課程名稱︰物理化學二
課程性質︰必帶
課程教師︰陳振中
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰97/12/14
考試時限（分鐘）：120 (有延長20-30分鐘)
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
1. Calculate the de Broglie wavelengths of the following:
(a) A 1g bullet with velocity 300m/s
(b) An H2 molecule with energy of 1.5kT at T=20K
Useful constant: k=1.381*(10^-23) J/K, H: 1.007825*(10^-3) kg/mol
^ ^ ^ ^
2. Evaluate the commutators [x, Px] and [y, Px].
3. Show that the wavefunctions for a particle in a one-dimensional (1-D) box
are orthogonal using
sinαsinβ = 0.5cos(α-β) - 0.5cos(α+β)
Hint: Wavefunction for a particle in a 1-D box is
Ψn = (2/a)^(0.5)*sin(nπx/a), where n is positive integer and a is length
of box.
4. For the wavefunction
│ΨA(1) ΨA(2)│
Ψ = │ │
│ΨB(1) ΨB(2)│
Show that
(a) the interchange of two columns or two rows changes the sign of the wave
function
(b) the two electrons cannot have the same spin orbital
5. Consider a particle in the rectangular box of dimension a×b:
b
┌───────────┐
│ │
a│ │
│ │
└───────────┘
(a) Derive the wavefunctions and the corresponding energies.
(b) Suppose we have 8 non-interacting particles placed in the box. If each
particle has a spin quantum number of 2, determine the position(s) in the
rectangular box where we have the highest probability to find a particle
at 0K.
(c) If each of the eight particles is of spin 3/2, determine the position(s)
in the rectangular box where we have the highest probability to find a
particle at 0K.
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