111年 - 111 台灣聯合大學系統_碩士班招生考試_電機類：近代物理#138511

1. For a particle with an energy of E tunneling through a finite barrier height of U and width of & solve the Schrodinger wave equation to calculate the tunneling probability and select the correct answer corresponding to various E, U, and 8 for different particles. (A) For a neutron with E = 50 meV incident on a barrier of U = 250 meV and 8 = 0.16 nm, the tunneling probability is 4.45×10^-11 = 0.0445 ppb (B) For a neutron with E = 50 meV incident on a barrier of U = 250 meV and 8 = 0.1 nm, the tunneling probability is 5.86×10^-10 = 0.586 ppb (C) For an electron with E = 1.0 eV incident on a barrier with U = 5.0 eV and 8 = 0.5 nm, the tunneling probability is 7.1×10^-7 = 0.71 ppm (D) For an electron with E = 1.0 eV incident on a barrier with U = 5.0 eV and 8 = 1.0 nm, the tunneling probability is 2.52×10^-9 =2.52 ppb (E) For an electron with E = 1.0 eV incident on a barrier with U = 5.0 eV and & = 1.25 nm, the tunneling probability is 1.5×10^-10 = 0.15 ppb

2．For a nuclear magnetic dipole of Hydrogen in magnetic field B (Tesla), calculate the Zeeman effect in a spectral line of various wavelengths λ and resolution Δλ (T=kg/C·s). (A)B=0.3T, λ=450nm, Δλ=1.5425×10⁻¹¹ m (B)B=2.0T, λ=450nm, Δλ=2.314×10⁻¹⁴ m=23.14 fm (C)B=7.5T, λ=360nm, Δλ=2.468×10⁻¹⁴ m=24.68 fm (D)B=2.0T, λ=675nm, Δλ=2.468×10⁻¹⁴ m=24.68 fm (E)B=7.5T, λ=450nm, Δλ=2.314×10⁻¹⁴ m=23.14 fm

3．Consider a p-n junction diode. Which of the following statements is wrong? (A)In the absence of any bias, there is no drift current in the junction. (B)A forward bias will result in a rapid increase in the current. (C)A reverse bias will turn off the diode. (D)A diffusion current exists in both forward and reverse bias. (E)The current-voltage curve is temperature sensitive.

4．The atomic radii r in terms of the lattice constant a, for the structure of (A)simple cubic a/2, FCC √2a/4, BCC √3a/4, diamond √3a/8 (B)simple cubic a/2, FCC √3a/4, BCC √2a/4, diamond √3a/8 (C)simple cubic a/2, FCC √3a/8, BCC √3a/4, diamond √2a/4 (D)simple cubic a/2, FCC √2a/4, BCC √3a/8, diamond √3a/4 (E)simple cubic a, FCC √3a/8, BCC √2a/4, diamond √3a/4

5．Which of the following statements is correct? (A)An LED from p-n junction with Eg=1.55 eV emits light at 80 nm. (B)π/6 of the available volume is occupied by hard spheres in a simple cubic arrangement. (C)Debye temperature for iron 360K, maximum frequency is 75 THz. (D)Fermi energy in gold is 5.54 eV; speed of free electrons at 0K is 9.9×10⁵ m/s. (E)Density of states ZdE=13.6×10²⁷√E dE; Fermi level for Cu (8.5×10²⁸/m³) is 9.35 eV.

6．Which of the following principles of classical physics is violated in the Bohr model? (A)Newton's F=m·a (B)Coulomb's law (C)Accelerating charges radiate energy (D)Particles always have a well-defined position and momentum (E)More than one of the above

7．Consider a particle in the relativistic regime, with the energy given by the expression E2= (c²p² + m²c4) (E = energy, p = momentum, m = mass, c = light speed). What is the leading-order relativistic
correction to the kinetic energy? (A)p²/(16m) (B)−p⁴/(8m³c²) (C)−p⁶/(16m⁵c⁴) (D)p⁶/(16m⁵c⁴) (E)None of the above

8．You found an interesting looking piece of metal. You want to find out what kind of metal that is and so you decide to replace the cathode in your photoelectric effect apparatus with that metal piece. You still
have the laser diode from the blue-ray player (405 nm Metal surface wavelength). In this setup you find a stopping potential of 0.16 eV. What kind of metal is it?
 (A)Sodium (Φ≈2.3 eV) (B)Calcium (Φ≈2.9 eV) (C)Silver (Φ≈4.7 eV) (D)Lead (Φ≈4.1 eV) (E)Some other material

9．A radio transmitter of 1 kW operates at 880 kHz. How many photons per second? (A)0.88×10³⁰ photons/s (B)1.13×10³⁰ photons/s (C)4.42×10³⁰ photons/s (D)1.72×10³⁰ photons/s (E)None of the above

10．A galaxy in the constellation Ursa Major is receding from the earth at 15,000 km/s. If one of the characteristic wavelengths of the light the galaxy emits is 550 nm, what is the corresponding
wavelength measured by astronomers on the earth? (A)578 nm (B)940 nm (C)340 nm (D)1.15 μm (E)405 nm

11． Consider the conduction band in the Na metal at T = 0 K (T = temperature). Which of the following statements are correct? (A)The band derives primarily from the 3s orbital of Na atom. (B)The band is completely filled. (C)The Fermi energy lies inside the conduction band. (D)Conduction band electrons do not bind the atoms together at all. (E)All of the above.

12．Let 'v' and 's' both be binary electron degrees of freedom, with v = K or K', and s = U or D. Below, we will use the following convention: a) A notation such as |K, U) represents an one-electron
state with v = K, and s = U; b) Aproduct such as |K, U)|K', D) denotes a two-electron state with the 1st electron in the state K, U) and the 2nd in |K', D). Which of the following states are consistent
with the Pauli exclusion principle?(A)|K,U＞|K',D＞ - |K',U＞|K,D＞ (B)|K,U＞|K',U＞ - |K',U＞|K,U＞ (C)|K,U＞|K',U＞ - |K',D＞|K,D＞ (D)|K,U＞|K',D＞ - |K',D＞|K,U＞ (E)None of the above

13．. (x) and 2(x) are both non-trivial solutions (i.e., ψ_1,2 are not zero everywhere) of the timeindependent 1D Schrodinger equation. Which of the following is      not      a solution to that Schrodinger
equation? (Note: A, B, and a are arbitrary, non-zero constants. This question only asks for 'mathematical solution' to the Schrodinger equation. You don't need to normalize the wave functions
nor fulfill any boundary conditions.)(A)Aψ₁(x) (B)Aψ₁(x)+Bψ₂(x) (C)(A+B)·(ψ₁(x)+ψ₂(x)) (D)ψ₁(x)·e^α + ψ₂(x)·e^-α (E)None of the above is a solution.

14．Assuming there are particles, whose de Broglie waves shown in the figure below. (A: amplitude of the de Broglie waves, λ: wavelength of the de Broglie waves. All three particles have the same mass.)
Which of the following relations about the velocity of particles are correct?

(A)I ＞ III (B)II = I (C)II ＞ I (D)III ＞ II (E)III = I

15．An electron has a matter wavelength of 2×10^-12 m and the rest energy E₀ = 511 keV, which of the following answers is correct? (A)The electron energy is 620 keV. (B)The kinetic energy (KE) is 292 keV. (C)The electron velocity is about 0.77c. (D)The group velocity v_g is about 0.77c. (E)The phase velocity v_p is about 1.3c.

16．Assume the Fermi energy of silver is 5.52 eV and the number of conduction electrons is 5.86×10²⁸m ³. Which of the following statements are correct?(A)The corresponding velocity of conduction electron is 1.39×10⁶ m/s. (B)If resistivity at room temperature is 1.62×10⁻⁸ Ωm, average time between collisions is 3.7×10⁻¹⁴ s. (C)The mean free path is 51.4 nm. (D)The corresponding velocity is 9.85×10⁵ m/s. (E)The mean free path is 36 nm.

17．Which are the following statements correct? (A)The splitting of spectrum lines in a magnetic field is known as Zeeman effect. (B)Energy spacing for H ground state at 1.0T is 9.27×10⁻²⁴ J. (C)Energy spacing for H ground state at 1.0T is 1.16×10⁻⁴ eV. (D)Splitting levels by equal amount in magnetic field is called normal Zeeman effect. (E)Splitting levels by equal amount in magnetic field is called anomalous Zeeman effect.

18．For an electron trapped in a quantum well with infinitely high barrier U(x)→ ∞ at the boundaries, x= 0 and 2L. Derive the wave function and calculate the expectation values of specified terms. Herein
p is the linear momentum operator given by p=

(A)

(B)

(C)

(D)

(E)

19．Which of the following statements are correct? (A)All motion is relative and the speed of light in free space is the same for all observers. (B)Although they lack rest mass, photons behave as though they have gravitational mass. (C)The de Broglie wave group associated with a moving body travels with the same velocity as the body. (D)The energies of electrons liberated by light depend on the frequency of the light. (E)Only the quantum theory of light can explain the origin of blackbody radiation.

20．Select the correct electron configurations and quantum numbers considering LS coupling for various atoms.

(A)Ca: 1s²2s²2p⁶3s²3p⁶4s²3d¹; 3d¹: n=3, ℓ=2, mℓ=0,±1,±2

(B)Cu: 1s²2s²2p⁶3s²3p⁶4s²3d⁹; 3d⁹: n=3, ℓ=2, mℓ=0,±1,±2

(C)Cr: 1s²2s²2p⁶3s²3p⁶4s¹3d⁵; 3d⁵: n=3, ℓ=2, mℓ=0,±1,±2, m_s=+or-

(D)Ca: 1s²2s²2p⁶3s²3p⁶4s²3d⁵; 3d⁵: n=3, ℓ=2, mℓ=0,±1,±2, m_s=+or- 

(E)K: 1s²2s²2p⁶3s²3p⁶4s¹; 4s¹: n=4, ℓ=0, mℓ=0, ms=±1/2, m_j=±

(a) Describe the generation of x-ray.

(b) Determine the minimum wavelength λmin.

(a) Determine electron matter wavelength A, when electron with velocity v = 10⁵ m/s and mass me =9.1095×10^-31 kg.

(b)Electron transport from source (I) to drain (III), electron will meet a potential barrier (II), which established by gate. Explain electron tunneling effect briefly.

(c) Give a reasonable minimum gate length (Lg) of MOSFET from the answer (a). (Hint: use tunneling effect.)