Things you should know when you leave Discussion today for one-electron atoms:

Transcription

1 E = -R Thigs ou should kow whe ou leave Discussio toda for oe-electro atoms: = J = -.6eV ΔEmatter=E-Em ; Ioizatio Eerg=E E(iitial) ΔΕlight=hνlight= IE +KE. Cosider the followig eerg levels of the hdroge atom as show below i the diagram: a. Sketch electro clouds correspodig to eerg levels up to =.( ext to the lies o the right ) = = = b. Whe electro cloud of the H atom at the lowest eerg iteracts with light of the lowest resoate frequec, sketch the resultig electro cloud(s). c. Whe electro cloud of the H atom at the lowest eerg iteracts with light of the d lowest resoate frequec, sketch the resultig electro cloud(s). d. Whe electro cloud of the He atom at the lowest eerg iteracts with light of the lowest resoate frequec, sketch the resultig electro cloud(s). Ol two: e. What are the two eerg levels ivolved i the ioizatio of a electro from H i the groud state? = ad = f. What is the groud state H atom ioizatio eerg? (H(g) H + (g) + e - ) E = J = -.6eV IE= J =.6eV= kj mol

2 g. What is the expressio for the ioizatio eerg of a electro from the = state of a atom with atomic umber this is for oe-electro atom? IE= R. A atom, X, has the followig groud state absorptio spectrum (displaed below), ad the groud state ioizatio eerg of the atom is 5eV (IE). Each of the absorptio lies correspods to a atural frequec of the electro cloud resultig from the mixig of electro wave with loop with electro wave with more tha oe loop (i.e. the atom alwas starts i its groud state i each absorptio). (I aswerig the followig questios, assume that the zero of eerg is the ioized atom) X X + + e -.

3 (a) What is the eerg of the groud state (of the electro cloud correspodig to oe loop) of X? (Careful of a sig!) 5ev (b) Costruct the eerg level diagram for X. (Hit: How ma eerg levels are ecessar to accout for the absorptio spectrum?) (c) = =6 -ev 0ev =5-7eV =4-8eV = -0eV = -4eV = -5ev (d) Usig the eerg level diagram ou just did draw: How ma lies will be preset i the electricall-excited emissio spectrum of this atom? At least 5 lies look at a repetitios of the differeces. (e) What is the eerg of the third excited state of X? -8eV How ma loops does that state have?4 (f) What is the eerg of the highest eerg state of X that is ecessar to accout for the absorptio spectrum? -ev (g) Is it possible for a electro i the groud state of atom X to absorb light of eerg ev or will it be trasparet to it? NO, it will be trasparet to it. (h) Ca atom X emit light of eerg ev? Yes (i) Is it possible for X to absorb light of eerg 6eV or will it be trasparet to it? Wh? Yes. The excess eerg will be carried awa as kietic eerg b the ioized electro. (j) Ca atom X emit light of eerg6 ev? NO (k) What is the lowest frequec of the light emitted from the atom? We eed to look for smallest E ad it is -ev; E =-ev= J= -hνlight νlight== Js (l) Draw the emissio spectrum: -9 J Hz

4 . What is the expressio for the eerg i J for the groud state of a electro cloud i Li +? E=-R 9Rhc a. Calculate wavelegth (i m) of the light correspodig to the Li + electro cloud resultig from mixig a loop electro wave with a loop electro wave? hc 9 9 ΔElight+ΔEatom=0 R( ) R( ) ; m 9 fial 4. What electro cloud eergies accout for the lie correspodig to the wavelegth 44 m i the gas discharge spectrum for the Balmer series of H atoms? (I the Balmer series i each of the emissio lies correspods to a atural frequec of the electro cloud resultig from the mixig of a electro wave with more tha two loop with the electro wave with loop) iitial A. Ol the = cloud eerg B. Ol the = 4 cloud eerg C. Ol the = 5 cloud eerg D. The = ad = 4 cloud eergies E. The = ad = 5 cloud eergies F. Noe of these. 5. Photos of eerg.6ev=r are able to ioize H i its = eerg level. Are photos of this eerg are able to ioize He + i its = eerg level? Yes For He + : E = -.6eV IE=0 - E=.6Ev 6. The light with wavelegth of 65 m will ioize H atom i the = eerg level. What effect will light with wavelegth = 657 m have? (Choose all that appl) a. Atom will be trasparet to the light of this wavelegth. b. Ioizatio will take place c. Ioizatio will ot take place d. The ioized electro will use excess eerg for kietic eerg 7. The light with wavelegth of 65m will ioize H atom i the = eerg level. What effect will light with wavelegth = 65m have? (Choose all that appl) a. Atom will be trasparet to the light of this wavelegth. b. Ioizatio will take place c. Ioizatio will ot take place d. The ioized electro will use excess eerg for kietic eerg 4

5 8. The photoelectric effect threshold frequec of a metal is υ0 = 0 5 Hz. Gamma radiatio of frequec 0 7 Hz ejects electros from the metal. Which of the followig occurs whe the itesit of the gamma radiatio is reduced b 50 %? KE= Elight- hυ0=hυlight- hυ0 chagig itesit does ot chage KE a. The velocit of the ejected electros will be reduced b a factor of two. b. The kietic eerg of the ejected electros will be reduced b a factor of two. c. The kietic eerg of the ejected electros will be reduced b a factor of four. d. Kietic eerg ad the velocit of the ejected electros will sta the same. e. Number of ejected electros will icrease f. Number of ejected electros will decrase 9. Assume light is able to eject electros from a metal. What do ou expect as the wavelegth of the light is hc icreased? hυ0 = KE a. If the light wavelegth reaches the lowest, electros will o loger be ejected. b. Electros will still be ejected but the will move faster ad faster. c. Electros will still be ejected but the will move slower ad slower. d. More ad more electros will be ejected but the will have the same kietic eerg. e. More iformatio eeded. 0. A electro is ioized from the groud state of a atom, with E = J, b light with frequec Hz. What is the kietic eerg (i ev) of the ejected electro? Elight=hν= J IE=- E =. 0-9 J KE= Eligh t- IE= J=.eV. The work fuctio (ioizatio eerg), of chromium metal is 7.x0-9 J. What is the maximum kietic eerg of a electro, if it is ejected from chromium metal b light of wavelegth 50.m? KE= ΔΕlight-IE( hc J J What will happe to the speed ad quatit of the ejected electros if the wavelegth of the light is icreased? Speed will be decrease but umber of ejected electros will be the same a. What will happe to the speed ad quatit of the ejected electros if the wavelegth of the light is decreased? Speed will be icrease but umber of ejected electros will be the same b. What will happe to the speed ad quatit of electros if the itesit of the light is icrease? Speed will be the same but umber of ejected electros will icrease. A atom has ol three eerg levels, -.5, -4.0, ad -4.5 ev. Draw the absorptio spectrum for a gas of these atoms excited b a electric discharge. (Hit: ou eed to draw eerg level diagrams to aswer this questio assume the most egative eerg is a eerg of the groud state) 0.5ev ev 4.5ev 5

6 b. Draw the emissio spectrum. (Hit: does it alwas just goes to the groud state?) 0.5ev.5ev. ev. Oe atom emits light of eerg.7 ev. A secod atom has ol three eerg levels: -0.9 ev, -.7 ev, ad -.9 ev. Assumig ioizatio is ot possible ca the secod atom absorb the light emitted b the first atom? No Thigs ou should kow whe ou leave Discussio toda. Atomic wave fuctio famil album a. Priciple quatum umber =,,, specifies eerg level = j+l b. Number of odal plaes (l). c. Agular mometum quatum umber (l=0,,, -) defies the shape of the orbital. d. ml= -l,.0 l e. Number of loops j (j=-l) f. S, P ad D ad F orbitals. g. Size of the orbital is proportioal to Electro cofiguratio a. Orbital, Shell, Subshell b. Shieldig c. Pauli Exclusio Priciple. Auf-bau. Hud s rule Periodic Treds (I.E., E.A., Radius, Ioic Radius, Electroegativit) eff 8 eff kj eff For ma electro atoms: E.6(eV).80 (J) mol Useful Iformatio Below dx, dx - ad dz orbital. Be sure to correctl oriet our orbitals i the x--z space. 6

7 Orbital l =j+l j= -l Shape Number of orbitals i a subshells(ml) l+ s 0 p d etc 4 etc 4 etc j= j=- j=- Sphere Dumbbell orietatio i space # e - that ca fit 6 Cloverleaf 5 0 f 4 5 etc j= For the two hdroge electro clouds below idetif the quatum umber, the quatum umber l, the umber of radial loops j, ad the specific ame of the orbital (ou must idicate orietatio, e.g. dx). A z z =4 l= j= =4 l= j= x x ame: 4d zx ame:4p x a. For the two hdroge electro clouds above, which has the largest ioizatio eerg? (Note: i H atom, all orbitals of same have the same eerg.) the same. What are the possible agular mometum quatum umbers for a orbital i the =4 shell? 0,,, How ma degeerate orbitals are i the = shell? What are the?(note: i H atom, all orbitals of same have the same eerg.) 4. The figure shows three H atom electro clouds. 7

8 a. Which of the followig H atom electro clouds has the largest ioizatio eerg? b. Write dow the umerical expressio that whe evaluated gives the value i ev of smallest ioizatio eerg of these three clouds.( Aswer: 0.85) A: B: C: S 4p d IE= E -Eiitial=.6 =.6eV/6 =0.85ev Additioal Practice problems:. The ioizatio wavelegth of H atom i the = eerg level is 65 m. Will light of this wavelegth ioize He + i the = level? No Εlight= hc IE (He + 8 ) =.8 0 (J) = J. A electro is ioized from the groud state of a atom, with E = 0 ev, b light for which a photo of light eerg is 6 ev. What is the kietic eerg (i ev) of the ejected electro? 6 ev. What is kietic eerg of the electro ioized from Li + i its = 6 level b light of wavelegth 0 m?(aswer: 0.94*0-9 ) KE= hc (J) 6 = J 4. I terms of the variables ( like: R, h, ad c) what is the smallest possible wavelegth of light that will be emitted b a He + atom startig with the eerg correspodig to 6 loops? hc 4 4 9hc R( ) R( ) ; 6 5R light fial iitial 5. What is the largest possible wavelegth of light that will be emitted b be the Li + atom with the eerg level correspodig to 6 loops? hc light R ( fial iitial ) R( ) 6 ; 00hc R 8

9 I preparatio for lectures ad ext week discussio: 6. Draw the electro cofiguratio diagram for C, but fill the diagram as if the C is i the groud state. Draw a dotted lie aroud a shell. Circle a subshell. Draw a triagle aroud a orbital. Is C atom paramagetic or diamagetic? a. Calculate eff of C, if IE = 086 kj/mol. 8 eff (Hit: IE= E -Eiitial =.8 0 (J) ) IE (J)= 086 kj/mol *0 /NA=8 0 0 J ; eff= IE Rhc =.8 9

10 Atom He Li Be 4 B 5 Electro cofiguratio IE kj mol eff Treds i IE is Explaied b: a. icreases b. Electro electro repulsio c. New shell d. l icreases or eff decreases (shieldig) Ios (Ios Electro cofiguratio) s 7.5 a He + s 548 s s 50.6 c, d s s s px s Li + s a,b Be + d s s IE kj mol B + 40 C 6 N 7 O 8 F 9 s p x p s s px p pz s s px p pz s 4.00 s px p pz s a C + s s px a N + s s p x p b O + s s p p p a x z F + 70 Ne 0 Na s px p pz s s s px p pz s [ Ne]s s s p Mg [ Ne]s x p p z s a,b Ne + s s p p p x z c, d Na + s s p p p x z a Mg + [ Ne ]s Al [ ]s px Ne d Al + [ Ne ]s 80 0

11 Atom He Ios (Ios Electro cofiguratio) Li Li + IE kj mol He + s 548 s Be 4 Be + B 5 s s B + 40 eff For the Ios Treds i IE is Explaied b: a. icreases b. Electro electro repulsio c. New shell d. l icreases or eff decreases (shieldig) C 6 C + s s px s s p x p N 7 N s s p p p O 8 O + F 9 x z F s s p p p Ne 0 Ne + x z s s p p p Na Na + x z Mg Mg + [ Ne ]s Al Al + [ Ne ]s

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