課程名稱︰普通物理學甲下 課程性質︰系定必修 課程教師︰林敏聰 開課學院：理學院 開課系所︰物理學系 考試日期（年月日）︰2008.6.14 考試時限（分鐘）：五小時 是否需發放獎勵金：是！ （如未明確表示，則不予發放） 試題 : 14.June 2008 1. Please use the Bragg relation in a low energy electron diffraction experi- ment to express the vertical interlayer distance d by the primary energy of the electron Ep, electron mass m, and the incident angleθ with respect the sample surface. (10%) 2. In an oscillation series RLC circuit, find the time required for the maximum energy present in the capacitor during an oscillation to fall to half its initial value. Assume q=Q at t=0. (10%) 3. As indicated in the Fig.1, on the flat table, there is a metal rod with mass m and resistor R sitting across two parallel conducting wires with separation of L. Over the whole system, there is an external uniform magnetic field B applied with the direction into the table. At the beginning, the rod is static without moving, and the switch S on the circuit contact at the point a. After the capacity C is completely charged by the battery of voltage V0, the switch S changes to contact point b and then the rod starts moving. (1) What's the maximum speed of this rod? (2) Define the efficiency Y=(kinetic energy of rod/ electric energy of capacity C fully charged), in what condition the Y is maximum and find out its value. (10%) 4. Please derive the relation of c=(μ0ε0)^(-1/2) and E/B=c in a traveling electromagnetic wave in application of Maxwell's equations. (10%) 5. In Thomson's atom model, there are number of Z electrons uniformly distributed inside an atom. As shown in the Fig.2 in the Thomson's αparticle scattering experiments, oneαparticle with mass m and initial speed v inserted into an atom with atomic number Z (Z>>2) and radius R. Assume the collides parameter b and the mass of αparticle is much larger than the electrons such that the electrons will be scattered out of atom by the αparticle and the interaction between the electrons and αparticle can be ignored. Find (1) when αparticle has distance r from the center of the Thomson atom, what are the lelctric forces of αparticle when r<R and r>R, respectively? (2) From the experiments, the scattering angle is very small for the α particle, try to estimate this angle. (3) Assume the 5MeV αparticle inserted into the fiol of gold with atomic number of 79 and radius of gold atom is 10^-9m, find out the scattering angle of αparticle. (15%) 6. Explain the concept of duality, and give two examples (described in details, please) for the "wave" behaving as "particle" and "particle" as "wave", respectively. Finally, if someone asks: "is" the light "particle" or "wave"?, what would your answer be? (10%) 7. Please write down the operator of linear momentum P in the one-dimensional Schrodinger equation. Please try to give a "heuristic derivation" of this operator. (10%) 8. Please write down the one-dimensional Schrodinger equation for a free particle with mass m, and find out the solution of the wave function. Give a brief interpretation of your solution. Is now the energy quantized? Why? (10%) 9. (a) What is the Stern-Gerlach experiment? Pleae give the interpretation of this experiment. (10%) (b) Consider a single electron passing through the Stern-Gerlach Magnet along the z-axis (y-axis is the moving direction), followed by an x-axis Stern-Gerlach Magnet. Please describe the possible result of the measurement on spi after passing these two Stern-Gerlach Magnets. (5%) 10. Good luck and have a nice summer vacation !!! (Total 100%) Fig.1 S a b × × × × × × × × × × ┌───↑───═══════╬════════─ │ │ × × × × x║× × × × × ↑ ─┴─ ─┴─ C ║R │L V0 ┬ ─┬─ × × × × x║× × × × × │ │ │ ║ ↓ └───┴───═══════╬════════─ × × × × × × × × × × m Fig.2 v ╭────┬────╮ ──→──────── │ │ │ ↑b │ │R │ ↓ │ │ │ -----------------------│--------‧--------│ │ │ │ 這是圓。 │ │ │ ╰─────────╯ --

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