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(chem222)[2007](s)mid~PPSpider^soL_10045.pdf
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CHEM 222 C Physical Chemistry II
Midterm Examination (1010 points; 50 minutes; Close-book examination)
26 March 2007, Friday, 2:00 C 2:50 pm; Rm# 3008
(Note: Use the two blank sheets in the back for your scratch; No question explanation intervene!)

NAME: (English) (Chinese) STUDENT ID#
Tips:
(a) Useful constants: Planck constant: h = 6.62610.34 J s . = h/2 = 1.05457 10.34 J s Speed of light: c = 2.998 108 m s-1 Mass of electron: me = 9.11 10.31 kg 1
(b) Energy in wavenumber (inverse wavelength): 1 cm.1 <==> 1.986 10.23 J = eV
8065.5
========================= GOOD LUCK ===========================
1. (52pts) Basic relations (M/C; choose the most appropriate one in each)
(i)
For a light of wavenumber 10.0 cm.1, the corresponding wavelength is

(a)
10 cm (b) 1.0106 nm (c) 1.0107 nm (d) 3.0105 nm

(ii)
The wavenumber of 10.0 cm.1 corresponds to the value of energy of

(a)
2.010.22 J (b) 5.01022 J (c) 2.010.23 J (d) 5.010.23 J


(iii) What type of molecular process would like to absorb of 10.0 cm.1 light?
(a)
translation (b) rotation (c) vibration (d) electronic transition

(iv)
What is the wavelength of a free electron moving at a speed of 1.0 km/second?

(a)
1.0103 m (b) 727 cm.3 (c) 727 nm (d) 7.27 nm

(v)
In a photoelectron experiment on metal, it is known that a light of wavelength of 500 nm can eject out a free-electron with zero kinetic energy. Therefore, a light of wavelength 600 nm can eject out a free-electron with the velocity of


-1 1.986 10-21 .1
(a) 4.67105 m s(b) 100 m s-1 (c) m s(d) no photoelectron at all
9.1110-31
2. (101pts) Basic concepts/results in quantum mechanics (True/False) (T/F) The wavefunction (x,t) in quantum mechanics is used to describe the wave.particle duality of matter (T/F) While (x,t) must be continuous function, its space-derivative .(x,t)/ .x can be
non-continuous function in space (T/F) Due to quantization that n=0,1,, the wavefunction (x) can be of multiple-value in space (T/F) The uncertainty relation xpx ./2 says that the coordinate and its conjugate momentum
cannot be measured simultaneously at arbitrary precision; but can do it individually (T/F) Tunneling occurs in both quantum and classical physics (T/F) Inference occurs in both quantum and classical physics (T/F) The phenomenon of zero-point energy is related to the uncertainty principle in quantum
mechanics
(T/F) If [ A., B. ] = 0, then there must have a common set of eigenfunctions for both . and B.
(T/F) Eigenvalues of a hermite operator . = .. are all real
(T/F) The eigenfunctions of a hermite operator associating with different eigenvalues are

usually non-orthogonal, unless they are both normalized
3. (42.5 pts) Basic relations and commutator algebra
(i) (30.5+1) Write down (without derivation)