課程名稱︰物理化學二 課程性質︰必修 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）︰98.11.21 考試時限（分鐘）：120 是否需發放獎勵金：yes （如未明確表示，則不予發放） 試題 : 1.(a) (8%) What is the de Broglie wavelength of a thermal neutron at 300K? (E=3kT/2) (b) (8%) The lifetime of a molecule on a certain electronic state is 10^-10 s. What is the uncertainty in energy of this state? Give the answer in J/mol. (c) (8%) Assume the form Ψ0 = N0 e^(-ax^2) for the ground-state wavefunction of the harmonic oscillator, and substitute this into the Schrodinger equation. Find the value of a that makes this an eigenfunction. (d) (20%) What are the reduced mass and moment of inertia of H(35)Cl? The equilibrium internuclear distance Re is 127.5 pm. What are the values of L, Lz, and E for the state with l=1? 2.(a) (8%) Calculate the ground-state ionization potentials for He+, Li2+, Be3+, C5+ . (b) (8%) Calculate the Rydberg constant R(H) for a hydrogen atom and the Rydberg constant R(D) for a deuterium atom. (c) (8%) Given that 1s wavefunction for a hydrogenlike atom is proportional to exp(-Zr/a0), calculate the normalization factor for this wavefunction. (d) (8%) Use the wavefunction for an electron on a 1s orbital to derive the expression for the average distance between the electron and the nucleus in a hydrogenlike atom. 3.(a) (6%) Consider a particle in a one-dimensional well, for which we have 0 for -L/2≦x≦L/2 V(x) = ∞ for x＞L/2 ∞ for x＜-L/2 Write down the wavefunction of the system. (b) (6%) Suppose we have two electrons in the above one-dimensional well. For simplicity, let us ignore the spin angular momentum and the electrostatic interaction between the two electrons. Assume that two electrons are at the state n=2 and n=3. Using y1 and y2 to denote the positions of the teo electrons, write down the corresponding normalized wavefunction of the system. (c) (6%) What is the normalized wavefunction in (b) if the particles are 14N? (d) (6%) Ignore spin angular momentum. Consider the following probability distribution function for two particles in a one-dimensional box. The x and y coordinates correspond to the positions of the particles. The figure on the right hand side is the contour plot of the left figure. (左圖略) (右圖略) Are the particles bosons or fermions? Explain. R(∞)= 1.097 x 10^7 1/m Electron mass: m(e)= 9.109 x 10^-31 kg Proton mass: m(p)= 1.673 x 10^-27 kg Neuron mass: m(n)= 1.675 x 10^-27 kg Deuteron mass: m(d)= 3.344 x 10^-27 kg Planck constant: h= 6.626 x 10^-34 Js --

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