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7/25/2019 Physics 73 3rd LE Samplex
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University of the PhilippinesCollege of Science
PHYSICS 731stsemester
AY 2014 - 2015
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INSTRUCTIONS: Choose the bestanswer and shade the corresponding circle inyour answer sheet. To change your answer, cross-out and sign your originalanswer and then shade your new answer.
Scientific Constants:
e= 1.602176462 x10-19
C
1 eV= 1.602176462 x 10-19Jme= 9.10938188 x 10
-31kg(electron mass)
mp= 1.67262158 x 10-27
kg(proton mass)
h= 6.62606876 x 10-34
Js= 4.135667273 x 10-15
eVs
= 1.054571596 x 10-34
Js= 6.582118893 x 10-16
eVs
B= 9.27400899 x 10-24
J/T(Bohr magneton)
0= 8.854187817 x 10-12
C2/(Nm
2)(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 emittedelectron?
A. 1.40 x 105
m/s
B. 1.72 x 105m/s
C. 1.98 x 105m/s
D. 1.82 x 106m/s
E. 2.58 x 106m/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 eVD. 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
mE. 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 104V
B. 1.07 x 104V
C. 2.48 x 104
V
D. 3.18 x 104VE. 3.98 x 10
4V
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. 4a0C. 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 2.00x103kg, length
10.0m and speed 0.800c?
A. 1 x 10-45
m
B. 1.32 x 10-46
m
C. 2.20 x 10-46mD. 1.38 x 10
-45m
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 de-
Broglie frequency? (c is the speed of light)
A. 5.47 x 1018
HzB. 6.34 x 10
24Hz
C. 1.79 x 1020
HzD. 7.52 x 10
27Hz
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 10-8J
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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/2C. 5b/h
D. 5b/2
E. b/h
16. Which of the following statements is/are true about the wave function
that describes a particle?
I. The wave function gives the probability of finding the particle at
any location and time .
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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 onlyB. 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]1/2E. 1/[4L]
1/2
18. The figure shows 2n(x) for n=2 for an electron in an infinite well whosewidth 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=100pmD. x=25pm, x=75pm
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E. x=50pm, x=100pm
19. A free particle is described by the wave function (x,t) = e i (px -Et)/, where is theparticle mostlikely to be found?
A. at x=0B. at x=1C. at x=-1D. 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:
(x, t= 0) =1
6 1(x)+C3 3(x)+
1
3 5(x),
where (x) =2
Lsin
n x
L
and En=
n2
2
2
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 particles average energy?A. (1/9)E1
B. (1/36)E1C. (95/9)E1
D. (95/36)E1
E. E1
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22. A particle is described by the wavefunction(x,t) = A11(x) e
- i E1t/
+ A22(x) e- i E
2t/
+ A33(x) e- i E
3t/
where the functions 1(x), 2(x)and 3(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. E1B.E2C. E3D. E1 +E2 + E3E. Any of E1, E2, E3
Hour 37
23 .A particle of mass m = 1.00 x 10-27kgis in a one-dimensional box of
lengthL = 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
24. Consider a particle with mass m in a one dimensional box of length L
centered at the origin (so that the ends are atx = 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.
A.
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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 thequantum 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 1stexcited state of a finite square well of depth U0=
6Ewhere Eis 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
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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. 0.00384C. 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 < U0is 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
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Hour 40
32. A particle is modelled as a quantum harmonic oscillator with = 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 meVC. 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.
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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, IC. 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 1stexcited
energy level?
A. 0B. 1
C. 2
D. 3
E. 4
37. Consider an anistropic harmonic oscillator with potential given by,
, withWhat is the energy eigenvalue of the first excited state of the oscillator?
A.
B.
C.
D.
E.
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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 onlyC. I and IV onlyD. II and III onlyE. 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 degenerateC. Three-fold degenerateD. Four-fold degenerateE. 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 fieldif 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. /2 and /2B. /2C./2D. 0, 1, 2, n-1E. 3 / 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. 2s
2
C. 2p
D. 2s22p
2
E. 2p3