Three Hurs Maximum Marks: 70 General Instructins (a) All questins are cmpulsry. (b) There are 30 questins in ttal. Questins 1 t 8 carry ne mark each, questins

More information

Q1. A) 48 m/s B) 17 m/s C) 22 m/s D) 66 m/s E) 53 m/s. Ans: = 84.0 Q2.

Q1. A) 48 m/s B) 17 m/s C) 22 m/s D) 66 m/s E) 53 m/s. Ans: = 84.0 Q2. Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 1 Q1. A string, f length 0.75 m and fixed at bth ends, is vibrating in its fundamental mde. The maximum transverse speed

More information

Hubble s Law PHYS 1301

Hubble s Law PHYS 1301 1 PHYS 1301 Hubble s Law Why: The lab will verify Hubble s law fr the expansin f the universe which is ne f the imprtant cnsequences f general relativity. What: Frm measurements f the angular size and

More information

Lab 11 LRC Circuits, Damped Forced Harmonic Motion

Lab 11 LRC Circuits, Damped Forced Harmonic Motion Physics 6 ab ab 11 ircuits, Damped Frced Harmnic Mtin What Yu Need T Knw: The Physics OK this is basically a recap f what yu ve dne s far with circuits and circuits. Nw we get t put everything tgether

More information

Applying Kirchoff s law on the primary circuit. V = - e1 V+ e1 = 0 V.D. e.m.f. From the secondary circuit e2 = v2. K e. Equivalent circuit :

Applying Kirchoff s law on the primary circuit. V = - e1 V+ e1 = 0 V.D. e.m.f. From the secondary circuit e2 = v2. K e. Equivalent circuit : TRANSFORMERS Definitin : Transfrmers can be defined as a static electric machine which cnverts electric energy frm ne ptential t anther at the same frequency. It can als be defined as cnsists f tw electric

More information

Honors Physics Final Review Summary

Honors Physics Final Review Summary Hnrs Physics Final Review Summary Wrk Dne By A Cnstant Frce: Wrk describes a frce s tendency t change the speed f an bject. Wrk is dne nly when an bject mves in respnse t a frce, and a cmpnent f the frce

More information

Find this material useful? You can help our team to keep this site up and bring you even more content consider donating via the link on our site.

Find this material useful? You can help our team to keep this site up and bring you even more content consider donating via the link on our site. Find this material useful? Yu can help ur team t keep this site up and bring yu even mre cntent cnsider dnating via the link n ur site. Still having truble understanding the material? Check ut ur Tutring

More information

PHYS College Physics II Final Examination Review

PHYS College Physics II Final Examination Review PHYS 1402- Cllege Physics II Final Examinatin Review The final examinatin will be based n the fllwing Chapters/Sectins and will cnsist f tw parts. Part 1, cnsisting f Multiple Chice questins, will accunt

More information

Chapter 2 GAUSS LAW Recommended Problems:

Chapter 2 GAUSS LAW Recommended Problems: Chapter GAUSS LAW Recmmended Prblems: 1,4,5,6,7,9,11,13,15,18,19,1,7,9,31,35,37,39,41,43,45,47,49,51,55,57,61,6,69. LCTRIC FLUX lectric flux is a measure f the number f electric filed lines penetrating

More information

NGSS High School Physics Domain Model

NGSS High School Physics Domain Model NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship

More information

Unit code: H/ QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY

Unit code: H/ QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY Unit 43: Plant and Prcess Principles Unit cde: H/601 44 QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY 3 Understand static and namic fluid systems with

More information

Wave Phenomena Physics 15c

Wave Phenomena Physics 15c Wave Phenmena Phsics 5c Lecture Gemetrical Optics (H&L Chapter ) Tw Mre Lectures T G!! Will inish gemetrical ptics tda! Next week will cver less serius material! Laser and hlgraph! Quantum Mechanics Hw

More information

Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.

Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic. Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage

More information

Supporting information

Supporting information Electrnic Supplementary Material (ESI) fr Physical Chemistry Chemical Physics This jurnal is The wner Scieties 01 ydrgen perxide electrchemistry n platinum: twards understanding the xygen reductin reactin

More information

Edexcel GCSE Physics

Edexcel GCSE Physics Edexcel GCSE Physics Tpic 10: Electricity and circuits Ntes (Cntent in bld is fr Higher Tier nly) www.pmt.educatin The Structure f the Atm Psitively charged nucleus surrunded by negatively charged electrns

More information

lecture 5: Nucleophilic Substitution Reactions

lecture 5: Nucleophilic Substitution Reactions lecture 5: Nuclephilic Substitutin Reactins Substitutin unimlecular (SN1): substitutin nuclephilic, unimlecular. It is first rder. The rate is dependent upn ne mlecule, that is the substrate, t frm the

More information

Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >

Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) > Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);

More information

Making and Experimenting with Voltaic Cells. I. Basic Concepts and Definitions (some ideas discussed in class are omitted here)

Making and Experimenting with Voltaic Cells. I. Basic Concepts and Definitions (some ideas discussed in class are omitted here) Making xperimenting with Vltaic Cells I. Basic Cncepts Definitins (sme ideas discussed in class are mitted here) A. Directin f electrn flw psitiveness f electrdes. If ne electrde is mre psitive than anther,

More information

Synchronous Motor V-Curves

Synchronous Motor V-Curves Synchrnus Mtr V-Curves 1 Synchrnus Mtr V-Curves Intrductin Synchrnus mtrs are used in applicatins such as textile mills where cnstant speed peratin is critical. Mst small synchrnus mtrs cntain squirrel

More information

Q1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string?

Q1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string? Term: 111 Thursday, January 05, 2012 Page: 1 Q1. A string f length L is fixed at bth ends. Which ne f the fllwing is NOT a pssible wavelength fr standing waves n this string? Q2. λ n = 2L n = A) 4L B)

More information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

CHAPTER Read Chapter 17, sections 1,2,3. End of Chapter problems: 25

CHAPTER Read Chapter 17, sections 1,2,3. End of Chapter problems: 25 CHAPTER 17 1. Read Chapter 17, sectins 1,2,3. End f Chapter prblems: 25 2. Suppse yu are playing a game that uses tw dice. If yu cunt the dts n the dice, yu culd have anywhere frm 2 t 12. The ways f prducing

More information

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b . REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but

More information

Chapter 23 Electromagnetic Waves Lecture 14

Chapter 23 Electromagnetic Waves Lecture 14 Chapter 23 Electrmagnetic Waves Lecture 14 23.1 The Discvery f Electrmagnetic Waves 23.2 Prperties f Electrmagnetic Waves 23.3 Electrmagnetic Waves Carry Energy and Mmentum 23.4 Types f Electrmagnetic

More information

Electromagnetic Radiation

Electromagnetic Radiation CLASSICALLY -- ELECTROMAGNETIC RADIATION Maxwell (1865) Electrmagnetic Radiatin http://apd.nasa.gv/apd/astrpix.html Classically, an electrmagnetic wave can be viewed as a self-sustaining wave f electric

More information

Chemistry 20 Lesson 11 Electronegativity, Polarity and Shapes

Chemistry 20 Lesson 11 Electronegativity, Polarity and Shapes Chemistry 20 Lessn 11 Electrnegativity, Plarity and Shapes In ur previus wrk we learned why atms frm cvalent bnds and hw t draw the resulting rganizatin f atms. In this lessn we will learn (a) hw the cmbinatin

More information

Chapter 3 Kinematics in Two Dimensions; Vectors

Chapter 3 Kinematics in Two Dimensions; Vectors Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs

More information

Chapter 30. Inductance

Chapter 30. Inductance Chapter 30 nductance 30. Self-nductance Cnsider a lp f wire at rest. f we establish a current arund the lp, it will prduce a magnetic field. Sme f the magnetic field lines pass thrugh the lp. et! be the

More information

Therefore the atomic diameter is 5 orders of magnitude ( times) greater than the m

Therefore the atomic diameter is 5 orders of magnitude ( times) greater than the m Orders f Magnitude Pwers f 10 are referred t as rders f magnitude e.g. smething a thusand times larger (10 3 ) is three rders f magnitude bigger. A prtn has a diameter f the rder ~10-15 m The diameter

More information

CHE 105 EXAMINATION III November 11, 2010

CHE 105 EXAMINATION III November 11, 2010 CHE 105 EXAMINATION III Nvember 11, 2010 University f Kentucky Department f Chemistry READ THESE DIRECTIONS CAREFULLY BEFORE STARTING THE EXAMINATION! It is extremely imprtant that yu fill in the answer

More information

Basics. Primary School learning about place value is often forgotten and can be reinforced at home.

Basics. Primary School learning about place value is often forgotten and can be reinforced at home. Basics When pupils cme t secndary schl they start a lt f different subjects and have a lt f new interests but it is still imprtant that they practise their basic number wrk which may nt be reinfrced as

More information

Name: Period: Date: BONDING NOTES HONORS CHEMISTRY

Name: Period: Date: BONDING NOTES HONORS CHEMISTRY Name: Perid: Date: BONDING NOTES HONORS CHEMISTRY Directins: This packet will serve as yur ntes fr this chapter. Fllw alng with the PwerPint presentatin and fill in the missing infrmatin. Imprtant terms

More information

Study Guide Physics Pre-Comp 2013

Study Guide Physics Pre-Comp 2013 I. Scientific Measurement Metric Units S.I. English Length Meter (m) Feet (ft.) Mass Kilgram (kg) Pund (lb.) Weight Newtn (N) Ounce (z.) r pund (lb.) Time Secnds (s) Secnds (s) Vlume Liter (L) Galln (gal)

More information

University Chemistry Quiz /04/21 1. (10%) Consider the oxidation of ammonia:

University Chemistry Quiz /04/21 1. (10%) Consider the oxidation of ammonia: University Chemistry Quiz 3 2015/04/21 1. (10%) Cnsider the xidatin f ammnia: 4NH 3 (g) + 3O 2 (g) 2N 2 (g) + 6H 2 O(l) (a) Calculate the ΔG fr the reactin. (b) If this reactin were used in a fuel cell,

More information

4F-5 : Performance of an Ideal Gas Cycle 10 pts

4F-5 : Performance of an Ideal Gas Cycle 10 pts 4F-5 : Perfrmance f an Cycle 0 pts An ideal gas, initially at 0 C and 00 kpa, underges an internally reversible, cyclic prcess in a clsed system. The gas is first cmpressed adiabatically t 500 kpa, then

More information

UNIT 5: ATOMIC THEORY & THE PERIODIC TABLE CHEMISTRY 215, DUFFEY, CHAPTER 4 & SECTION 6.1

UNIT 5: ATOMIC THEORY & THE PERIODIC TABLE CHEMISTRY 215, DUFFEY, CHAPTER 4 & SECTION 6.1 UNIT 5: ATOMIC THEORY & THE PERIODIC TABLE CHEMISTRY 215, DUFFEY, CHAPTER 4 & SECTION 6.1 BIG IDEAS (we will tuch n small parts f Chp.5 as well) 4.1 Early Ideas Abut Matter 4.2 Defining the Atm 4.3 Hw

More information

Chapters 29 and 35 Thermochemistry and Chemical Thermodynamics

Chapters 29 and 35 Thermochemistry and Chemical Thermodynamics Chapters 9 and 35 Thermchemistry and Chemical Thermdynamics 1 Cpyright (c) 011 by Michael A. Janusa, PhD. All rights reserved. Thermchemistry Thermchemistry is the study f the energy effects that accmpany

More information

Chem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra

Chem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra Chem 115 POGIL Wrksheet - Week 8 Thermchemistry (Cntinued), Electrmagnetic Radiatin, and Line Spectra Why? As we saw last week, enthalpy and internal energy are state functins, which means that the sum

More information

37 Maxwell s Equations

37 Maxwell s Equations 37 Maxwell s quatins In this chapter, the plan is t summarize much f what we knw abut electricity and magnetism in a manner similar t the way in which James Clerk Maxwell summarized what was knwn abut

More information

Bicycle Generator Dump Load Control Circuit: An Op Amp Comparator with Hysteresis

Bicycle Generator Dump Load Control Circuit: An Op Amp Comparator with Hysteresis Bicycle Generatr Dump Lad Cntrl Circuit: An Op Amp Cmparatr with Hysteresis Sustainable Technlgy Educatin Prject University f Waterl http://www.step.uwaterl.ca December 1, 2009 1 Summary This dcument describes

More information

AP Physics. Summer Assignment 2012 Date. Name. F m = = + What is due the first day of school? a. T. b. = ( )( ) =

AP Physics. Summer Assignment 2012 Date. Name. F m = = + What is due the first day of school? a. T. b. = ( )( ) = P Physics Name Summer ssignment 0 Date I. The P curriculum is extensive!! This means we have t wrk at a fast pace. This summer hmewrk will allw us t start n new Physics subject matter immediately when

More information

Fall 2013 Physics 172 Recitation 3 Momentum and Springs

Fall 2013 Physics 172 Recitation 3 Momentum and Springs Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.

More information

PHY 2054C Review guide Fall 2018 Chapter 17 Wave optics

PHY 2054C Review guide Fall 2018 Chapter 17 Wave optics PHY 2054C Review guide Fall 2018 Chapter 17 Wave ptics Light acts as a wave, ray, particle, and phtn. Refractive index n = c/v Light waves travel with speed c in a vacuum they slw dwn when they pass thrugh

More information

CHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review

CHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review Review Accrding t the nd law f Thermdynamics, a prcess is spntaneus if S universe = S system + S surrundings > 0 Even thugh S system

More information

General Chemistry II, Unit I: Study Guide (part I)

General Chemistry II, Unit I: Study Guide (part I) 1 General Chemistry II, Unit I: Study Guide (part I) CDS Chapter 14: Physical Prperties f Gases Observatin 1: Pressure- Vlume Measurements n Gases The spring f air is measured as pressure, defined as the

More information

Thermodynamics Partial Outline of Topics

Thermodynamics Partial Outline of Topics Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)

More information

ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS

ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS On cmpletin f this tutrial yu shuld be able t d the fllwing. Define viscsity

More information

Lecture 5: Equilibrium and Oscillations

Lecture 5: Equilibrium and Oscillations Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if

More information

ATOMIC ORBITAL MODEL OF THE ATOM Be able to draw rough sketches of s, p and d orbitals with different principal quantum numbers

ATOMIC ORBITAL MODEL OF THE ATOM Be able to draw rough sketches of s, p and d orbitals with different principal quantum numbers Chapter 7 Atmic Structure and Peridicity ATOMIC ORBITAL MODEL OF THE ATOM Be able t draw rugh sketches f s, p and d rbitals with different principal quantum numbers ELECTRONIC CONFIGURATIONS Knw the difference

More information

Lim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)?

Lim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)? THESE ARE SAMPLE QUESTIONS FOR EACH OF THE STUDENT LEARNING OUTCOMES (SLO) SET FOR THIS COURSE. SLO 1: Understand and use the cncept f the limit f a functin i. Use prperties f limits and ther techniques,

More information

Pipetting 101 Developed by BSU CityLab

Pipetting 101 Developed by BSU CityLab Discver the Micrbes Within: The Wlbachia Prject Pipetting 101 Develped by BSU CityLab Clr Cmparisns Pipetting Exercise #1 STUDENT OBJECTIVES Students will be able t: Chse the crrect size micrpipette fr

More information

4 electron domains: 3 bonding and 1 non-bonding. 2 electron domains: 2 bonding and 0 non-bonding. 3 electron domains: 2 bonding and 1 non-bonding

4 electron domains: 3 bonding and 1 non-bonding. 2 electron domains: 2 bonding and 0 non-bonding. 3 electron domains: 2 bonding and 1 non-bonding [4.3D VSEPR] pg. 1 f 7 Curriculum The use f VSEPR thery t predict the electrn dmain gemetry and the mlecular gemetry fr species with tw, three and fur electrn dmains. Shapes f species are determined by

More information

ENGI 4430 Parametric Vector Functions Page 2-01

ENGI 4430 Parametric Vector Functions Page 2-01 ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr

More information

Surface and Contact Stress

Surface and Contact Stress Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated

More information

Equilibrium of Stress

Equilibrium of Stress Equilibrium f Stress Cnsider tw perpendicular planes passing thrugh a pint p. The stress cmpnents acting n these planes are as shwn in ig. 3.4.1a. These stresses are usuall shwn tgether acting n a small

More information

I. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is

I. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is Length L>>a,b,c Phys 232 Lab 4 Ch 17 Electric Ptential Difference Materials: whitebards & pens, cmputers with VPythn, pwer supply & cables, multimeter, crkbard, thumbtacks, individual prbes and jined prbes,

More information

A Mechanistic Approach to Bond Formation in H 2

A Mechanistic Approach to Bond Formation in H 2 A Mechanistic Apprach t Bnd Frmatin in H Frank Riux Department f Chemistry Cllege f Saint Benedict Saint Jhnʹs University St. Jseph, MN 5674 Intrductin Ruedenbergʹs innvative analysis f the cvalent bnd

More information