110年 - 110 國立清華大學碩士班考試入學試題_聯合招生:近代物理#105281

Part A. Please answer the questions "in brief'. (Explanation is NOT necessary.)
1. Please specify the (1) Symbols, (2) Values of Ranges and their Correlations
of the (A) Principal, (B) Orbital angular and (C) Magnetic quantum numbers.

(1) a Co atom (atomic number = 27)

and (2) , in terms of s, p, d.

3. Please write down THREE Phenomena concemning photons transferring energies to matters/particles.

4. Which experiment(s) or phenomenon(a) is/are related to the concept of "Quantum"? (A) Blackbody radiation, (B) Photoelectric effect, (C) Compton scattering, (D) Bremsstrahlung and (E) Zeeman effect.

5. Which equipment(s) is/are related to the theories or concepts of "Quantum"? (A) Scanning tunneling microscope,(B) Transmission electron microscope, (C) Atomic absorption spectrometry and (D) Rutherford backscattering spectrometry. Part B. Please answer the questions "in detail".

6. (1) What the is the Heisenberg Uncertainty Principle? (Please write down TWO types of equations and explain their meanings.)

(2) Is the uncertainty due to the inaccuracy of measurement? (Yes or No) _

7. Please write down the Equation of one-dimensional time-independent Schrodinger equation (THREE terms) and explain each component of this equation.

8. Please draws the Allowed Projections of the orbital angular momentum of a state with / = 2. (Please specify their z components and the length of the vector .)

Part B. Please answer the questions "in detail".

9. (1) Please define Zero-Point Energy (ZPE). (2) Please explain zero-point energy in terms of both (A) Harmonic oscillator and (B) A trapped particle in a one- dimensional box.

10. Please draw the (1) Potential well and Energy levels with specifying their ZPEs) and (2) Correlation between En and their quantum number of (A) Harmonic oscillator for n = 0 ~ 3 and (B) Infinite square well potential for n =1~ 3. (3) Please specify if their energy level intervals are equal?

11. How did Davisson and Germer prove the electron's wave property? (Please answer this question by simply drawing and explaining the experimental results, and prove the electron's wave property by using some relations/equations for its de Broglie wavelength from known or/and measured parameters.)

(1) Kinetic energy,

(2) Phasc velocity, and

(3) Group velocities of its de Broglie waves. (Relativistic effects should be considered.)

13.For a free particle, y = A eitbxw#, please calculate the Expectation Value of Momentum.

(1) Wavelength (nm),

(2) Frequency (Hz) and

(3) Energy (eV) of the electromagnetic wave emitted.

15. Please calculate the Change in Wavelength (nm) of the 2p -7 Is photon when a H atom is under a magnetic field of 1 T.

110年 - 110 國立清華大學碩士班考試入學試題_聯合招生:近代物理#105281

試卷資訊

選擇題 (0)

申論題 (21)