14. The average position, or expectation value, of a particle whose wave function ψ(x) depends only on the value of x, is given by ＜ x＞ = ?
(A)
(B)
(C)
(D)
(E)

10. A binary star system in the constellation Orion has an angular separation between the two stars of 1.2 × 10-5radians. If λ = 5 × 10–7 m, what is the smallest aperture (diameter) telescope that may be used to resolve the two stars? (A) 10 cm (B) 5 cm (C) 50 cm (D) 1 m (E) 4 m

11. We wish to coat flat glass (n=1.5) with a transparent material (n=1.25) so that reflection of light at wavelength 600 nm is eliminated by interference. What minimum thickness can the coating have to do this? (A) 30 nm (B) 100 nm (C) 120 nm (D) 400 nm (E) 480 nm

12. The figure shows a circuit that contains three identical resistors with resistance R=9.0Ω, two identical inductors with inductance L=4.0 mH, and an ideal battery with emf ξ=36 V. IA is the current just after the switch is closed, and IB is the current through the battery long after the switch has been closed. What is the current ratio IA/IB? (A) 1/3 (B) 1/2 (C) 1 (D) 2 (E) 3

13. A long cylindrical wire (radius = 2.0 cm) carries a current of 40 A that is uniformly distributed over a cross section of the wire. What is the magnitude of the magnetic field at a point which is 1.5 cm from the axis of the wire? (A) 0.53 mT (B) 28 mT (C) 0.30 mT (D) 40 mT (E) 1.9 mT

15. A company that produces pulsed gas heaters claims their efficiency is approximately 90%. If an engine operates between 250 °C and 25 °C, what is its maximum thermodynamic efficiency? (A) 43% (B) 56% (C) 65% (D) 83% (E) 90%

16. A quantum particle (A) can be localized in space. (B) can be represented by an infinitely long wave having a single frequency. (C) can be represented by a wave packet. (D) travels at the phase speed of the infinitely long wave having the highest frequency. (E) has the highest probability of being present in those regions of space where its component waves interfere destructively.

17. An electron is in a state with l =3. What is the smallest value of the semiclassical angle θ between the direction of ? (A) 0。 (B) 30 。 (C) 60 。 (D) cos-1(1/3) (E) 90 。

18. A charged capacitor connected to a resistor and a switch, which is open for t＜0. After the switch is closed at t=0, the capacitor C is discharged through the resistor R. The energy stored in the capacitor decreases with time as it discharges. After how many time constants is this stored energy one eighth of its initial value? (ln2=0.693) (A) 0.347 RC (B) 0.693 RC (C) 1.040 RC (D) 1.386 RC (E) 2.079 RC

19. Water enters a house through a pipe with an inside diameter of 2.0 cm at an absolute pressure of 4.0×105 Pa. A 1.0 cm-diameter pipe leads to the second-floor bathroom 5.0 m above. When the flow speed at the inlet pipe is 1.5 m/s, find the water pressure in the bathroom. (ρwater=1000 kg/m3 ) (A) 0.17×105 Pa (B) 0.32×105 Pa (C) 0.49×105 Pa (D) 0.66×105 Pa (E) 3.3×105 Pa

20. A cart with mass 450 g moving on a frictionless linear air track at an initial speed of 1.5 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision, the first cart continues in its original direction at 0.70 m/s. What is the mass of the second cart? (A) 0.16 kg (B) 0.47 kg (C) 1.24 kg (D) 2.14 kg (E) 3.40 kg