Note from Barney:  The questions in blue italics do not address material for the part of the exam over the new material, but they are exemplars of what you might find in the comprehensive part.   The questions that have been striken will not be on your exam.

Practice Exam 4

Discussion - complete the following as indicated in a concise manner.

  • Discuss the Superposition Principle.
  • Why was Compton's experiment important?
  • Compare and contrast Wavelength and Period of a periodic wave. In what ways are they similar and in what ways are they very different?
  • One of the first attempts to explain blackbody radiation failed so badly it was referred to as the "ultraviolet catastrophe." What did this mean?
  • Discuss how standing waves are produced.
  • Why was the double slit experiment for electrons important?
  • How did Planck change the theory that tried to explain blackbody radiation in order to make it work?
  • What did Davisson and Germer discover that lead to de Broglie's Nobel Prize?
  • What are the allowed numbers for the electron's spin?  Is there a classical analog to this quantity?
  • How does stimulated emission differ from spontaneous emission?
  • How is nuclear binding energy related to Einstein's famous equation?
  • Give a reason why the beta particle is deflected more in a magnetic field than an alpha particle

 

1. a) How does the brightness of the light in a photoelectric effect experiment affect the results? (i.e Does the cutoff frequency change? Does the maximum KE change? Does the stopping potential change? Does the number of electrons produced change?)

b) How did Einstein explain this?

c) What did the wave theory predict should have happened?

 

 

    Sketching -

  • Sketch the third harmonic wave for the following organ pipe. Label the nodes and anti-nodes. (3 points)

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    Quickies -

  • Define: longitudinal wave, transverse wave, wave number, diffraction
  • What is the rotational equivalent of each of the following: mass, force, momentum, position
  • When does refraction occur?
  • If you were given a wave function for a particle, how could you find the probablility of the particle being located in a certain place, for example, between -1 and +1?
  • When a sound wave travels from one place to another, what is transported? Explain.
  • What does work function mean
  • The distance from equilibrium to the top of the crest of a periodic wave is called its
    • a. frequency
    • b. period
    • c. amplitude
    • d. wavelength
    • e. none of the above
  • Two point sources produce waves of the same wavelength and are completely in-phase (that is both sources produce crests at the same time). At a point that is 0.25 wavelength closer to one source than the other, you would expect to find an oscillation with
    • a. an amplitude equal to twice that of one wave alone
    • b. an amplitude equal to that of one wave alone
    • c. an amplitude that is 4 times that of one wave alone
    • d. an amplitude that is approximately zero
    • e. none of the above

     

      Short problems:

      1.  The frequency of TV channel 2 is 54 megaHertz. The speed of EM waves is 3x108 m/s. What is the wavelength of a channel 2 EM wave?

      2.  A guitar string is 1.2 m long and has a mass of 9.7 grams. What must be the tension in the string to obtain a wave speed of 432 m/s?

      3.  Assume that you are 15.9 m away from a 500 watt street lamp. What is the intensity of the light at your location?

    4.  The separation between the center maxima and first minima in a double slit experiment is .25 cm. The wavelength of the light is 628 nm, and the screen is 1.3 m away from the slits. What is the separation of the slits?

    5. Red light from a laser (640 nm) passes through a single slit which is 2mm wide.   How far from the center of the screen is the third minimum if the screen is 3 meters away from the slit?

    6.  An electron is moving at a speed of 3 x 107 m/s .  What is its wavelength?

    7.  If the uncertainty in position of the electron in problem 6 is equal to one wavelength, what is the minimum uncertainty in its momentum that is possible?

    8.  What is the energy of a photon that will cause the electron of the hydrogen atom to move from the n=2 to the n=5 state?

    9.  What are the allowed values for the quantum numbers that comprise the levels known as 4f?

    10.  In interstellar space the size of hydrogen atoms can be quite large as the proton and electron are attracted to each other.  What is the approximate quantum number for a hydrogen atom that has a radius of 1 cm? 

    11.  What is the speed of an electron with a de Broglie wavelength of 10-6 m?

    12.  The ground state for a 1-Dim, Particle-In-A-Box  has an energy of 2.0eV.   What photon is needed to cause the particle to jump to the n=3 state?

    13.  The momentum of an electron is measured within an uncertainty of 1.23x10-29 kg m/s.  What is the uncertainty in the electron's position?

    14.  If a hydrogen atom jumps from the n=100 to n=1 state, what wavelength photon is emitted? 

     

      Longer Problems

    1.  The equation of a transverse wave traveling along a very long string is given by

            y(x,t) = .02 sin (3x +4t )  where x and y are in meters and t in seconds.

    What is the a) amplitude, b) wave number, c) wavelength, d) angular frequency, e) direction of propagation, f) velocity of the section of the rope located at x=.2m at the instant t=.9 seconds, and g) the tension in the string if its linear density is .0026 kg/m?

    2.  What is the longest wavelength that can be produced by a 2m organ pipe that is open at both ends?  What is the frequency of the fundamental and the fourth harmonic? 

    3.  A diffraction grating is made up of slits of width 200nm which are 1,200 nm apart.   a) When light of wavelength 500nm passes through the grating, at what angle does the first (not counting the central one) maximum appear?  How many orders will be visible?

    4.  A disk is rotating on a frictionless shaft of negligible radius.  The disk has a mass of 440 g and a radius of 3.0 cm. It is rotating at 180 rad/s.   Another disk that is initially not rotating is dropped on top of it and frictional forces act to bring the two disks to a common rotational speed.  If the second disk has a mass of 270 g and a radius of 2.0 cm, what is the final angular speed of the two disks?  (for a disk I = 1/2 m r2)

    5.  a) A certain star has a surface temperature of about 7940 K and emits its maximum intensity in its blackbody spectrum at 378 nm. If the star cools down to 7500 K, where will its peak wavelength will now occur?

    1. How much less total energy does it emit now than it did before?

    6.  a) If a photon of 6.35 x 1014 Hz is the lowest frequency which will eject an electron from a certain metal, what is the work function of the metal?

    1. If a photon with a frequency of 7.50 x 1014 Hz hits this metal, what is the largest kinetic energy the ejected electron could possibly have?

    7.  A 0.40 meter diameter grinding wheel (I=0.80 kg m2) is spinning at 240 rev/min.  A torque of 10 N-m is applied to slow it down.  a) What is its final angular momentum, if the torque is applied for 2.0 seconds?  b) If the torque is created by a force of 60 N applied to the rim of the wheel, at what angle is the force applied?  c)  What is the acceleration of the wheel during the two seconds?   d)  How many revolutions did the wheel make during the two seconds?

    Possible types of Questions/Problems on the nuclear material

    Suppose that neon has two isotopes, 2110Ne and 2010Ne .  Why are the justified is calling both neon - ie why do both have the same chemistry?

    If the relative abundance of the isotopes in the previous problem is 22 and 78%, respectively, what would you expect the Atomic Weight as listed on the periodic table to be for neon?

    What is the binding energy of 2010Ne?

    Suppose that 2010Ne is produced as part of a nuclear chemistry experiment and it is unstable, and decays by beta minus.  What is the daughter nucleus of the 2010Ne?

    Suppose that 12x105 nuclei of the 2010Ne are created in the sample.  After 5 hours, the number of nuclei is down to 3x105.   What is the half-life of the nuclei?

    What is the initial activitity of the 2010Ne?  

    What are effective shielding material thicknesses for typical alpha, beta and gamma rays?