12. A quantum system has a set of energy eigenstates |B_i). The system is in the state , where the energies are given by E_n = nE₁. What is the probability that a measurement of energy yields the value of 3E₁?
(A)
(B)
(C) 1/10
(D) 3/10
(E) 9/10.

8. Which of the following is incorrect: (A) The blackbody radiation displays a continuous spectrum. (B) The distribution of energy of the emitters obeys the equipartition of energy in each degree of freedom in blackbody radiation. (C) The radiated wavelength of maximal intensity is inversely proportional to the temperature. (D) The energy of the oscillator is quantized. It can have only certain discrete amounts of energy En = nhf, where n is a positive integer and f is the frequency of oscillation. (E) The correspondence principle states that quantum results must blend smoothly with classical results when the quantum number becomes large.

9. In photoelectric effect experiments, two different materials are illuminated by light of frequency f. The induced electrons passing a pair of parallel plates form a current that can be measured. The pair of plates are applied a voltage to decrease the current. The extinction voltage V is the minimal value of voltage such that the measured current becomes 0. Which of the following plots mostly represents the f-V relation?(A)(B)(C)(D)(E)

10. In the Davisson-Germen experiment, a beam of 60 eV electrons is directed at a crystal, and diffracted electrons are found at an angle θ = 74° relative to the original beam. What is the spacing of the atomic planes of the crystal? (A) 0.1 nm (B) 0.5 nm (C) I nm (D) 2 nm (E) 5 nm.

11. How many wave functions are possible in the n = 5 shell? (A) 9 (B) 16 (C) 20 (D) 25 (E) 30.

複選題13. In an infinite square well, for which of the following states will the particle never be found in the center of the well? (A) The ground state (B) The first excited state (C) the second excited state (D) Any of the above (E) None of the above.

14. An electron is in an infinite square well of width a:If the clectron is in the state at what position is the probability function a maximum? (A)0(B)a/2 (C) a/3(D) a/4 (E) a/5.

15. An electron is in an infinite square well of width a with the same potential form as in Problem 14, with a = 300 pm wide. What is the probability that one can detect the electron in the first excited state within an interval betwe x = 0.50a and x = 0.75a? (A) 0(B) 1/2 (C) 1/3(D) 1/4(E) 1/6.

16. A system consists of 4 non-interacting electrons localized inside an infinite square well of width a. What is the total energy of this system at T = 0K? (A)(B)(C)(D)(E)

17. In the polar coordinate (ρ,θ,Φ), a particle is described by the wave function φ(ρ,Φ)= . What is the probability that a measurement of Lz yields the value 2h for this particle? (A)1/2 (B) 1/3 (C) 1/4 (D) 1/5 (E) 1/6.

18. A ruby laser consists mostly of alumina (Al2O3) and a small amount of chromium, which is responsible for the red color of the ruby. This laser emits a pulse of light (λ = 685 nm) with a power of 3.00 kW over a period of 10.0 ns. How many chromium atoms undergo stimulated emission to produce this pulse? (A) 1.03 x 1013 (B) 1.03 X 1014 (C) 1.03 X 1015 (D) 1.03 x 1016 (E) 1.03 x 1017.