Problem 4
Which quantum number (n, l, mi, ms) is not a possible set of a 2p electron?
(A) (2, 1, +1, +1/2)
(B) (2, 1, +1, -1/2)
(C) (2, 1, 0, +1/2)
(D) (2, 0, -1, +1/2)
(E) (2, 1, -1, -1/2)

Problem 5According to band theory, beryllium, an alkaline earth metal, is predicted to behave as an insulator.However, it acts as a conductor due to:(A) The presence of a half-filled 2s band.(B) The overlap between the filled 2s band and the empty 2p band.(C) The presence of an empty 2p band.(D) The overlap between the filled 2p band and the empty 3s band.(E) The presence of a half-filled 3s band.

Problem 6 Consider the transmission of an incident electron with energy E through the one dimensional step potential barrier V(x) with V(x ＜ 0) = 0 outside the barrier, and V(x ＞ 0) = Vo in the barrier (V0 ＞ 0). Which of the following statements is CORRECT about the transmission coefficient T? (A) If the incident electron comes from x = +infinity, with E＞ V0,then the corresponding T = 1. (B) If the incident electron comes from x = - infinity, with E ＞V0, then the corresponding T = 1. (C) If the incident electron comes from x = - infinity, with E＜V0, then it has a nonvanishing probability in the barrier as well as T ＞ 0 due to quantum tunneling. (D) Replace V(x) by a potential barrier of finite width, with V(0 ＜ x ＜W) = Vo in the barrier and V(x) = 0 outside the barrier. An incident electron with E＜V0 has T ＞ 0 due to quantum tunneling. (E) None of the above.

Problem 7An electron is bound in a potential well. The wave function of the electron is:Y(x,t) = v(x)e-iEtn, where φ(x) is shown as below and E is a real number. Which one ofthe following potential wells would fit best to this wave function?(A)(B)(C)(D)(E)

Problem 8 A one-dimensional infinite potential well locating between -0.5 nm to 0.5 nm and contains 10 electrons. It has 10 electrons inside. What is the least energy, in eV, the incident light must have in order to excite a ground-state electron (i.e., at the lowest n quantum value) in this system to the lowest higher state it can occupy when T=0? (A) ~8.7 eV, (B) ~13.6 eV, (C) ~5.61 eV, (D) ~13.2 eV, (E) ~44.9 eV.

Problem 9In Bohr's hydrogen model, if the Coulomb interaction between the electron and the nucleus changes to a power-law potential: V(r) = krN, where k and N are positive constants. Applying Bohr's hypothesis to calculate the energy of hydrogen atom, the energy will be proportional to the quantumnumber n as(A)(B) (C)(D) , and (E) n-2.

Problem 10Which one of the following statements about free bosons, fermions, and classical particles is correct?(A) Bosons possess integer spin and follow the Maxwell-Boltzmann distribution in the low-temperature regime.(B) Fermions are indistinguishable particles that obey the Pauli exclusion principle and follow the FermiDirac distribution in all temperature range.(C) Classical particles can either be distinguishable or indistinguishable depending on the type of atoms or particles.(D) In the low-temperature limit, bosons and fermions cannot occupy the same quantum state, in contrast to classical particles.(E) In Bose-Einstein condensation, particles follow the Bose-Einstein distribution, with most particles occupying either the same excited state or the ground state. This phenomenon can be observed macroscopically.

複選題Problem 11Which of the following statements are correct?(A) A light source with a shorter wavelength could have improved the sensitivity in the MichelsonMorley experiment.(B) In an inertial frame S, if event A occurs prior to event B, then in any inertial frame, event A must occur prior to event B.(C) The twin paradox showed that the twin who returned to Earth was younger than the twin who stayed at home.(D) The Galileo transformations are consistent with Einstein's postulates of relativity.(E) It is possible for the electron beam in a television picture tube to move across the screen at a speed faster than the speed of light.

複選題Problem 12Consider the ground state of an Al atom with Z=13. Find the correct descriptions:(A) The electron configuration is: 1s2 2s2 2p6 2d³.(B) The magnitude of the angular momentumh.(C) The magnitude of the sin angular momentums is (D) The magnitude of the total angular momentumcan be(E) The magnitude of the total angular momentumcan be

複選題Problem 13:Here is the Davisson and Germer experiment, illustrating electron diffraction from a Ni crystal.Which of the following modifications can increase the diffraction angle?(A) Increase the electron velocity.(B) Decrease the electron velocity.(C) Keep the same velocity but replace the electron with an alpha particle (He+).(D) It is not possible to change the diffraction angle.(E) Use a crystal with a smaller lattice spacing (more dense periodic structure).

複選題Problem 14Which of the following statements are correct regarding Bohr's theory, the Franck-Hertz experiment, and Rutherford's atomic model? (A) In the Franck-Hertz experiment, the accelerating voltage exhibits sudden drops at multiples of 4.9 volts. The energy levels of 4.9 volts and 9.8 volts correspond to transitions to the ground state and the first excited state of mercury atoms, respectively. (B) In Bohr's theory, energy is assumed to be quantized, meaning that the quantum state of a hydrogen atom can only occupy specific, discrete energy levels. (C) Rutherford's atomic model is inconsistent with Maxwell's equations, as accelerating charged particles, such as orbiting electrons, would radiate electromagnetic waves. Consequently, electrons would lose energy and spiral into the atomic nucleus. (D)In Bohr's theory, the relativistic effects on the electron can be negligible. (E) According to Bohr's model, the ratio of the electron's speed in the second excited state to its speed in the fifth excited state is exactly 2.

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