复旦大学2009年物理化学AI期末考试

复旦大学化学系

2008～2009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

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:

s J 1063.634⋅⨯=-h kg 1011.931-⨯=e m C 1060.119-⨯=e 18s m 109989.2-⋅⨯=c eV 10036.1mol kJ 12-1-⨯=⋅ 1231K J 10381.1cm 581.109677---⋅⨯==H R J 10986.1cm 1231--⨯= eV 212.27cm 219470Hartree 11==-

23A 1002.6⨯=N

mv

h =

λ π2h

n

M = ⎪⎪⎭

⎫ ⎝⎛-=2221111n n R λ φθcos sin r x =

φθsin sin r y =

θcos =z

φθθθθ

θ22

22222

sin 1sin sin 11∂∂+∂∂∂∂+∂∂∂∂=∇r r r r r r

φθθd drd r dxdydz sin 2=

ωI M =

l x n l x πψsin 2)(= 22

28ml

h n E n = ν

h v E v ⎪⎭⎫ ⎝

⎛

+=21

μ

π

ωk 21

=

)1(822+=

J J I

h E J π 2

21

n E -

=(atomic unit) ()()1*=⎰μμαμαd ()()1*=⎰μμβμβd ()()()()0**==⎰⎰μμαμβμμβμαd d

22

222221c

l b k a h d ++= ij R

j i g R R δχχ=∑)()(

()R R g a a R

χχ∑Γ=

)(1*

atomic mass: N-14 Ca-40 F-19

1. (12 points) This problem concerns a one-dimensional box of length a , fill with two particles.

a) (2 points) Assume the particles are not identical, and have unequal masses

1m and 2m . Write the Hamiltonian for this system inside the box.

b) (4 points) Write a wave-function ),(21x x ψ describing the two-particle

ground state, and give the quantum numbers 1n and 2n and the energy ),(21n n E of that state.

c) (4 points ）Assume the masses are equal, i.e. m m m ==21. Give the energies

of the first four 2-particle states ),(21n n E , and indicate and degeneracies. d) (2 points) Assume the particles in the box have spin 2/1=s , the same as the

electron. Write the total 2-particle ground state wave-function )2,1(ψ, including both spatial and spin parts, making sure that you account for the fact that the particles are indistinguishable and the wave-function has the proper total unsymmetry. Normalize your wave-function.

2. (6 points) Helium cations (He+) are found above the surface of the sun. They are examples of one electron atoms.

a) (1 points) Give the Hamiltonian for Helium cations in atomic unit.

b) (1 points) Calculate the energy of He+ if the electron occupies an n= 2 orbital

c) (1 points) Calculate the energy of He+ if the electron occupies an n= 4 orbital

d) (1 points) Calculate the wavenumber of a photon required to move the electron

from an n= 2 orbital to an n= 4 orbital.

e) (2 points) Please give the atomic term symbols for the ground state of He+.

3．( 6 points)The work function of silver is 4.6 eV.

a)(2 points) Calculate the kinetic energy of electrons emitted from a silver

surface when it is irradiated with UV radiation with a wavelength of 212

nm.

b)(2 points) What is the deBroglie wavelength of the emitted electrons?

c)(2 points) What light wavelength would be needed to ionize a H atom in

its ground state and produce a liberated electron with the same kinetic

energy that you calculated in part (a)?