10.7. Electrolysis. Electrolytic Cells

Size: px
Start display at page:

Download "10.7. Electrolysis. Electrolytic Cells"

Transcription

1 Elctrolysis As discussd in Sction 10.6, corrosion is th outcom of a spontanous rdox raction. An imprssd currnt (on mthod that is usd to provid cathodic protction) can stop corrosion by rvrsing th spontanous corrosion raction and driving it in th non-spontanous dirction. An imprssd currnt passs an lctric currnt through th structur bing protctd, such as a piplin. An xtrnal lctrical sourc supplis th currnt. Othr non-spontanous rdox ractions can b forcd to occur in a similar way. On xampl is rcharging th scondary clls in a battry. A battry uss a spontanous rdox raction to produc an lctric currnt. Rcharging a battry involvs applying an xtrnal nrgy sourc to driv th rdox raction in th rvrs, nonspontanous dirction. For xampl, a lad storag battry in a car can b rchargd by applying a currnt to it (Figur 1). In this sction, you will larn how som usful non-spontanous ractions can b forcd to occur. Many of ths ractions hav important consumr and industrial applications Figur 1 A car with a dad battry can b rstartd by conncting th dad battry to a working battry. It is important to follow th manufacturr s dirctions whn stting up jumpr cabls. Othrwis, a spark might caus th hydrogn gas that is producd to xplod. Elctrolytic Clls A galvanic cll producs a currnt whn an oxidation rduction raction happns spontanously. Anothr kind of cll, calld an lctrolytic cll, uss a currnt from an outsid sourc to mak an lctrolytic raction occur. In a procss calld lctrolysis, th currnt is forcd through th cll to produc a chmical chang for which th cll potntial is ngativ. That is, lctrical nrgy causs an othrwis non-spontanous chmical raction to occur. Elctrolysis has grat practical importanc. For xampl, lctrolysis is usd to rcharg a battry, produc aluminum mtal, and covr objcts with a layr of chrom. lctrolytic cll a cll that uss lctrical nrgy to produc a chmical chang that would not occur spontanously lctrolysis th application of currnt through a cll to produc a chmical chang 10.7 Elctrolysis 663

2 Figur 2 shows th diffrncs btwn a galvanic cll and an lctrolytic cll. Th galvanic cll (Figur 2(a)) runs spontanously to produc 1.10 V. Anod half-raction quation: Zn 1s2 S Zn21 1aq Cathod half-raction quation: Cu21 1aq S Cu 1s2 Figur 2(b) shows an xtrnal nrgy sourc forcing lctrons through th cll in th dirction opposit to that shown in Figur 2(a). This rquirs an xtrnal potntial gratr than 1.10 V, bcaus th xtrnal potntial must b applid in opposition to th natural cll potntial. Th dvic in Figur 2(b) is an lctrolytic cll. Notic that th anod and th cathod ar rvrsd in Figurs 2(a) and 2(b). In a galvanic cll, zinc is th anod. In an lctrolytic cll, coppr is th anod. Also, ions flow through th salt bridg in opposit dirctions in th two clls. powr supply gratr than 1.10 V cations Zn(s) (a) cations Cu(s) anions Zn(s) Cu(s) anions Zn2 (aq) SO42 (aq) Cu2 (aq) SO42 (aq) Zn2 (aq) SO42 (aq) Cu2 (aq) SO42 (aq) 1.0 mol/l Zn2 solution 1.0 mol/l Cu2 solution 1.0 mol/l Zn2 solution 1.0 mol/l Cu2 solution anod cathod Zn(s) h Zn2 (aq) + 2 Cu2 (aq) + 2 h Cu(s) (oxidation) (rduction) Galvanic cll cathod anod (b) Zn2 (aq) + 2 h Zn(s) Cu(s) h Cu2 (aq) + 2 (rduction) (oxidation) Elctrolytic cll Figur 2 (a) A galvanic cll producs a currnt from a spontanous rdox raction: Zn 1s2 1 Cu21 1aq2 S Zn21 1aq2 1 Cu 1s2 (b) An lctrolytic cll rquirs a powr sourc to driv th opposit, non-spontanous raction: Cu 1s2 1 Zn21 1aq2 S Cu21 1aq2 1 Zn 1s2 Elctrolysis of watr In Sction 10.3, you larnd that th raction in which hydrogn and oxygn combin spontanously to form watr can b usd to produc an lctric currnt in a ful cll. Th rvrs raction is non-spontanous and is an xampl of lctrolysis. Elctric currnt must b supplid to carry out th lctrolysis of watr. During lctrolysis, watr is oxidizd at th anod and rducd at th cathod. Thrfor, watr is both th oxidizing agnt and th rducing agnt in this raction. Only two quations in Tabl 1, Appndix B7, involv just watr as an oxidizing agnt or a rducing agnt: O2(g) 1 4 H1(aq) S 2 H2O(l) E r V 2 H2O(l) S H2(g) 1 2 OH2(aq) E r V Not that th watr in ths two quations forms an upward diagonal to th right. This mans that th lctrolysis raction is non-spontanous. Howvr, w can forc it to occur by applying a currnt. Th raction quations can b writtn as follows: 664 Chaptr 10 Elctrochmical Clls 7924_Chm_CH10.indd 664 5/4/12 3:50 PM

3 or Anod half-raction quation: 2 H 2 O(l) S O 2 (g) 1 4 H 1 (aq) Cathod half-raction quation: 4 H 2 O(l) S 2 H 2 (g) 1 4 OH 2 (aq) [multiply by 2 to balanc lctrons] Nt ionic quation: 6 H 2 O1l2 S 2 H 2 1g2 1 O 2 1g2 1 4 H 1 1aq2 1 4 OH 2 1aq2 2 H 2 O1l2 S 2 H 2 1g2 1 O 2 1g2 4 H 2 O1l2 Th standard cll potntial for th lctrolysis of watr can b dtrmind using th sam quation that is usd for galvanic clls: g E r (cll) 5 E r (cathod) 2 E r (anod) V2 (11.23 V) E r (cll) V If you trid to lctrolyz pur watr by using platinum lctrods connctd to a 6 V battry, you would obsrv no raction. This is bcaus pur watr contains so fw ions that almost no currnt can flow. Howvr, dissolving vn a small amount of an lctrolyt, such as a solubl salt or a strong acid, in th watr causs th immdiat production of bubbls of hydrogn and oxygn (Figur 3). Th lctrolysis of watr supplis oxygn to submarin crws and to astronauts in th Intrnational Spac Station. Figur 3 Th lctrolysis of watr producs hydrogn gas at th cathod (on th right) and oxygn at th anod (on th lft). Not that twic as much hydrogn as oxygn is producd. Comparing Galvanic and Elctrolytic Clls A galvanic cll and an lctrolytic cll ar both typs of lctrochmical cll. Thy hav som charactristics in common and som diffrncs. Th main charactristics of galvanic clls and lctrolytic clls ar compard in Tabl 1. A galvanic cll convrts chmical nrgy into lctrical nrgy through a spontanous chmical raction that taks plac at th lctrods. Oxidation occurs at th anod, giving th anod a ngativ charg. Rduction occurs at th cathod, giving th cathod a positiv charg. A wir conncts th anod and th cathod, allowing lctrons to mov from th anod to th cathod. Th lctrods ar also connctd by a salt bridg or a similar ionic conductor, which prmits ions to flow btwn thm. Th flow of ions prvnts a charg from building up in on of th lctrods. Sinc th rdox raction that taks plac in a galvanic cll is spontanous, a galvanic cll can b usd as an nrgy sourc for an lctrical dvic. In contrast, an lctrolytic cll rquirs an xtrnal nrgy sourc to oprat. Th basis for an lctrolytic cll is a non-spontanous rdox raction. Thrfor, nrgy must b providd to driv th raction. Lik a galvanic cll, an lctrolytic cll has an anod (th sit of oxidation) and a cathod (th sit of rduction). Elctrons lav th anod along th wir, pass through th sourc of lctrical nrgy, and travl to th cathod. lctrochmical cll a gnral trm that is usd to rfr to both a galvanic cll and an lctrolytic cll Tabl 1 Comparison of Galvanic and Elctrolytic Clls Galvanic cll involvs a spontanous rdox raction producs lctrical nrgy uss a salt bridg to prvnt a charg buildup Elctrolytic cll involvs a non-spontanous rdox raction rquirs lctrical nrgy to driv th raction may or may not us a salt bridg rsults in oxidation at th anod and rduction at th cathod rsults in oxidation at th anod and rduction at th cathod Th lctrod that would b th anod of a galvanic cll is th cathod of an lctrolytic cll. Th lctrod that would b th cathod of a galvanic cll is th anod of an lctrolytic cll Elctrolysis 665

4 powr supply Commrcial Elctrolytic Procsss An important charactristic of mtals is thir ability to donat lctrons (bcom oxidizd) to form ions. Sinc mtals ar usually good rducing agnts, most ar found in natur in ors. Ors ar mixturs of ionic compounds, which oftn contain oxid, sulfid, and silicat anions. Th nobl mtals, such as gold, silvr, and platinum, ar mor difficult to oxidiz and ar mor oftn found as pur mtals. anod (graphit) anions cations cathod (iron) solution containing Zn 2 (aq) ions Figur 4 A modl of th lctrolytic cll that is usd industrially to lctroplat zinc onto iron Elctrolysis of Aquous Solutions Many industris us lctrolytic clls. On important application of lctrolysis involvs plating on mtal onto anothr mtal. For xampl, in Sction 10.6 you larnd that an ffctiv way to prvnt iron from corroding is to coat it with zinc. In this procss, calld galvanizing, th mtal objct to b platd is mad th cathod of th lctrolytic cll by attaching it to th positiv trminal of th lctrical nrgy supply (Figur 4). An inrt lctrod, such as graphit, is oftn usd as th anod. Th lctrods ar thn placd in an aquous solution that contains cations of th mtal to b platd onto th cathod. For galvanizing, a zinc sulfat solution is usd. As th cll oprats, a shiny layr of zinc prcipitats onto th iron cathod. Bubbls of oxygn ris from th anod, suggsting that th watr is oxidizd. Th raction quations ar givn blow: Anod half-raction quation: 2 H 2 O(l) S O 2 (g) 1 4 H 1 (aq) Cathod half-raction quation: 2 Zn 21 (aq) S 2 Zn(s) [multiply by 2 to balanc lctrons] Nt ionic quation: 2 H 2 O(l) 1 2 Zn 21 (aq) S 2 Zn(s) 1 O 2 (g) 1 4 H 1 (aq) 4 H 2 O1l2 Th standard cll potntial for this cll is E r (cll) V2 (11.23 V) E r (cll) V In practic, a potntial diffrnc of mor than 1.99 V must b applid for zinc to plat onto iron. mini Invstigation Pncil Elctrolysis mini Invstigation Skills: Prforming, Obsrving, Analyzing SKILLS HANDBOOK A1 In this invstigation, you will us lctrical nrgy to mak a nonspontanous raction occur. Th graphit in pncil lad srvs as th lctrod for both anod and cathod half-ractions. Equipmnt and Matrials: chmical safty goggls; lab apron; Ptri dish; 2 small pncils sharpnd at both nds; 2 conncting wirs with alligator clips; 9 V battry; 0.5 mol/l potassium iodid, KI(aq); droppr bottl of phnolphthalin indicator 1. Put on your chmical safty goggls and lab apron. 2. Half-fi ll th Ptri dish with th potassium iodid solution. 3. Add about 10 drops of phnolphthalin to th solution. 4. Plac on nd of ach pncil in th dish. Kp th pncils far apart from ach othr. 5. Us th conncting wirs to connct th dry nd of ach pncil to a trminal on th battry. 6. Aftr about 30 s, disconnct th pncils from th battry. 7. Look for vidnc of chmical chang. Rmov ach pncil, and chck for an odour. 8. Dispos of th contnts of th dish according to your tachr s instructions. A. Idntify th anod and th cathod of this cll. T/I B. What vidnc of chmical chang did you obsrv whil th pncils wr connctd? T/I C. Basd on your vidnc, prdict th idntity of on substanc that was producd at th anod and on substanc that was producd at th cathod. Justify your prdictions. T/I 666 Chaptr 10 Elctrochmical Clls

5 Aluminum Production Sinc aluminum is a vry activ mtal, it occurs naturally as an oxid in an or calld bauxit. Th production of aluminum mtal from its or provd to b mor difficult than th production of most othr mtals. In 1854, a procss for producing mtallic aluminum using sodium was discovrd. Howvr, aluminum rmaind xtrmly xpnsiv. In 1886, Charls M. Hall in th Unitd Stats and Paul Héroult in Franc almost simultanously discovrd a practical lctrolytic procss for producing aluminum. Th ky factor in th Hall Héroult procss is th us of moltn cryolit, Na 3 AlF 6 (l), as th solvnt for th aluminum oxid (also calld alumina). Today, aluminum is rlativly inxpnsiv and has a wid varity of applications, such as building matrials (Figur 5). Elctrolysis is possibl only if ions can mov to th lctrods. A common mthod for making ions mobil is to dissolv th substanc to b lctrolyzd in watr. Howvr, watr cannot b usd for th lctrolysis of th aluminum salt bcaus watr is mor asily rducd than aluminum ions: 2 H 2 O1l S H 2 1g2 1 OH 2 1aq2 E r V Al 31 1aq S Al1s2 E r V Thus, aluminum mtal cannot b platd out of an aquous solution of aluminum ions. Gnrally, ions can b mad mobil by mlting th salt. Howvr, th mlting point of aluminum oxid, Al 2 O 3, is much too high (2050 C) for lctrolysis of th moltn oxid to b practical. A mixtur of aluminum oxid and cryolit, howvr, has a mlting point of 1000 C, and th rsulting moltn mixtur can b lctrolyzd to obtain aluminum mtal. As a rsult of th Hall Héroult discovry, th pric of aluminum plungd and its widsprad us bcam conomically fasibl. Th industrial production of aluminum still uss th Hall Héroult procss. Bauxit is not pur aluminum oxid. It also contains oxids of iron, silicon, and titanium, along with various silicat matrials. To obtain th pur hydratd aluminum oxid, Al 2 O 3 # nh 2 O, th bauxit is tratd with aquous sodium hydroxid. Aluminum oxid is amphotric and thus racts in a basic solution: Al 2 O 3 1s2 1 2 OH 2 1aq2 S 2 AlO 22 1aq2 1 H 2 O1l2 Th othr mtal oxids, which ar basic, rmain as solids. (Rcall Sction 8.6.) Th solution that contains th aluminat ion, AlO 2 2 (aq), is sparatd from th sludg of th othr oxids and is acidifid with carbon dioxid gas, causing th hydratd alumina to r-form: 2 CO 2 1g2 1 2 AlO 22 1aq2 1 1n 1 12H 2 O1l2 S 2 HCO 32 1aq2 1 Al 2 O 3 # nh 2 O(s) Thn, th purifid aluminum oxid is mixd with cryolit, Na 3 AlF 6, and mltd at about 1000 C. Th dissociatd aluminum ions ar rducd to aluminum mtal in an lctrolytic cll (Figur 6). Figur 5 Th low mass, th lustr, and th corrosion rsistanc of aluminum mak it a usful matrial for cladding th outsids of buildings. anods (graphit rods) carbon dioxid formd at anods carbon-lind iron tank moltn aluminum to xtrnal powr supply moltn Al 2 O 3 /Na 3 AlF 6 (l) mixtur plug Figur 6 This lctrolytic cll is usd to produc aluminum by th Hall Héroult procss. Sinc moltn aluminum is dnsr than th moltn mixtur of cryolit and alumina, th mtal sttls to th bottom of th cll and is drawn off priodically Elctrolysis 667

6 Th lctrolyt solution in th Hall-Héroult cll includs many diffrnt ions that contain aluminum, so th chmistry is not compltly clar. Howvr, aluminum oxid probably racts with th cryolit anion: Al 2 O 3 1s2 1 4 AlF l2 S 3 Al 2 OF l2 1 6 F 2 1l2 Th following half-cll ractions ar also thought to occur: Cathod half-raction quation: AlF l S Al1s2 1 6 F 2 1l2 Anod half-raction quation: 2 Al 2 OF l F 2 1l2 1 C1s2 S 4 AlF l2 1 CO 2 1g Th ovrall cll raction quation can b writtn as 2 Al 2 O 3 1s2 1 3 C1s2 S 4 Al1s2 1 3 CO 2 1g2 Th aluminum producd in this lctrolytic procss is 99.5 % pur. Most applications of aluminum us alloys that includ othr mtals. For xampl, to b usful as a structural matrial, aluminum is alloyd with mtals such as zinc (for trailr and aircraft construction) and mangans (for cooking utnsils, storag tanks, and highway signs). Unfortunatly, th production of aluminum has ngativ ffcts on th nvironmnt. Sinc a grat dal of nrgy is consumd during th procss of aluminum rfining, aluminum production contributs to grnhous gas missions, such as prfluorocarbons (PFCs), polycyclic aromatic hydrocarbon (PAH), fluorid, F (aq), sulfur dioxid, SO 2 (g), and carbon dioxid, CO 2 (g). Placing aluminum smlting plants nar rnwabl sourcs of lctrical nrgy, such as watrfalls, rducs th missions from lctricity production. Howvr, th consumption of th carbon lctrods during th lctrolytic procss also producs PAH and carbon dioxid. Rcycling usd aluminum rquirs only about 5 % of th nrgy that is usd to mak nw aluminum. Effctiv rcycling programs not only rduc manufacturing costs, but also rduc th harmful missions associatd with producing aluminum. Elctrorfining Mtals Th purification of mtals is anothr important application of lctrolysis. Impur coppr from th chmical rduction of coppr or is cast into larg slabs that srv as th anods for lctrolytic clls. Aquous coppr sulfat is th lctrolyt. Thin shts of ultrapur coppr function as th cathods (Figur 7). Whn a potntial diffrnc is applid across th lctrods, only coppr is dpositd on ths cathods. All th Figur 7 Ultrapur coppr shts, which srv as th cathods of an lctrolytic cll, ar lowrd btwn slabs of impur coppr, which srv as th anods. It taks about four wks for th anods to dissolv and for th pur coppr to b dpositd on th cathods. 668 Chaptr 10 Elctrochmical Clls

7 othr impuritis ar lft as sludg in th cll. Ultrapur coppr is important for th production of smiconductors and othr lctronic componnts. Th main anod half-raction quation can b writtn as follows: powr supply Cu1s2 S Cu 21 1aq Othr mtals, such as zinc and iron, ar also oxidizd from th impur anod: Zn1s2 S Zn 21 1aq and F1s2 S F Nobl mtal impuritis in th anod, such as silvr, gold, and platinum, ar not oxidizd at th voltag usd. Thy fall to th bottom of th cll to form a sludg, which is thn procssd to rmov thm. Th coppr(ii) ions from th solution ar rducd and dpositd onto th cathod: Anod half-raction quation: Cu 21 1aq S Cu1s2 This procss producs coppr mtal that is % pur. High-purity gold is also producd by lctrorfining. Elctroplating Mtals Mtals that radily corrod can oftn b protctd by applying a thin coating, or plating, of a mtal that rsists corrosion. Exampls ar tin cans (which ar actually stl cans with a thin coating of tin), chrom-platd stl car bumprs, and silvrplatd jwllry and dcorativ itms. An objct can b platd by making it th cathod in a tank that contains ions of th plating mtal. Silvr plating is an xampl of this lctrolytic procss (Figur 8). Th silvr plating solution contains ions that form complxs with th silvr ion. By lowring th concntration of availabl silvr ions, a smooth, vn coating of silvr forms ovr th surfac of th objct (Figur 9). CAREER LINK Ag anod Ag Ag Ag cathod Figur 8 In an lctroplating cll, th itm to b platd (th spoon) is th cathod and a silvr bar is th anod. Silvr is platd out at th cathod: Ag 1 1aq2 1 2 S Ag1s2 Not that a salt bridg is not ndd bcaus silvr ions ar involvd at both lctrods. Figur 9 Silvr plating is oftn usd to bautify and protct cutlry and tablwar, such as this lgant ta st. Mtal plating procsss hav brought many bnfits but also pos a rang of nvironmntal concrns. Havy mtals, such as chromium, lad, and cadmium, ar usd in ths procsss. Cyanid is a poisonous compound that is usd in plating baths. Th rlas of any of ths toxic mtals or thir ions into th nvironmnt can caus srious halth problms for organisms and prsistnt damag to cosystms Elctrolysis 669

8 10.7 Rviw Summary Elctrolysis involvs forcing a currnt through a cll to caus a nonspontanous rdox raction to occur. Elctrolytic and galvanic clls ar both lctrochmical clls. Thy contain an anod whr oxidation occurs and a cathod whr rduction occurs. An lctrolytic cll, unlik a galvanic cll, rquirs an xtrnal nrgy sourc and involvs a non-spontanous rdox raction rathr than a spontanous rdox raction. Industrial applications of lctrolysis includ th lctrolysis of watr and othr aquous solutions, as wll as rcharging battris, producing aluminum, lctrorfining mtals, and lctroplating. Qustions 1. Explain, using a graphic organizr of your choic, th diffrncs btwn a galvanic cll and an lctrolytic cll. Rfr to typ of raction and nrgy flow. K/U 2. Dscrib a consumr product that contains a galvanic cll or battry and is somtims usd as part of an lctrolytic cll. A 3. Prdict th half-raction that will tak plac at th cathod and anod whn ach salt is mltd and lctrolyzd. T/I (a) NiBr 2 (l) (b) AlF 3 (l) (c) MnI 2 (l) 4. Explain why aluminum rcycling can b good for both businss and th nvironmnt. T/I 5. A stl ring can b lctroplatd with gold in an aquous solution that contains gold(iii) ions. Sktch and labl a diagram of a cll that could b usd to produc gold-platd stl. Idntify th anod and th cathod in th cll. Indicat th dirction of lctron flow. T/I 6. Draw a diagram of a procss that can b usd to lctroplat coppr onto a stl objct, such as a coin. Includ in your diagram suggstd lctrods, th ions in solution, powr supply and connctors, th sign of th lctrods, and th dirction of lctron and ion flow. T/I C 7. During th lctrolysis of a tin(ii) chlorid solution, SnCl 2 (aq), a silvr-colourd mtal, is dpositd onto th cathod. Bubbls of a gas ar obsrvd at th anod. A blach-lik odour is dtctd. Us a rdox tabl to prdict th anod, th cathod, and th nt ionic quation. T/I C 8. An lctrolytic cll is st up using inrt lctrods in an aquous coppr(ii) sulfat solution. Aftr an hour of lctrolysis, th solution is tstd. Th concntration of coppr(ii) ions has dcrasd, whil th concntration of hydrogn ions has incrasd. Th mass of on lctrod has also incrasd. Explain ths obsrvations using th half-raction quation for ach lctrod. T/I 9. Considr th quations for th anod and cathod half-ractions for th Hall Héroult procss, givn in this sction. T/I A (a) Combin ths two quations to dtrmin th ovrall cll raction quation. (b) Combin your answr in (a) with th quation for th raction of aluminum oxid with th cryolit ion, AlF 32 6 (l), to giv th ovrall quation for th production of aluminum: 2 Al 2 O 3 (s) 1 3 C(s) S 4 Al(s) 1 3 CO 2 (g) 10. Rsarch and xplain th stps involvd in rmoving tarnish from a silvr objct using aluminum foil and baking soda. Includ th quation for th chmical raction. T/I 11. Elctroplating companis us a varity of hazardous substancs. Rsarch answrs to th following qustions, and summariz your findings in a brif rport: T/I A C What nvironmntal hazards ar associatd with th lctroplating industry? What halth and safty hazards ar associatd with th wast that is gnratd by lctroplating companis? What stps do lctroplating companis tak to minimiz any ngativ halth or nvironmntal ffcts of thir industry? WEB LINK 670 Chaptr 10 Elctrochmical Clls

Electrochemistry L E O

Electrochemistry L E O Rmmbr from CHM151 A rdox raction in on in which lctrons ar transfrrd lctrochmistry L O Rduction os lctrons xidation G R ain lctrons duction W can dtrmin which lmnt is oxidizd or rducd by assigning oxidation

More information

The following information relates to Questions 1 to 4:

The following information relates to Questions 1 to 4: Th following information rlats to Qustions 1 to 4: QUESTIN 1 Th lctrolyt usd in this ful cll is D watr carbonat ions hydrogn ions hydroxid ions QUESTIN 2 Th product formd in th ful cll is D hydrogn gas

More information

INTERMEDIATE2 1 Corrosion

INTERMEDIATE2 1 Corrosion INTERMEDIATE2 1 Corrosion CORROSION OF METALS Corrosion is a chmical raction which involvs th surfac of a mtal changing from an lmnt to a compound. Th mor ractiv th mtal th quickr it corrods. Many of th

More information

A central nucleus. Protons have a positive charge Electrons have a negative charge

A central nucleus. Protons have a positive charge Electrons have a negative charge Atomic Structur Lss than ninty yars ago scintists blivd that atoms wr tiny solid sphrs lik minut snookr balls. Sinc thn it has bn discovrd that atoms ar not compltly solid but hav innr and outr parts.

More information

ph People Grade Level: basic Duration: minutes Setting: classroom or field site

ph People Grade Level: basic Duration: minutes Setting: classroom or field site ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:

More information

Voltage, Current, Power, Series Resistance, Parallel Resistance, and Diodes

Voltage, Current, Power, Series Resistance, Parallel Resistance, and Diodes Lctur 1. oltag, Currnt, Powr, Sris sistanc, Paralll sistanc, and Diods Whn you start to dal with lctronics thr ar thr main concpts to start with: Nam Symbol Unit oltag volt Currnt ampr Powr W watt oltag

More information

Electrochemical Energy Systems Spring 2014 MIT, M. Z. Bazant. Midterm Exam

Electrochemical Energy Systems Spring 2014 MIT, M. Z. Bazant. Midterm Exam 10.66 Elctrochmical Enrgy Systms Spring 014 MIT, M. Z. Bazant Midtrm Exam Instructions. This is a tak-hom, opn-book xam du in Lctur. Lat xams will not b accptd. You may consult any books, handouts, or

More information

Give the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds.

Give the letter that represents an atom (6) (b) Atoms of A and D combine to form a compound containing covalent bonds. 1 Th diagram shows th lctronic configurations of six diffrnt atoms. A B C D E F (a) You may us th Priodic Tabl on pag 2 to hlp you answr this qustion. Answr ach part by writing on of th lttrs A, B, C,

More information

Molecules and Covalent Bond

Molecules and Covalent Bond Molculs and ovalnt ond Qustion Papr 1 Lvl IGSE Subjct hmistry (0620/0971) Exam oard ambridg Intrnational Examinations (IE) Topic toms, lmnts and compounds Sub-Topic Molculs and covalnt bonds ooklt Qustion

More information

7.4 Potential Difference and Electric Potential

7.4 Potential Difference and Electric Potential 7.4 Potntial Diffrnc and Elctric Potntial In th prvious sction, you larnd how two paralll chargd surfacs produc a uniform lctric fild. From th dfinition of an lctric fild as a forc acting on a charg, it

More information

A=P=E M-A=N Alpha particle Beta Particle. Periodic table

A=P=E M-A=N Alpha particle Beta Particle. Periodic table Nam Pr. Atomic Structur/Nuclar Chmistry (Ch. 3 & 21) OTHS Acadmic Chmistry Objctivs: Undrstand th xprimntal dsign and conclusions usd in th dvlopmnt of modrn atomic thory, including Dalton's Postulats,

More information

The pn junction: 2 Current vs Voltage (IV) characteristics

The pn junction: 2 Current vs Voltage (IV) characteristics Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n

More information

Seebeck and Peltier Effects

Seebeck and Peltier Effects Sbck and Pltir Effcts Introduction Thrmal nrgy is usually a byproduct of othr forms of nrgy such as chmical nrgy, mchanical nrgy, and lctrical nrgy. Th procss in which lctrical nrgy is transformd into

More information

Physics 312 First Pledged Problem Set

Physics 312 First Pledged Problem Set Physics 31 First Pldgd Problm St 1. Th ground stat of hydrogn is dscribd by th wavfunction whr a is th Bohr radius. (a) Comput th charg dnsity à (r) = 1 p ¼ µ 1 a 3 r=a ; ½ (r) = jã (r)j : and plot 4¼r

More information

Part 7: Capacitance And Capacitors

Part 7: Capacitance And Capacitors Part 7: apacitanc And apacitors 7. Elctric harg And Elctric Filds onsidr a pair of flat, conducting plats, arrangd paralll to ach othr (as in figur 7.) and sparatd by an insulator, which may simply b air.

More information

Classical Magnetic Dipole

Classical Magnetic Dipole Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg

More information

Alpha and beta decay equation practice

Alpha and beta decay equation practice Alpha and bta dcay quation practic Introduction Alpha and bta particls may b rprsntd in quations in svral diffrnt ways. Diffrnt xam boards hav thir own prfrnc. For xampl: Alpha Bta α β alpha bta Dspit

More information

September 23, Honors Chem Atomic structure.notebook. Atomic Structure

September 23, Honors Chem Atomic structure.notebook. Atomic Structure Atomic Structur Topics covrd Atomic structur Subatomic particls Atomic numbr Mass numbr Charg Cations Anions Isotops Avrag atomic mass Practic qustions atomic structur Sp 27 8:16 PM 1 Powr Standards/ Larning

More information

Chapter 8: Electron Configurations and Periodicity

Chapter 8: Electron Configurations and Periodicity Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how

More information

CHAPTER 16 HW: CONJUGATED SYSTEMS

CHAPTER 16 HW: CONJUGATED SYSTEMS APTER 6 W: JUGATED SYSTEMS NAMING PLYENES. Giv th IUPA nam for ach compound, including cis/trans or E/Z dsignations whr ndd. ompound no E/Z trans or E 2 3 4 3 Nam trans-2-mthyl-2,4-hxadin 2-mthoxy-,3-cyclohptadin

More information

3.2.3 Molecules and Covalent Bonds

3.2.3 Molecules and Covalent Bonds Sav My Exams! Th Hom of Rvision For mor awsom GSE and lvl rsourcs, visit us at www.savmyxams.co.uk/ 3.2.3 Molculs and ovalnt onds Qustion Papr Lvl IGSE Subjct hmistry (0620) Exam oard ambridg Intrnational

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic

More information

NARAYANA I I T / P M T A C A D E M Y. C o m m o n P r a c t i c e T e s t 1 6 XII STD BATCHES [CF] Date: PHYSIS HEMISTRY MTHEMTIS

NARAYANA I I T / P M T A C A D E M Y. C o m m o n P r a c t i c e T e s t 1 6 XII STD BATCHES [CF] Date: PHYSIS HEMISTRY MTHEMTIS . (D). (A). (D). (D) 5. (B) 6. (A) 7. (A) 8. (A) 9. (B). (A). (D). (B). (B). (C) 5. (D) NARAYANA I I T / P M T A C A D E M Y C o m m o n P r a c t i c T s t 6 XII STD BATCHES [CF] Dat: 8.8.6 ANSWER PHYSIS

More information

DIELECTRIC AND MAGNETIC PROPERTIES OF MATERIALS

DIELECTRIC AND MAGNETIC PROPERTIES OF MATERIALS DILCTRIC AD MAGTIC PROPRTIS OF MATRIALS Dilctric Proprtis: Dilctric matrial Dilctric constant Polarization of dilctric matrials, Typs of Polarization (Polarizability). quation of intrnal filds in liquid

More information

Chapter 6 Current and Resistance

Chapter 6 Current and Resistance Chaptr 6 Currnt and Rsistanc 6.1 Elctric Currnt... 1 6.1.1 Currnt Dnsity... 1 6. Ohm s Law... 3 6.3 Elctrical Enrgy and Powr... 6 6.4 Summary... 6.5 Solvd Problms... 8 6.5.1 Rsistivity of a Cabl... 8 6.5.

More information

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon.

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon. PART I TRUE/FALSE/UNCERTAIN (5 points ach) 1. Lik xpansionary montary policy, xpansionary fiscal policy rturns output in th mdium run to its natural lvl, and incrass prics. Thrfor, fiscal policy is also

More information

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator. Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r

More information

Background: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals.

Background: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals. Chaptr 7 Th Hydrogn Atom Background: W hav discussd th PIB HO and th nrgy of th RR modl. In this chaptr th H-atom and atomic orbitals. * A singl particl moving undr a cntral forc adoptd from Scott Kirby

More information

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw

More information

Hydrogen Atom and One Electron Ions

Hydrogen Atom and One Electron Ions Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial

More information

Higher order derivatives

Higher order derivatives Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of

More information

6. The Interaction of Light and Matter

6. The Interaction of Light and Matter 6. Th Intraction of Light and Mattr - Th intraction of light and mattr is what maks lif intrsting. - Light causs mattr to vibrat. Mattr in turn mits light, which intrfrs with th original light. - Excitd

More information

There is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real.

There is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real. Midtrm #, Physics 37A, Spring 07. Writ your rsponss blow or on xtra pags. Show your work, and tak car to xplain what you ar doing; partial crdit will b givn for incomplt answrs that dmonstrat som concptual

More information

Precise Masses of particles

Precise Masses of particles /1/15 Physics 1 April 1, 15 Ovrviw of topic Th constitunts and structur of nucli Radioactivity Half-lif and Radioactiv dating Nuclar Binding Enrgy Nuclar Fission Nuclar Fusion Practical Applications of

More information

Derivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian

Derivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian Drivation of Elctron-Elctron Intraction Trms in th Multi-Elctron Hamiltonian Erica Smith Octobr 1, 010 1 Introduction Th Hamiltonian for a multi-lctron atom with n lctrons is drivd by Itoh (1965) by accounting

More information

Quasi-Classical States of the Simple Harmonic Oscillator

Quasi-Classical States of the Simple Harmonic Oscillator Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats

More information

Molecular Orbitals in Inorganic Chemistry

Molecular Orbitals in Inorganic Chemistry Outlin olcular Orbitals in Inorganic Chmistry Dr. P. Hunt p.hunt@imprial.ac.uk Rm 167 (Chmistry) http://www.ch.ic.ac.uk/hunt/ octahdral complxs forming th O diagram for Oh colour, slction ruls Δoct, spctrochmical

More information

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches. Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M

More information

On the Hamiltonian of a Multi-Electron Atom

On the Hamiltonian of a Multi-Electron Atom On th Hamiltonian of a Multi-Elctron Atom Austn Gronr Drxl Univrsity Philadlphia, PA Octobr 29, 2010 1 Introduction In this papr, w will xhibit th procss of achiving th Hamiltonian for an lctron gas. Making

More information

SCIENCE Student Book. 5th Grade Unit 5

SCIENCE Student Book. 5th Grade Unit 5 SCIENCE Studnt Book 5th Grad Unit 5 Unit 5 TRANSFORMATION OF ENERGY SCIENCE 505 TRANSFORMATION OF ENERGY Introduction 3 1. Enrgy and Work...4 Enrgy 6 Work 13 Slf Tst 1 17 2. Work from Enrgy... 20 Hat Enrgy

More information

EXST Regression Techniques Page 1

EXST Regression Techniques Page 1 EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy

More information

Electrical Energy and Capacitance

Electrical Energy and Capacitance haptr 6 Elctrical Enrgy and apacitanc Quick Quizzs. (b). Th fild xrts a forc on th lctron, causing it to acclrat in th dirction opposit to that of th fild. In this procss, lctrical potntial nrgy is convrtd

More information

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin

More information

First derivative analysis

First derivative analysis Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points

More information

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005 PHYS1444-,Fall 5, Trm Exam #1, Oct., 1, 5 Nam: Kys 1. circular ring of charg of raius an a total charg Q lis in th x-y plan with its cntr at th origin. small positiv tst charg q is plac at th origin. What

More information

Voltage and Current. Objectives 2.1 INTRODUCTION 2.2 ATOMS AND THEIR STRUCTURE. I e V

Voltage and Current. Objectives 2.1 INTRODUCTION 2.2 ATOMS AND THEIR STRUCTURE. I e V oltag and Currnt 2 Objctivs Bcom awar of th basic atomic structur of conductors such as coppr and aluminum and undrstand why thy ar usd so xtnsivly in th fild. Undrstand how th trminal voltag of a battry

More information

Forces. Quantum ElectroDynamics. α = = We have now:

Forces. Quantum ElectroDynamics. α = = We have now: W hav now: Forcs Considrd th gnral proprtis of forcs mdiatd by xchang (Yukawa potntial); Examind consrvation laws which ar obyd by (som) forcs. W will nxt look at thr forcs in mor dtail: Elctromagntic

More information

REGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds

REGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds How dos light intract with mattr? And what dos (this say about) mattr? REGISTER!!! If Schrödingr s Cat walks into a forst, and no on is around to obsrv it, is h rally in th forst? sourc unknown Phys 1010

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

PHYS-333: Problem set #2 Solutions

PHYS-333: Problem set #2 Solutions PHYS-333: Problm st #2 Solutions Vrsion of March 5, 2016. 1. Visual binary 15 points): Ovr a priod of 10 yars, two stars sparatd by an angl of 1 arcsc ar obsrvd to mov through a full circl about a point

More information

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012 Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor

More information

A 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m.

A 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m. 1. Young s doubl-slit xprint undrlis th instrunt landing syst at ost airports and is usd to guid aircraft to saf landings whn th visibility is poor. Suppos that a pilot is trying to align hr plan with

More information

Chapter 13 Aggregate Supply

Chapter 13 Aggregate Supply Chaptr 13 Aggrgat Supply 0 1 Larning Objctivs thr modls of aggrgat supply in which output dpnds positivly on th pric lvl in th short run th short-run tradoff btwn inflation and unmploymnt known as th Phillips

More information

Electromagnetism Physics 15b

Electromagnetism Physics 15b lctromagntism Physics 15b Lctur #8 lctric Currnts Purcll 4.1 4.3 Today s Goals Dfin lctric currnt I Rat of lctric charg flow Also dfin lctric currnt dnsity J Charg consrvation in a formula Ohm s Law vryon

More information

surface of a dielectric-metal interface. It is commonly used today for discovering the ways in

surface of a dielectric-metal interface. It is commonly used today for discovering the ways in Surfac plasmon rsonanc is snsitiv mchanism for obsrving slight changs nar th surfac of a dilctric-mtal intrfac. It is commonl usd toda for discovring th was in which protins intract with thir nvironmnt,

More information

Differentiation of Exponential Functions

Differentiation of Exponential Functions Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of

More information

Exam 2 Thursday (7:30-9pm) It will cover material through HW 7, but no material that was on the 1 st exam.

Exam 2 Thursday (7:30-9pm) It will cover material through HW 7, but no material that was on the 1 st exam. Exam 2 Thursday (7:30-9pm) It will covr matrial through HW 7, but no matrial that was on th 1 st xam. What happns if w bash atoms with lctrons? In atomic discharg lamps, lots of lctrons ar givn kintic

More information

SPH4U Electric Charges and Electric Fields Mr. LoRusso

SPH4U Electric Charges and Electric Fields Mr. LoRusso SPH4U lctric Chargs an lctric Fils Mr. LoRusso lctricity is th flow of lctric charg. Th Grks first obsrv lctrical forcs whn arly scintists rubb ambr with fur. Th notic thy coul attract small bits of straw

More information

PHYSICS 489/1489 LECTURE 7: QUANTUM ELECTRODYNAMICS

PHYSICS 489/1489 LECTURE 7: QUANTUM ELECTRODYNAMICS PHYSICS 489/489 LECTURE 7: QUANTUM ELECTRODYNAMICS REMINDER Problm st du today 700 in Box F TODAY: W invstigatd th Dirac quation it dscribs a rlativistic spin /2 particl implis th xistnc of antiparticl

More information

ANSWERS C C =

ANSWERS C C = 107 CHAPTER E1 ANSWERS 1.2 No. of xcss lctrons -0.1 10-6 C -1.6 10-19 C 6.2 1011 6.2 10 11 lctrons hav bn transfrrd from your hair to th comb. 1.3 Elctrical: 1, 2, 3, 4, 6, 8, 12, 13 Non-lctrical: 5, 11

More information

Electrons and Conductors

Electrons and Conductors Elctrons and Conductors Atoms consist primarily of lctrons, protons, and nutrons. A modifid Bohr modl of th atom is shown blow. nuclus composd of a clustr of protons and nutrons orbital lctrons lctron

More information

Unit II: Atoms Molecules & Ions

Unit II: Atoms Molecules & Ions Unit II: Atoms Molculs & Ions A. B. C. D. Th Priodic Tabl Why and how compounds form Ruls for writing ions Writing formulas and naming compounds 1. 2. 3. Binary compounds Non-binary compounds Formula writing

More information

PH300 Modern Physics SP11 Final Essay. Up Next: Periodic Table Molecular Bonding

PH300 Modern Physics SP11 Final Essay. Up Next: Periodic Table Molecular Bonding PH Modrn Physics SP11 Final Essay Thr will b an ssay portion on th xam, but you don t nd to answr thos qustions if you submit a final ssay by th day of th final: Sat. 5/7 It dosnʼt mattr how smart you

More information

(1) Then we could wave our hands over this and it would become:

(1) Then we could wave our hands over this and it would become: MAT* K285 Spring 28 Anthony Bnoit 4/17/28 Wk 12: Laplac Tranform Rading: Kohlr & Johnon, Chaptr 5 to p. 35 HW: 5.1: 3, 7, 1*, 19 5.2: 1, 5*, 13*, 19, 45* 5.3: 1, 11*, 19 * Pla writ-up th problm natly and

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th

More information

Estimation of apparent fraction defective: A mathematical approach

Estimation of apparent fraction defective: A mathematical approach Availabl onlin at www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 011, (): 84-89 ISSN: 0976-8610 CODEN (USA): AASRFC Estimation of apparnt fraction dfctiv: A mathmatical

More information

MCE503: Modeling and Simulation of Mechatronic Systems Discussion on Bond Graph Sign Conventions for Electrical Systems

MCE503: Modeling and Simulation of Mechatronic Systems Discussion on Bond Graph Sign Conventions for Electrical Systems MCE503: Modling and Simulation o Mchatronic Systms Discussion on Bond Graph Sign Convntions or Elctrical Systms Hanz ichtr, PhD Clvland Stat Univrsity, Dpt o Mchanical Enginring 1 Basic Assumption In a

More information

AP Biology. AP Biology Photosynthesis: Life from Light and Air

AP Biology. AP Biology Photosynthesis: Life from Light and Air 2007-2008 Photosynthsis: Lif from Light and Air 2007-2008 1 Enrgy nds of lif All lif nds a constant input of nrgy Htrotrophs (Animals) consumrs producrs gt thir nrgy from ating othrs at food = othr organisms

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat

More information

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More information

1.2 Faraday s law A changing magnetic field induces an electric field. Their relation is given by:

1.2 Faraday s law A changing magnetic field induces an electric field. Their relation is given by: Elctromagntic Induction. Lorntz forc on moving charg Point charg moving at vlocity v, F qv B () For a sction of lctric currnt I in a thin wir dl is Idl, th forc is df Idl B () Elctromotiv forc f s any

More information

orbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the

orbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly

More information

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula 7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting

More information

Lecture 18 - Semiconductors - continued

Lecture 18 - Semiconductors - continued Lctur 18 - Smiconductors - continud Lctur 18: Smiconductors - continud (Kittl C. 8) + a - Donors and accptors Outlin Mor on concntrations of lctrons and ols in Smiconductors Control of conductivity by

More information

Chapter 6 Folding. Folding

Chapter 6 Folding. Folding Chaptr 6 Folding Wintr 1 Mokhtar Abolaz Folding Th folding transformation is usd to systmatically dtrmin th control circuits in DSP architctur whr multipl algorithm oprations ar tim-multiplxd to a singl

More information

Division Ave. High School AP Biology

Division Ave. High School AP Biology 2007-2008 Photosynthsis: Lif from Light and Air 2007-2008 Enrgy nds of lif All lif nds a constant input of nrgy u Htrotrophs (Animals) gt thir nrgy from ating othrs consumrs w at food = othr organisms

More information

Photosynthesis: Life from Light and Air

Photosynthesis: Life from Light and Air Photosynthsis: Lif from Light and Air SUN CO 2 12/7/2016 1 12/7/2016 2 Enrgy nds of lif All lif nds a constant input of nrgy Htrotrophs (Animals) gt thir nrgy from ating othrs at food = othr organisms

More information

dr Bartłomiej Rokicki Chair of Macroeconomics and International Trade Theory Faculty of Economic Sciences, University of Warsaw

dr Bartłomiej Rokicki Chair of Macroeconomics and International Trade Theory Faculty of Economic Sciences, University of Warsaw dr Bartłomij Rokicki Chair of Macroconomics and Intrnational Trad Thory Faculty of Economic Scincs, Univrsity of Warsaw dr Bartłomij Rokicki Opn Economy Macroconomics Small opn conomy. Main assumptions

More information

What are those βs anyway? Understanding Design Matrix & Odds ratios

What are those βs anyway? Understanding Design Matrix & Odds ratios Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.

More information

Brief Notes on the Fermi-Dirac and Bose-Einstein Distributions, Bose-Einstein Condensates and Degenerate Fermi Gases Last Update: 28 th December 2008

Brief Notes on the Fermi-Dirac and Bose-Einstein Distributions, Bose-Einstein Condensates and Degenerate Fermi Gases Last Update: 28 th December 2008 Brif ots on th Frmi-Dirac and Bos-Einstin Distributions, Bos-Einstin Condnsats and Dgnrat Frmi Gass Last Updat: 8 th Dcmbr 8 (A)Basics of Statistical Thrmodynamics Th Gibbs Factor A systm is assumd to

More information

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration

More information

PHA 5127 Answers Homework 2 Fall 2001

PHA 5127 Answers Homework 2 Fall 2001 PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring

More information

Unit 7 Charge-to-mass ratio of the electron

Unit 7 Charge-to-mass ratio of the electron Unit 7 Charg-to-ass ratio of th lctron Kywords: J. J. Thoson, Lorntz Forc, Magntic Filds Objctiv: Obsrv th rsults of lctron ba influncd by th agntic fild and calculat th charg-to-ass ratio of th lctron.

More information

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0 unction Spacs Prrquisit: Sction 4.7, Coordinatization n this sction, w apply th tchniqus of Chaptr 4 to vctor spacs whos lmnts ar functions. Th vctor spacs P n and P ar familiar xampls of such spacs. Othr

More information

GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia

GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES Eduard N. Klnov* Rostov-on-Don, Russia Th articl considrs phnomnal gomtry figurs bing th carrirs of valu spctra for th pairs of th rmaining additiv

More information

PH2200 Practice Final Exam Spring 2004

PH2200 Practice Final Exam Spring 2004 PH2200 Practic Final Exam Spring 2004 Instructions 1. Writ your nam and studnt idntification numbr on th answr sht. 2. This a two-hour xam. 3. Plas covr your answr sht at all tims. 4. This is a closd book

More information

SECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero.

SECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero. SETION 6. 57 6. Evaluation of Dfinit Intgrals Exampl 6.6 W hav usd dfinit intgrals to valuat contour intgrals. It may com as a surpris to larn that contour intgrals and rsidus can b usd to valuat crtain

More information

Sec 2.3 Modeling with First Order Equations

Sec 2.3 Modeling with First Order Equations Sc.3 Modling with First Ordr Equations Mathmatical modls charactriz physical systms, oftn using diffrntial quations. Modl Construction: Translating physical situation into mathmatical trms. Clarly stat

More information

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17) MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl

More information

5.80 Small-Molecule Spectroscopy and Dynamics

5.80 Small-Molecule Spectroscopy and Dynamics MIT OpnCoursWar http://ocw.mit.du 5.80 Small-Molcul Spctroscopy and Dynamics Fall 008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. Lctur # 3 Supplmnt Contnts

More information

General Notes About 2007 AP Physics Scoring Guidelines

General Notes About 2007 AP Physics Scoring Guidelines AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation

More information

CS 152 Computer Architecture and Engineering

CS 152 Computer Architecture and Engineering CS 152 Computr Architctur and Enginring Lctur 11 VLSI I 2005-2-22 John Lazzaro (www.cs.brkly.du/~lazzaro) TAs: Td Hong and David Marquardt www-inst.cs.brkly.du/~cs152/ Last Tim: Piplin Hazard Rsolution

More information

Contemporary, atomic, nuclear, and particle physics

Contemporary, atomic, nuclear, and particle physics Contmporary, atomic, nuclar, and particl physics 1 Blackbody radiation as a thrmal quilibrium condition (in vacuum this is th only hat loss) Exampl-1 black plan surfac at a constant high tmpratur T h is

More information

Differential Equations

Differential Equations Prfac Hr ar m onlin nots for m diffrntial quations cours that I tach hr at Lamar Univrsit. Dspit th fact that ths ar m class nots, th should b accssibl to anon wanting to larn how to solv diffrntial quations

More information

Thermodynamical insight on the role of additives in shifting the equilibrium between white and grey tin

Thermodynamical insight on the role of additives in shifting the equilibrium between white and grey tin hrmodynamical insight on th rol of additivs in shifting th quilibrium btwn whit and gry tin Nikolay Dmntv Dpartmnt of Chmistry, mpl Univrsity, Philadlphia, PA 19122 Abstract In this study mthods of statistical

More information

A Control Strategy for Photovoltaic-Solid Polymer Electrolysis System Based on Surface Temperature of PV Panel

A Control Strategy for Photovoltaic-Solid Polymer Electrolysis System Based on Surface Temperature of PV Panel Amrican Journal of Applid Scincs 5 (7): 5-, ISSN 1546-939 Scinc Publications Corrsponding Author: A Control Stratgy for Photovoltaic-Solid Polymr Elctrolysis Systm Basd on Surfac Tmpratur of PV Panl 1

More information

Math-3. Lesson 5-6 Euler s Number e Logarithmic and Exponential Modeling (Newton s Law of Cooling)

Math-3. Lesson 5-6 Euler s Number e Logarithmic and Exponential Modeling (Newton s Law of Cooling) Math-3 Lsson 5-6 Eulr s Numbr Logarithmic and Eponntial Modling (Nwton s Law of Cooling) f ( ) What is th numbr? is th horizontal asymptot of th function: 1 1 ~ 2.718... On my 3rd submarin (USS Springfild,

More information

Solid State Theory Physics 545 Band Theory III

Solid State Theory Physics 545 Band Theory III Solid Stat Thory Physics 545 Band Thory III ach atomic orbital lads to a band of allowd stats in th solid Band of allowd stats Gap: no allowd stats Band of allowd stats Gap: no allowd stats Band of allowd

More information

Bifurcation Theory. , a stationary point, depends on the value of α. At certain values

Bifurcation Theory. , a stationary point, depends on the value of α. At certain values Dnamic Macroconomic Thor Prof. Thomas Lux Bifurcation Thor Bifurcation: qualitativ chang in th natur of th solution occurs if a paramtr passs through a critical point bifurcation or branch valu. Local

More information