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)

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

21. The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 2.5 s. Assuming R=0.5 m and m=2.0 kg, calculate the structure’s rotational inertial about the axis of rotation.     (A) (B) (C) (D) (E)

22. What is the de Broglie wavelength of an electron with a kinetic energy of 1.822×10-16 J? ( ) (A) 0.3639 pm (B) 3.639 pm (C) 36.39 pm (D) 363.9 pm (E) 3639.0 pm

23. An LED is constructed from a p-n junction based on a certain Ga-As-P semiconducting material whose energy gap is 1.9 eV. What is the wavelength of the emitted light? (h=6.63×10-34 J•s, c=3.00 ×108 m) (A) 10.47 nm (B) 16.75 nm (C) 37.79 nm (D) 113.37 nm (E) 654.28 nm

24. An electron moves through a uniform magnetic field given by . At a particular instant, the electron has velocity m/s and the magnetic force acting on it is (6.4×10-19 N) . Find Bx. (A) -1.6×10-19 T (B) -3.2×10-19 T (C) -0.22T (D) -1.0T (E) -2.0T

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