7. A radioisotope X has a half life time of 10 years. A sample has an initial decay rate of 1.38 x 10:3 decay/year. How many nuclei decay in 10 years? (In 2 = 0.69)
(A) 10¹¹
(B) 10¹²
(C) 10¹³
(D) 10¹⁴
(E) 10¹⁵.  

3. A positroniumn is an exotic atom consisting of an electron and its anti-particle, a positron, bound together. Its ground state energy is (A) -3.2 eV(B) -6.8 eV(C) -9.4 eV (D) -11.4eV(E) -13.6 ev.

4.A particle of rest mass 1 MeV has a momentum 7.1 x 10-22 kg m/s. The kinetic energy is (A) 0.25 MeV (B) 0.33 MeV (C) 0.50 MeV (D) 0.67 MeV (E) 1.2 MeV.

5. The ground state of a harmonic oscillator is , where  The corresponding uncertainty of the momentum observable is(A)(B)(C)(D)

6. Following 5. Determinc the wave function of the first excited state of a harmonic oscillator: (A)(B)(C)(D) (E) .

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.

12. A quantum system has a set of energy eigenstates |Bi). The system is in the state , where the energies are given by En = 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.

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.