物理化学A
2006~2007学年第一学期期末考试试卷
发布时间: 2009-08-11   浏览次数: 591

 

复旦大学化学系
20062007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: 卷    成绩:       
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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:
 
                 
            
                                                     
         
                                                          (atomic unit)    
    
                
                      
Relative atomic mass:  Ca-40 O-16
 

 

1.      Work functions, , are usually listed in units of electron volts, , where 1 = . What is the velocity of an electron emitted by Li ( ) if light having a frequency of  is absorbed?  (4 points)
 
2.      Calculate the de Broglie wavelength of an electron traveling at 1% of the speed of light ( ). (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) , ;         2) , ;  
3) , ;                  4)
 
4.      Using Bohr interpretation, for an electron having a one-dimensional wavefunction  in the range  to 1,
1)      Normalize the wavefunction;
2)      Calculate the probability that the electron is in the first half of the range, from  to ;
3)      Calculate the probability that the electron is in the middle half of the range, from  to .
4)      Calculate the energy of this electron (assume that the potential energy is zero, or ).
5)      Calculate the average value of the position of this electron in the range of  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 . If this transition corresponds to an  to  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  for the hydrogen atom? (5 points)
 
7.      For a body-centered cubic lattice, please calculate the inter-planar spacing  between the (100), (110) and (111) planes, respectively. (6 points)
 
8.       For two the  hybrid orbits on the same atom  and   ,
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)
 
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) (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