28. The pK_b of die base cyclohexamine, C₆H₁₁NH₂, is 3.36. What is the pK_a of the conjugate acid, C₆H₁₁NH₃⁺? (K_w=1.0X10^-14 at25°C)
(A) 3.36
(B) 14.00
(C) 10.64
(D)7.64
(E)-10.64

24. How many electrons can be described by the quantum numbers n = 4, l = 4, ml= 1? (A) 14 (B)6 (C)10 (D)0 (E)2

25. The concentration of OH- ions in a solution is 5.62 mM. Determine the pH of the solution. (A) 11.7 (B)2.2 (C) 14.7 (D) 13.3 (E)5.6

26. In which of the following techniques are we measuring the amount of light absorbed as a function oi wavelength? (A) atomic absorption spectroscopy (B) X-ray difiraction (C) inductively coupled plasma-optical emission spectrometry (lCP-OES) (D) gas chromatography (E) none of the above

27. A gas releases 2.0 J of heat and then performs 11.8 Jof woric. What is the change in the internal energy of the gas? (A)-13.8 J (B)9.8J (C)-9.8J (D)2.0J (E) 13.8 J

29. Ellipsometry is commonly used to measure the thickness of films. Which of the following signal is detected in ellipsometry? (A) resonance angle (B) reflected laser spot (C) second-harmonic generation (D) polarized light (E) none of the above

30. Which of the following is not a feature of carrier g^s used in gases chromatogr/)hy? (A) The carrier gas should be chemically inert. (B) The carrier gas should be inexpensive. (C) The purity of carrier gas should not be very high. (D) The carrier gas should be suitable for tiie detector employed. (E) None of the above.

31. Determine tiie correct unit and magnitude of the electric field at distance x from the midpoint of a very long line of unifonnly distributed positive charge. Assume x is much smaller then the length of the wire, and let λ be the charge par unit length.(A)(B)(C)(D)(E)

32. The plates of a parallel-plate capacitor have area』and separation d. Two different dielectrics each All half the space between the plates of a parallel-plate capacitor (as shown in figure). Determine ti)e correct unit and the capacitance in terms of K1, K2, tiie area A of the plates, and die separation d, where K1and K2 are the dielectric constants of two dielectrics . is the vacuum permittivity. (A)(B) (C) (D)(E)

33. A system comprises three particles with masses of 2.0 kg, 3.0 kg, and 5.0 kg, respectively. A force F = 3.0i + 4.0j (N) acts on the 2,0-kg particle, where i and/ are unit vectors that point along x and y coordinate axes, respectively. What is the acceleration of the center of mass ac caused by the force? (A) ac = 0.30i+ 0.40j (m/s2) (B) ac = 0.60i + 0.80j (m/s2) (C) ac = 3.0i +1.0j  (m/s2) (D) ac = 3.0i + 4.0j (m/s2) (E) ac = 15i + 20j (m/s2)

34. Assume that a satellite of mass jl/oibits Earth in a perfect circle of radius R. If the satellite is replaced with another one with mass 2Mbut with the same circling radius, what is the ratio of the period of the first satellite to the period of the second one (i.e., T1/T2)? (A) 1/2 (B)l (C)l (D)(E)2