复旦大学化学系 2006~2007学年第一学期期末考试试卷 □A卷 课程名称: Physical Chemistry,课程代码 开课院系: Chemistr考试形式:闭卷成绩: 姓名 学号 专业 S core 0. 10 14 16 Score This is a closed book exam. Use of a calculator and an English dictionary is permitted. Show all of your work and check your units carefully. Don' t give help to, or get help from, others. Thanks for your cooperation. GOOD LUCK! Some useful constants and results are h=663×1034sm。=9.1×10-1kge=1.60×10-Cc=29989×105ms-1 kJ/mol=1.036×102eRn=109677581cm-1=1381×10-23JK-1 lcm-1=1.986×1023J1 Hartree=219470cm1N4=6.02×1023 E=hv=hc/a,h △xAp≥h △EM≥hM=n 元一(x=如m9y=如Om=O sin088 a8 r sin 089 dxdydz=rsin Adrdado y(x) 2 nI E (v+1/2)h
复旦大学化学系 2006～2007 学年第一学期期末考试试卷 □A 卷 课程名称： Physical Chemistry 课程代码：____________________ 开课院系：__ Chemistry _ 考试形式：闭 卷 成绩： 姓 名： 学 号： 专 业： No. 1 2 3 4 5 6 7 8 Score No. 9 10 11 12 13 14 15 16 Score This is a closed book exam. Use of a calculator and an English dictionary is permitted. Show all of your work and check your units carefully. Don’t give help to, or get help from, others. Thanks for your cooperation. GOOD LUCK！ Some useful constants and results are: h Js 34 6.63 10− = me kg 31 9.11 10− = e C 19 1.60 10− = 8 1 2.9989 10 − c = ms kJ mol eV 2 1 / 1.036 10− = 1 23 1 109677.581 1.381 10 − − − RH = cm = JK cm J 1 23 1 1.986 10 − − = 1 1 219470 − Hartree = cm 23 NA = 6.0210 E = h = hc / mv h = xp h Et h 2 h M = n = − 2 2 2 1 1 1 1 n n R x = rsin cos y = rsin sin z = cos 2 2 2 2 2 2 2 sin 1 sin sin 1 1 + + = r r r r r r dxdydz r sin drdd 2 = M = I l n x l x sin 2 ( ) = 2 2 2 8ml n h En = Ev = (v +1/ 2)h
E 82√(+1) E (atomic unit) 2T V 2 ∫a"(a(uk=1∫+()(=1Ja+()p(nd=JB*(nkl(M=0 n( 2ax) xsin bxdx 4 sin( 2bx)---cos(2bx) d 2 h2k212 b x1(R)(R)=g6 ∑x(R)z2( Relative atomic mass: Ca-40 0-16 Work functions, o, are usually listed in units of electron volts, el wheree 1.602x10-J. What is the velocity of an electron emitted by Li(o=2.90ev )if light having a frequency of 4.77x10's" is absorbed? (4 points 2. Calculate the de broglie wavelength of an electron traveling at 1% of the speed of ight (0.01c=3.00x10%m/).(4 points) 3. Which of the following expressions are acceptable wavefunctions, and which are not? For those that are not, state why? (8 points 1)f(x)= 0<x<10 2)f(x)= 0<x<3 4 3)f(x) √x ,x≥0 4)f(x)=x2+1 4. Using Bohr interpretation, for an electron hav ing a one-dimensional wavefunction y=Nsin( a)in the range x=0 to 1, 1)Normalize the wavefunction 2) Calculate the probability that the electron is in the first half of the range, from x=0to0.5 3)Calculate the probability that the electron is in the middle half of the range, from x=0.25 to 0.75 4)Calculate the energy of this electron(assume that the potential energy is zero
k v 2 1 = ( 1) 8 2 2 = J J + I h EJ 2 2 1 n E = − (atomic unit) *( ) ( ) = 1 d *( ) ( ) = 1 d *( ) ( ) = *( ) ( ) = 0 d d ( ) sin( 2 ) 4 1 2 1 sin 2 ax a dx ax = x − 2 cos 2 2 2 c = a + b + ab cos(2 ) 8 1 sin( 2 ) 4 4 sin 3 2 2 bx b bx b x x x bxdx = − − 2 2 2 2 2 2 2 1 c l b k a h d = + + ij R i (R) j (R) = g R (R) g a a R = ( ) 1 * Relative atomic mass: Ca-40 O-16 1. Work functions, , are usually listed in units of electron volts, eV , where 1 eV = J 19 1.602 10− . What is the velocity of an electron emitted by Li ( = 2.90eV ) if light having a frequency of 15 1 4.77 10 − s is absorbed? （4 points） 2. Calculate the de Broglie wavelength of an electron traveling at 1% of the speed of light ( 0.01c 3.00 10 m /s 6 = ). (4 points) 3. Which of the following expressions are acceptable wavefunctions, and which are not? For those that are not, state why? （8 points） 1) x f x − = 4 1 ( ) , 0 x 10 ; 2) x f x − = 4 1 ( ) , 0 x 3 ; 3) f (x) = x , x 0 ; 4) ( ) 1 2 f x = x + 4. Using Bohr interpretation, for an electron having a one-dimensional wavefunction = N sin(x) in the range x = 0 to 1, 1) Normalize the wavefunction; 2) Calculate the probability that the electron is in the first half of the range, from x = 0 to 0.5 ; 3) Calculate the probability that the electron is in the middle half of the range, from x = 0.25 to 0.75. 4) Calculate the energy of this electron (assume that the potential energy is zero
or V(x)=0) 5)Calculate the average value of the position of this electron in the range of x=0 to 1.(12 points) 5.B- Carotenes(B-胡萝卜素) are highly conjugated polyenes found in many vegetables. They can be oxidized and used to synthesize pigments that play important roles in the chemistry of mammalian vision. The parent compound B-carotene, has a maximum absorption of light that occurs at 480nm. If this transition corresponds to an n=ll to n=12 transition of an electron in a particle-in-one-dimension-box system, what is the approximate length of the molecular“box? 6. what is the average value of the total angular momentum for P, for the hydrogen atom? (5 points 7. For a body-centered cubic lattice, please calculate the inter-planar spacing d between the (100),(110) and(111)planes, respectively.(6 points) 8. For two the sp" hy brid orbits on the same atom, d,=J3$+V3P, and F Pa Py 1)Show that they are orthogonal; 2)Show that they have same energy 3)Show that they are oriented 120 apart. (12 points) 9. Predict the bond order in each of the following species 2)H 3)Li2t;4)C2 10. A metallic solid is characterized by a unit cell with an atom of element X located at each of the corners of the cell. one atom of element y at the center and an atom of element Z located at each of the edges. Please give the empirical formula of the solid. (5 points)
or V (x) = 0 ). 5) Calculate the average value of the position of this electron in the range of x = 0 to 1. (12 points) 5. -Carotenes （ -胡萝卜素） are highly conjugated polyenes found in many vegetables. They can be oxidized and used to synthesize pigments that play important roles in the chemistry of mammalian vision. The parent compound, -carotene, has a maximum absorption of light that occurs at 480 nm . If this transition corresponds to an n =11 to n =12 transition of an electron in a particle-in-one-dimension-box system, what is the approximate length of the molecular “box”? (6 points) 6. What is the average value of the total angular momentum for 3 p for the hydrogen atom? （5 points） 7. For a body-centered cubic lattice, please calculate the inter-planar spacing d between the (100), (110) and (111) planes, respectively. (6 points) 8. For two the 2 sp hybrid orbits on the same atom， px s 3 2 3 1 1 = + and px py s 2 1 6 1 3 1 3 = − − , 1) Show that they are orthogonal; 2) Show that they have same energy. 3) Show that they are oriented 120▫ apart. (12 points) 9. Predict the bond order in each of the following species: 1) N2 + ; 2) H2 -； 3）Li2 + ; 4) C2 + 10. A metallic solid is characterized by a unit cell with an atom of element X located at each of the corners of the cell, one atom of element Y at the center, and an atom of element Z located at each of the edges. Please give the empirical formula of the solid. (5 points)
I 1. The ionic radius of Cat and o--are 100pm and 140pm, respectively. (12 points) 1)Which kind of coordination polyhedra does calcium oxide belong to? 2) If adjacent Ca?+ and O- spherical ions are touching, calculate the edge length of the unit cell 3) Calculate the density for this solid 12. The valence electron configuration of gold is 5d6s. Recent stud ies show that the onding property of gold is quite similar to hydrogen. Please using Huckel molecular-orbital theory to determine whether the gold trimer cation(Au3)is a stable molecule or not. If it is stable, please tell the most stable structure of the cation(12 points) 13. Both CO and H,o molecules can be used as ligands. It is found that iron atom can coordinate five CO molecules to form Fe(CO)5, which is quite stable. However, no stable Fe(H2O)5 molecule has been observed. Why? (6 3) 14. What different point groups may the biphenyl molecule belong to, depend ing on the rotational relationship of the two rings about the central C-C bond? Consider the same question for ferrocene(6 points) 15. For a bent AB2 molecule, taking the p orbital perpendicular to the molecular plane of each B atom as bases, work out the symmetry-adapted linear combination orbitals using projection operators(8 points) EC20(x-)O,(z) B y,R
11. The ionic radius of Ca++ and O2- are 100pm and 140pm, respectively. (12 points) 1) Which kind of coordination polyhedra does calcium oxide belong to? 2) If adjacent Ca2+ and O2- spherical ions are touching, calculate the edge length of the unit cell; 3) Calculate the density for this solid. 12. The valence electron configuration of gold is 5d106s1 . Recent studies show that the bonding property of gold is quite similar to hydrogen. Please using Huckel molecular-orbital theory to determine whether the gold trimer cation (Au3 + ) is a stable molecule or not. If it is stable, please tell the most stable structure of the cation. (12 points) 13. Both CO and H2O molecules can be used as ligands. It is found that iron atom can coordinate five CO molecules to form Fe(CO)5, which is quite stable. However, no stable Fe(H2O)5 molecule has been observed. Why?(6 分) 14. What different point groups may the biphenyl molecule belong to, depending on the rotational relationship of the two rings about the central C-C bond? Consider the same question for ferrocene. (6 points) 15. For a bent AB2 molecule, taking the p orbital perpendicular to the molecular plane of each B atom as bases, work out the symmetry-adapted linear combination orbitals using projection operators (8 points). C2v E C2 σv (xz) ' v (yz) A 1 1 1 1 z , x2 , y2 ,z2 A2 1 1 -1 -1 Rz xy B1 1 -1 1 -1 x,Ry xz B2 1 -1 -1 1 y ,Rx yz
