13. A proton is projected toward a fixed nucleus of charge +Ze with velocity V₀ . Initially the two particles are very far apart.When the proton is at a distance R from the nucleus, its velocity has decreased to1/2 V₀ .How far from the nucleus will the proton be when its velocity has dropped to1/4 V₀? 
(A) 1/16 R
(B) 1/4 R
(C) 1/2 R
(D) 4/5 R
(E) 6/7 R

9. Suppose that the temperature at the center of the Sun is 2.00×107 K, what is the average translational kinetic energy of a proton in the Sun’s center? （kB=1.3810−23 × J/K） (A) 1.38×10−16J (B)4.14×10−16J (C) 5.52×10−16J (D) 7.64×10−16J (E) 8.96 ×10−16J

10. A nonconducting sphere of radius 10 cm has charge uniformly distributed throughout its volume. The electric field is directed radially outward and its strength at 5 cm from the center is 2000 N/C. What is the volume charge density of the sphere? (∈0 =8.85×10−12C2 /N·m 2 ）. (A) 1.06 µC/m3 (B) 2.12 µC/m3 (C) 3.16 µC/m3 (D) 4.06 µC/m3 (E) 5.18 µC/m3

11.When radiation of wavelength 350 nm is incident on a surface, the maximum kinetic energy of the photoelectrons is 1.2 eV. What is the stopping potential for a wavelength of 230 nm?（ h=6.63×10−34 J·s, qe = –1.60×10−19  C, c=3×108 m/s） (A) 1.65 V (B) 2.04 V (C) 2.55 V (D) 3.05 V (E) 4.82 V

12. An electron in the hydrogen atom makes a transition from the n=5 level to the n=2 level. What is the wavelength of the emitted photon? （qe = –1.60×10−19 C, h=6.63×10−34 J·s） (A) 326 nm (B) 435 nm (C) 578 nm (D) 662 nm (E) 769 nm

14. An important observation that led Bohr to formulate his model of the hydrogen atom was the fact that . (A) the emission of light by an atom did not appear to conserve energy. (B) electrons were found to have a wave nature. (C) the peak of the blackbody radiation moved to shorter wavelengths as the temperature was increased. (D) neutrons formed a diffraction pattern when scattered from a nickel crystal. (E) a low density gas emitted a series of sharp spectral lines.

15. If the peak electric field in an electromagnetic wave is 1200 V/m , what is the peak magnetic field for the same wave? (A)2.2×10−6T  (B)3.4×10−6T (C)4.0 ×10−6T(D)8.7×10−6T (E)9.6×10−6T

16. The square plates of a 9000 pF capacitor measure 90 mm by 90 mm and are separated by a dielectric which is 0.29 mm thick. The voltage rating of the capacitor is 300 V. The dielectric strength of the dielectric, in kV/m , is closest to . (A) 930 (B) 1000 (C) 1100 (D) 1200 (E) 1300

17. Electromagnetic standing waves are set up in a conducting cavity resonator in the form of a hollow metal box. The waves bounce back and forth between two parallel surfaces separated by 0.8 cm. What is the minimum resonant frequency for such a resonator? (A) 3.30 GHz (B) 4.42 GHz (C) 12.4 GHz (D) 15.5 GHz (E) 18.8 GHz

18. The potential energy function of a particle moving in one dimension is U=kx2e−x2/a2where  a = 7.50nm . At what value of x is a point of stable equilibrium located? (A) 6.81 nm (B) 7.50 nm (C) 7.80 nm (D) 11.03 nm (E) 12.62 nm

19. A proton with speed  v = 3.00×105m/s orbits just outside a charged sphere. The radius of the orbit is 1.0 cm. What is the charge on the sphere? (The mass of a proton is 1.67×10−27kg.) (A)1.04×10−9C  (B)3.47×10−8C (C)6.23×10−8C (D)6.50×10−8C (E)8.28×10−7C