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

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

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 stillhave 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 correspondingwavelength measured by astronomers on the earth? (A)578 nm (B)940 nm (C)340 nm (D)1.15 μm (E)405 nm

複選題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.

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