Modern Physics 1Final ExamFall 2011
- Automobile A moving north at 40 km/h sees another automobile B pass it moving north with a relative velocity of 30 km/h. What is the speed of B relative to the ground?
(A)10 km/h
(B)30 km/h
(C)40 km/h
(D)50 km/h
(E)70 km/h
- Which of the following models of the atom was the first to correctly predict the spectrum of the hydrogen atom?
(A)Greek model of the hydrogen atom.
(B)Thompson’s plum pudding model of the hydrogen atom.
(C)Rutherford’s nuclear model of the hydrogen atom.
(D)Bohr’s model of the hydrogen atom.
(E)Quantum mechanical model of the hydrogen atom.
- The work function of a metal is the potential energy barrier height a conduction electron must surmount in order to leave the interior of the metal. In certain types of vacuum tubes the metal is shaped into a thin filament wire and heated until the kinetic energies of the electrons are sufficiently high to drive them out of the metal. In the photoelectric effect, photons supply the energy to emit the electrons out of the metal. In the case of field emission, how are the electrons able to escape the metal?
(A)The electric field lowers the height of the potential barrier at the surface of the metal and outside the metal so the electrons can escape.
(B)The electric field lowers the height and narrows the width of the potential barrier outside the surface of the metal so the electrons can tunnel through.
(C)The electric field supplies the electrons with the potential energy needed to overcome the barrier.
(D)The electric field supplies the electrons with the kinetic energy needed to overcome the barrier.
(E)The electric field supplies the metal with the necessary voltage to allow the electrons to escape.
- Which of the following experiments did not confirm the quantization of matter and/or energy?
(A)Hertz’s experiments on electromagnetic waves.
(B)Faraday’s experiments on electrolysis.
(C)Thompson’s e/me experiments.
(D)Millikan’s oil drop experiments.
(E)Compton’s experiments on x-rays scattered off electrons.
- A spaceship passes the earth with a constant velocity of 0.5 c. After passing the earth it emits a beam of electrons directed back toward the earth at a velocity of 0.8 c relative to the spaceship. What is the velocity of the beam relative to the earth?
(A)0.3 c in the same direction as the spaceship.
(B)0.3 c opposite to the direction of the spaceship.
(C)0.5 c opposite to the direction of the spaceship.
(D)0.8 c opposite to the direction of the spaceship.
(E)None of these are correct.
- The spacetime diagram shown below illustrates three spaceships A, B, and C. Spaceships A and B are at rest with respect to one another at a distance of 8.66 light-years and C is moving from A to B with a constant speed of 0.866 c. The clocks for all three spaceships are synchronized at time tA = tB = tC = 0 at the instant when C passes A relative to all observers. According to spaceship C, what does B’s clock read at that same instant?
(A)0
(B)4.33 years.
(C)5 years.
(D)7.5 years.
(E)8.66 years.
- An organ pipe is closed on one end and open on the other. If it has a fundamental frequency of 200 Hz, what is the frequency of its first overtone (i.e. the frequency of its second mode of vibration)?
(A)200 Hz
(B)300 Hz
(C)400 Hz
(D)500 Hz
(E)600 Hz
- Which of the following functions satisfy the differential equation ?
(A)
(B)
(C)
(D)
(E)
- Einstein’s gravitational field equation relates which of the following quantities?
(A)The curvature of spacetime to the distribution of matter.
(B)The gravitational force to the distribution of matter.
(C)The curvature of spacetime to the gravitational force.
(D)The gravitational force to the acceleration of the masses.
(E)The distribution of matter to the acceleration of the masses.
- Let represent the state of horizontal polarization for a photon traveling horizontally and represent its state of vertical polarization, where is the phase angle between the states such that = 0 for linearly polarized light and where is the imaginary square root of minus one. Then according to the principle of superposition of states, one state of circular polarization would be which of the following?
(A)
(B)
(C)
(D)
(E)
- Which of the following surfaces exhibit the negative type of curvature considered in general relativity?
(A)Surface of a cone.
(B)Surface of a cylinder.
(C)Surface of a plane.
(D)Surface of a sphere.
(E)Surface of a saddle.
- A block of metal of mass 1 kg is heated from 25oC to 75oC. Which of the following quantities is needed in order to calculate the time required to do the heating?
(A)Specific heat capacity of the metal.
(B)Specific heat capacity of the metal and the rate of heating.
(C)Molar heat capacity of the metal.
(D)Molar heat capacity of the metal and the rate of heating.
(E)The rate of heating.
- Which of the following statements is NOT true?
(A)At low temperatures, bosons tend to concentrate together into the same energy state.
(B)At low temperatures, fermions tend to occupy different energy states.
(C)At high temperatures, bosons tend to obey Maxwell-Boltzmann statistics.
(D)At high temperatures, fermions tend to obey Maxwell-Boltzmann statistics.
(E)At room temperature, Maxwell-Boltzmann statistics are always valid.
- A block of mass 1 kg moving at a speed of 20 m/s collides with a second block of mass 5 kg at rest. After the collision, the first mass recoils directly backwards at a speed of 10 m/s. What is the loss of total kinetic energy for the complete two-body system?
(A)50 J
(B)60 J
(C)90 J
(D)140 J
(E)150 J
- The four momentum vector of a particle has the components px = 3 MeV/c, py = 4 MeV/c, pz = 0, E = 13 MeV. What is the rest mass of the particle?
(A)12 MeV/c2.
(B)13 MeV/c2.
(C)13.9 MeV/c2.
(D)20 MeV/c2.
(E)The rest mass of the particle cannot be determined from the information given.
- The wave function (x) of a particle is a wave packet in the shape of a sin(x)/x function as shown in the figure below.
According to the Fourier transform and quantum mechanics, what is the shape of its momentum distribution function (p)?
(A)Pure cosine function.
(B)Sin(x)/x function.
(C)Gaussian distribution function.
(D)Step function.
(E)Dirac delta function
- Which of the following conditions is necessary to insure that the angular momentum of a particle be quantized in both magnitude and direction.
(A)Rectangular symmetry.
(B)Cylindrical symmetry.
(C)Spherical symmetry.
(D)Inverse square force.
(E)None of these require angular momentum to be quantized.
- According to the special theory of relativity, which of the following statements is FALSE.
(A)A moving object contracts along its direction of motion by a factor of gamma.
(B)A moving object contracts perpendicular to its direction of motion by a factor of gamma.
(C)A moving clock runs slow by a factor of gamma.
(D)The total mass-energy of a moving mass increases by a factor of gamma.
(E)The volume of a moving object decreases by a factor of gamma.
- In the figure below the potential energy function U(x) is plotted as a function of x (the boldest line with arrows at the two ends.) Five energy levels (A), (B), (C), (D), and (E) are also shown on the figure (the thin horizontal lines) with their energies En signifying the n’th quantum level. Qualitative wave functions n (medium bold lines) are drawn for each energy level with the -axis of the wave function corresponding to the respective energy level. Which one of the indicated wave functions is qualitatively CORRECT for its respective energy level?
- In a particular substance the phase velocity of the waves is proportional to the reciprocal of the wavelength. If vp represents the central phase velocity of a wave group and vg represents the group velocity, which of the following equations is valid?
(A)vg = 1/vp.
(B)vg = ½ vp.
(C)vg = vp.
(D)vg = 2 vp.
(E)vg = 4 vp.
- Which of the following statements is FALSE in regards to quantum mechanics applied to a single particle?
(A)Observables are represented by operators that operate on eigenstates to render eigenvalues times the respective eigenstates.
(B)The wave function is a mathematical expression that includes all the information that can be known about the physical state of the particle.
(C)Schrödinger’s equation describes the behavior of the wave function in both space and time.
(D)The square of the wave function represents the probability of finding the particle within a small volume near a certain location in space.
(E)The expectation value of an observable is the value most frequently obtained when that observable is measured experimentally.
- A free neutron spontaneously decays into a proton, electron, and antineutrino. Given that mn = 939.6 MeV/c2, mp = 938.3 MeV/c2, me = 0.511 MeV/c2, m 0 MeV/c2, and assuming that the antineutrino carries away a total mass-energy of 0.189 MeV, what is the approximate kinetic energy of the electron?
(A)0.3 MeV.
(B)0.5 MeV.
(C)0.6 MeV.
(D)0.8 MeV.
(E)1.3 MeV.
- A quantum particle in a one-dimensional box is in its first excited state. What is the probability of finding the particle in the left quarter of the box?
(A)0
(B)¼
(C)½
(D)/4
(E)1
- Two small non-rotating spaceships are floating freely in interstellar space well outside the influence of any other objects in the universe. Which of the following conditions must be true?
(A)Both spaceships must remain forever together side by side.
(B)Both spaceships must be in the same inertial frame.
(C)Each spaceship must be in its own respective inertial frame.
(D)The distance between the two spaceships must remain constant.
(E)The distance between the two spaceships must change at a constant rate.
- Which of the following experimental observations have NOT been used to confirm one or another aspect of the general theory of relativity?
(A)Perihelion shift of the planet Mercury.
(B)Deflection of starlight near the surface of the sun.
(C)Gravitational red shift of light waves.
(D)Black Holes.
(E)Gravitational waves from supernovae.
- How many different ways can three identical particles of spin one-half be arranged into a quantum system consisting of three energy states if the energy of the particle is spin independent?
(A)1
(B)4
(C)10
(D)20
(E)56
- According to the quantum model of the hydrogen atom, when the atom is in its ground state which of the following is true?
(A)The electron is at rest with zero momentum.
(B)The electron is in an orbit with a radius equal to the Bohr radius.
(C)The electron has an orbital angular momentum equal to zero.
(D)The electron has an electron cloud shaped like a fuzzy donut.
(E)The electron has an electron cloud most dense above and below the nucleus.
- A photon of wavelength 500 nm strikes a photoelectric surface composed of sodium with a work function of 2.28 eV. If c = 2.998x108 m/s, h = 6.626x10-34 J.s, e = 1.602x10-19 C, and me = 9.109x10-31 kg, what is the maximum speed of a photoelectron emitted from the surface?
(A)2.7x104 m/s
(B)2.7x105 m/s
(C)2.7x106 m/s
(D)2.7x107 m/s
(E)2.7x108 m/s
- An x-ray of wavelength 0.1 nm is Compton scattered off of an electron initially at rest. Under what conditions does the scattered photon have a shorter wavelength than the incident photon?
(A)The photon is scattered straight back through an angle of 180 degrees.
(B)The photon is hardly scattered at all through an angle approaching 0 degrees.
(C)The photon is scattered through an angle of 90 degrees.
(D)The electron is scattered at an angle of 90 degrees.
(E)None of the above.
- According to the free-electron gas theory of metals, which of the following statements is TRUE?
(A)At absolute zero, none of the energy levels above the Fermi energy contain electrons.
(B)Near absolute zero, the kinetic energy of all the electrons in a metal approaches zero.
(C)At the Fermi temperature, the electrons in a metal are at rest.
(D)Bose-Einstein statistics are used to develop the free-electron gas theory of metals.
(E)At absolute zero, all metals become superconducting.
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