Physics 73 3rd LE Samplex

University of the Philippines College of Science

PHYSICS 73 1st semester AY 2014 - 2015

INSTRUCTIONS: Choose the best answer and shade the corresponding circle in your answer sheet. To change your answer, cross-out and sign your original answer and then shade your new answer.

Scientific Constants: e = 1.602176462 x10-19 C 1 eV = 1.602176462 x 10-19 J me = 9.10938188 x 10-31 kg (electron mass) mp = 1.67262158 x 10-27 kg (proton mass) h = 6.62606876 x 10-34 J·s = 4.135667273 x 10-15 eV·s

ħ = 1.054571596 x 10-34 J·s = 6.582118893 x 10-16 eV·s μB = 9.27400899 x 10-24 J/T (Bohr magneton) ε0 = 8.854187817 x 10-12 C2/(N·m2) (permittivity of vacuum) Uncertainty Principle:

Hour 29

1. A photon has a frequency of . It strikes a copper with a work function of . What is the maximum speed of the emitted electron? A. 1.40 x 105 m/s B. 1.72 x 105 m/s C. 1.98 x 105 m/s D. 1.82 x 106 m/s E. 2.58 x 106 m/s 2. What is the lowest energy of a photon in the Balmer series ( A. 3.40 eV B. 17.5 eV C. 1.89 eV D. 7.63 eV E. 13.6 eV

)?

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3. In a photoelectric effect experiment, the results yield the following stopping potential versus frequency plot.

What is the work function of the material used in the experiment? A. 1.0 J B. 1.6 x 10-19 J C. 4.0 J D. 64 x 10-19 J E. 0 J Hour 30

4. Which of the following statements is/are TRUE about the Bremmsstrahlung? I. The emitted photon wavelength depends on the material. II. Work function of the material is not needed in obtaining the wavelength of the photon. III. The minimum wavelength of the emitted photon depends on the potential applied between the anode and the cathode of the x-ray machine. A. I only B. II only C. III only D. I and II only E. II and III only

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5. A photon strikes a stationary electron. The photon scatters at an angle of . How long is the increase in photon wavelength? A. 6.69 x 10-12 m B. 4.46 x 10-12 m C. 1.42 x 10-12 m D. 7.10 x 10-13 m E. 1.13 x 10-13 m 6. What is the minimum potential difference required to produce x-rays with wavelength 0.050 nm? A. 1.24 x 104 V B. 1.07 x 104 V C. 2.48 x 104 V D. 3.18 x 104 V E. 3.98 x 104 V Hour 31

7. In a one-electron hydrogen atom, the difference between the orbital radius of the n = 2 and n = 4 states is given by A. 2a0 B. 4a0 C. 12a0 D. 8a0 E. 3a0 8. A singly ionized helium (He+) behaves much like a hydrogen atom except that its nuclear charge is twice as great. What is the ground energy level of a He+ atom? A. 13.6 eV B. 27.2 eV C. -13.6 eV D. -27.2 eV E. -54.4 eV

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Hour 32

9. What is the de Broglie wavelength of a train with mass 2.00x103 kg, length 10.0m and speed 0.800c? A. 1 x 10-45 m B. 1.32 x 10-46 m C. 2.20 x 10-46 m D. 1.38 x 10-45 m E. 8.28 x 10-46 m 10. If a proton (mass = 1.672 x 10-27 kg), an electron (mass = 9.11 x 10-31), and a neutron (mass = 1.675 x 10-27 kg) have the same kinetic energy, which of the following has the smallest de Broglie wavelength? A. Proton B. Electron C. Neutron D. The proton and the neutron have the same de Broglie wavelengths E. All of them have the same de Broglie wavelengths 11. A relativistic electron is moving with a speed of 0.721c. What is its deBroglie frequency? (c is the speed of light) A. 5.47 x 1018 Hz B. 6.34 x 1024 Hz C. 1.79 x 1020 Hz D. 7.52 x 1027 Hz E. 4.67 x 1031 Hz Hour 33

12. An atom spends an average time of 6.4 × 10-8 s in one of its excited states before making a transition back to its ground state. What is the uncertainty in energy of that excited state? A. 6.1 × 1026 J B. 8.2 × 10-28 J C. 1.0 × 1026 J D. 2.5 × 10-28 J E. 6.4 × 10-8 J ____________________________________________________________________________________ A-5

13. A particle was located within 4.93nm. What is the uncertainty in its momentum? A. 7.31 x 10-21 kg m/s B. 1.07 x 10-26 kg m/s C. 5.68 x 10-24 kg m/s D. 3.94 x 10-28 kg m/s E. 9.45 x 10-19 kg m/s Hour 34

14. Which of the following expressions correspond to the wave function of a free particle moving to the right (+x direction)? , , are positive, real constants. A. B. C. D. E. 15. The wave function of a particle is given as

where f is some function of x, and a and b are real, positive constants. If this wave function is a solution to the Schrodinger equation, what is the energy of the particle? A. 5b B. 5ab/2π C. 5b/h D. 5b/2π E. b/h 16. Which of the following statements is/are true about the wave function that describes a particle? I. The wave function any location and time .

gives the probability of finding the particle at

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II. The value of at each point is independent of time if the particle is in a state of definite energy. III. If the particle is in a stationary state, the wave function is a product of a function and a function that depends only on time. A. I only B. II only C. III only D. I and II only E. II and III only Hour 35

17. The initial wave function of a particle is defined as

If the wave function is normalizable, what is the value of A? A. 2 B. 4 C. 1/2L D. 1/[2L]1/2 E. 1/[4L]1/2 18. The figure shows ψ2n(x) for n=2 for an electron in an infinite well whose width L is 100pm. Where can the electron be most likely detected?

A. x=0 B. x=0, x=25pm, x=75pm C. x=0, x=50pm, x=100pm D. x=25pm, x=75pm ____________________________________________________________________________________ A-7

E. x=50pm, x=100pm 19. A free particle is described by the wave function Ψ(x,t) = e i (px - Et)/ħ, where is the particle most likely to be found?

A. at x=0 B. at x=1 C. at x=-1 D. The particle is equally probable everywhere E. The particle does not exist Hour 36

For the next two numbers, consider the wavefunction of a particle in an infinite square well to be: 1 1 Y(x, t = 0) = y1 (x) + C3y3 (x) + y5 (x) , 6 3 n 2p 2 2 2 æ np x ö where y (x) = and . E = sin ç ÷ n L è L ø 2mL2 20. What is the probability of finding the particle in the second excited state? A. 1/36 B. 1/9 C. 31/36 D. 4/9 E. 11/36 21. What would be the particle’s average energy? A. (1/9)E1 B. (1/36)E1 C. (95/9)E1 D. (95/36)E1 E. E1

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22. A particle is described by the wavefunction Ψ(x,t) = A1 ψ1(x) e- i E1t/ħ + A2 ψ2(x) e- i E2t/ħ + A3 ψ3(x) e- i E3t/ħ where the functions ψ1(x), ψ2(x) and ψ3(x) are normalized solutions to the time independent Schrodinger Equation corresponding to the ground, first and second excited energy states, respectively. If we measure its energy, what will be the result? A. E1 B.E2 C. E3 D. E1 + E2 + E3 E. Any of E1, E2, E3 Hour 37

A particle of mass m = 1.00 x 10-27 kg is in a one-dimensional box of length L = 4.00 x 10-12 m. What is the ground state of the particle? A. 342 eV B. 5.35 eV C. 42.8 eV D. 21.4 eV E. 13.6 eV 23 .

24. Consider a particle with mass m in a one dimensional box of length L centered at the origin (so that the ends are at x = ±L/2). The ground energy level eigenfunction is shown in the figure. What is the wave function of the 4th excited state? Hint: the eigenstates maybe thought as a standing wave solution of a string with both ends fixed.

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B. C. D. E. 25. A particle confined to a one-dimensional box has ground energy level equal to 0.4 eV. When irradiated by a light of certain frequency, it makes a transition to an excited state. When decaying from this excited state towards the next lower state, it emits a radiation of frequency 442.9 nm. What is the quantum number of the state to which the particle has decayed? A. 2 B. 3 C. 4 D. 6 E. 8 Hour 38

26. A particle is in the 1st excited state of a finite square well of depth U0 = 6E∞ where E∞ is the ground state energy of an infinite square well of the same width. If the particle relaxes to the ground state, how much energy is released?

A. 1.81 E∞ ____________________________________________________________________________________ A-10

B. 2.66 E∞ C. 4.47 E∞ D. 5.38 E∞ E. 3.57 E∞ 27. Which of the following is true about a particle confined in a finite square well? A. There is zero probability of finding the particle outside the well. B. The number of eigen-values is finite. C. The ground state eigen-function has two nodes. D. The wave functions are not normalizable. E. The energy levels are equally spaced. 28. Consider a potential well defined by the following function,

Consider a particle with mass and kinetic energy that is trapped in the well. What is the physically correct wavefunction for regions I & II? Use:

A. B. C. D. E.

, , , , ,

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Hour 39

29. An electron (me = 9.11 x 10-31 kg) with an energy of 100meV encounters a potential barrier of height 250meV and thickness 2.00nm. If the wide barrier assumption is true, what is the probability of tunnelling? A. 0.00337 B. 0.00384 C. 0.00137 D. 0.00724 E. 0.0724 30. A particle moving towards the +x direction encounters a potential barrier. The eigen-function solution to the time-independent Schrodinger equation for a potential barrier for the case E < U0 is given below.

Which of the following is true? A. refers to the incident wave B. refers to the incident wave C. refers to the transmitted wave D. refers to the incident wave E. refers to the reflected wave 31. Which of the following increases the probability of the particle to tunnel through a potential barrier? I. Use a more massive particle. II. Decreasing the height of the barrier. III. Decreasing the thickness of the barrier. A. I only B. II only C. III only D. I and II E. II and III ____________________________________________________________________________________ A-12

Hour 40

32. A particle is modelled as a quantum harmonic oscillator with ω = 1.00 x 1012 rad/s. How much energy does the particle need to go from the ground state to the 2nd excited state? A. 0.329 meV B. 0.658 meV C. 0.987 meV D. 1.32 meV E. 1.64 meV 33. Consider a particle in a harmonic potential. What happens to the spacing between energy levels when particle's mass is increased four times? A. Reduced by half. B. Reduced by one-fourth C. It will be doubled D. Increased four times E. Same 34. The energy eigen-functions of the quantum harmonic oscillator is given by,

Initially, the energy of a particle in a harmonic oscillator was measured to be equal to . After time , which of the following wavefunctions correctly describes the particle if it is in a definite energy state? A. B. C. D. E. ____________________________________________________________________________________ A-13

Hour 41

35. A particle is confined in a three dimensional square box of length . Written in the list are the states where the particle is located. Which of the choices represents the ascending order of energy of the particle? I. II. III. A. I, III, II B. II, III, I C. III, II, I D. III, I, II E. II, I, III 36. A particle is confined in a two-dimensional infinite square well. The sides of the well have the same length. What is the degeneracy of the 1st excited energy level? A. 0 B. 1 C. 2 D. 3 E. 4 37. Consider an anistropic harmonic oscillator with potential given by, , with What is the energy eigenvalue of the first excited state of the oscillator? A. B. C. D. E. ____________________________________________________________________________________ A-14

Hour 42

38. Which of the following set/s is/are the allowed quantum numbers of an electron in the hydrogen atom? I. II. III. IV. A. I only B. III only C. I and IV only D. II and III only E. I, II, and III only 39. Consider a hydrogen atom. What is the degeneracy of the first excited energy state? A. Non-degenerate B. Two-fold degenerate C. Three-fold degenerate D. Four-fold degenerate E. Five-fold degenerate Hour 43

40. The 3rd excited energy level of the hydrogen atom is 16-fold degenerate. Into how many energy levels does this split upon exposure to a magnetic field if we ignore spin? A. 0 B. 3 C. 5 D. 7 E. 9

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41. What are the only possible components of the spin angular momentum of an electron? A. ħ/2 and –ħ/2 B. ħ/2 C. –ħ/2 D. 0, 1, 2, … n-1 E. √3 ħ/ 2 Hour 44

42. The carbon atom has six electrons. Which of the following gives the correct orbital of the valence electron/s? A. 2s B. 2s2 C. 2p D. 2s22p2 E. 2p3

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