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

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

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

20. A 1.0µF capacitor with an initial stored energy of 0.50 J is discharged through a 1.0 MΩ resistor. What is the current through the resistor when the discharge starts? (A)1.0×10−3A  (B)2.0×10−3A  (C)1.0×10−2A  (D)2.0×10−2A  (E)5.0×10−2A 

21. A hollow sphere of inner radius 8.0 cm and outer radius 9.0 cm floats half-submerged in a liquid of density 800kg/m3 . What is the density of the material of which the sphere is made? (A)1.1×103kg/m3  (B)1.3×103kg/m3(C)1.8×103kg/m3 (D)2.4×103kg/m3 (E)4.8×103kg/m3

22. Three sinusoidal waves of the same frequency travel along a string in positive direction of an x axis. Their amplitudes are y1 ,y1/ 2and y1/3 , and their phase constants are 0, π/2, and π, respectively. What is the phase constant of resultant wave? (A) 30° (B) 37° (C) 45° (D) 53° (E) 60°

23. A girl is sitting near the open window of a train that is moving at a velocity 10.00m/s to the east. The girl’s uncle stands near the tracks and watches the train move away. The locomotive whistle emits sound at the frequency of 500.0 Hz. The air is still. What frequency does the uncle hear? (The speed of sound is 343m/s.) (A) 471.7 Hz (B) 485.8 Hz (C) 500.0 Hz (D) 515.0 Hz (E) 530.0 Hz

24. Two point charges q1=2.1×10-8C and q2 = −4q1 are fixed in two places 50 cm apart. The point charge  q1 is at the right side of  q2 . Find the point at which the electric field is zero, along the straight line passing through the two charges. The point is . (A) 50 cm to the right of  q1  (B) 50 cm to the left of  q2  (C) 100 cm to the right of  q1  (D) 100 cm to the left of q2  (E) The middle point between  q1 and  q2