26. For an atom with one valence electron in a p-subshell (l = 1, s = 1/2), which statement about spin-orbit coupling is correct?
(A) Spin-orbit coupling splits the p-level into j = and j = states.
(B) The only allowed total angular momentum is j = 1/2 because s = 1/2.
(C) Spin-orbit coupling does not occur unless the atom is placed in an external magnetic field.
(D) The degeneracy of the j = level is 4 and the degeneracy of the j = level is 2.
(E) Spin-orbit coupling combines n and l into a new quantum number j while leaving s unchanged.

27. How many electrons can be described by the quantum numbers n = 3, l = 1, ml = -1? (A) 14 (B) 6 (C) 10 (D) 0 (E) 2

28. C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(l), ΔH = -1.37 × 103 kJ Which of the following statement(s) is(are) true for the combustion of ethyl alcohol as described in the above equation? I. The reaction is exothermic. II. The enthalpy change would be different if gaseous water were produced. III. The reaction is not a redox reaction. IV. The products of the reaction occupy a larger volume than the reactants. (A) I, II (B) I, III, IV (C) I only (D) III, IV (E) I, II, III

29. From the following list of observations, choose the one that most clearly supports the conclusion that the mass of the atom is mainly located in the nucleus. (A) the emission spectrum of hydrogen (B) the photoelectric effect (C) diffraction (D) the scattering pattern of α particles by metal foil (E) cathode "rays"

30. In UV-Vis spectroscopy, the absorption characteristics of a molecule can be altered by the presence of certain functional groups. Which of the following statements correctly describes the roles of chromophores and auxochromes? (A) A chromophore is a saturated functional group that does not absorb radiation but increases the absorption intensity of the entire molecule. (B) An auxochrome is a functional group, such as -OH or -NH2, which does not itself absorb significantly in the UV region but can cause a bathochromic shift and a hyperchromic effect when attached to a chromophore. (C) The addition of an auxochrome to a conjugated system typically leads to a hypsochromic shift (blue shift) because it increases the energy gap between the π and π* orbitals. (D) Chromophores are only capable of undergoing n→σ* transitions, while auxochromes are responsible for π→π* transitions. (E) The intensity of absorption is determined solely by the chromophore, and auxochromes only affect the wavelength of the maximum absorption.

31. The motion of a car can be described by the equation x(t)=15t-2t2, where x and t are in meters and seconds, respectively. What is the acceleration of the car after 3 seconds? (A) 27 m/s2 (B) 12 m/s2 (C) 4 m/s2 (D) -4 m/s2 (E) -12 m/s2

32. A solid cylinder and a thin hoop of the same mass m and radius R are released from rest (at the same moment) at the top of an incline. If they roll without slipping, which object will have a greater translational velocity at the bottom of the incline? (A) The solid cylinder. (B) The thin hoop. (C) They will have the same velocity. (D) The velocity depends on the angle of the incline. (E) None of the above.

33. Two blocks of equal mass m are connected by a spring with the spring constant k and placed on a frictionless surface. If the right block is given an initial velocity v while the left block is at rest, what is the minimum kinetic energy of the system during the subsequent oscillation? (A) 0 (B) (1/8)mv2 (C) (1/4)mv2 (D) (1/2)mv2 (E) mv2

34. An ice cube is floating in a glass of pure water. The system remains at 0°C as the ice melts. How does the water level change? (A) It increases. (B) It decreases. (C) It remains exactly the same. (D) It depends on the size of the ice cube. (E) None of the above.

35. A cylindrical water tank with a height of 1 meter (m) and a base area of 0.1 m2 contains 50 kg of pure water. A mass of 10 kg of salt is added to the water and allowed to dissolve completely. What is the gauge pressure at the bottom of the tank? (Assume gravitational acceleration g = 10 m/s2 for simplicity). [unit: pascal (Pa)] (A) 400 Pa (B) 600 Pa (C) 4000 Pa (D) 5000 Pa (E) 6000 Pa

36. Two people with masses of 60 kg and 80 kg are initially at rest on a frictionless level surface, separated by a distance of 20 meter (m). They both pull on opposite ends of a massless rope to move towards one another. If the total distance between them decreases by 14 m, how far has the 80-kg person traveled? (A) 10 m (B) 8 m (C) 6.4 m (D) 6 m (E) 3.6 m

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