Modern Physics Exam
Do your own work.
Physics 103
Due Tuesday, 10 June
You may share resources (exchange sources of information, etc., not answers)
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3 points each.
[1] An astronomer observes two stars explode in simultaneous supernovae. The stars are
200 light years apart. To an observer traveling at 0.5c, the explosions will
(a) still be simultaneous.
(b) occur at different times.
(d) take twice as long to happen.
(e) be farther apart.
[2] A massive K is produced at point A and travels to point B where it decays. A
stationary observer in the lab and an observer moving by at 0.6c will agree on
(a) the time it takes the particle to travel from A to B.
(b) the distance from A to B.
(c) the speed the K particle was moving.
(d) event A happening before event B.
[3] Below are three wave functions representing solutions to a particular quantum physics
problem. Which of the choices list the functions in order of increasing energy?
(a) X < Y < Z
(b) Y < Z < X
(c) Z < Y < X
(d) Y < X < Z
[4] Particles with mass are prevented from moving at the speed of light by
(a) the physics police.
(b) the limited amount of energy available.
(c) the uncertainty principle.
(d) the lack of quantum levels.
[5] The momentum of a photon is
(a) zero because it has no mass.
(b) depends on its velocity.
(c) perpendicular to the direction of travel.
(d) is proportional to its energy.
[6] Viewed as a stream of particles, light or electrons produce an interference pattern
after passing through a double slit because {Check all that apply}
(a) they bounce off the edges of the slits.
(b) the particles pass through both slits at once.
(c) the interference pattern is the probability for where the particles hit the screen.
(d) the bright spots represent allowable quantum states.
[7] When a particle’s energy is less than the potential in a region, the wave function
(a) equals zero.
(b) is a decaying exponential function.
(c) oscillates wildly.
(d) becomes imaginary.
Matching: Match the physical quantity for each number with the letter for the correct
quantization.
[8] time
(a) n ħ
[9] angular momentum
(b) hf
[10] charge
(c) N e
[11] light energy
(d) not quantized
_____________________________________________________________________
For a particle in a potential well, tell whether each of the following changes will
(a) increase the energy of the states (b) decrease the energy of the states or
(c) leave the energies of the states unchanged.
[12] The width of the well is decreased.
[13] The mass of the particle is increased.
_____________________________________________________________________
[14] A particle is trapped in a well of length L. The momentum of the particle must be
(a) equal to ħ/L.
(b) < ħ/L.
(c) uncertain within ħ/L. (d) > ħ/L.
[15] Two travelers pass each other at a relative speed of 0.8c. From Stein’s point of
view, Ayn’s clock runs slow. According to Ayn, Stein’s clock runs slow. The theory of
relativity says that
(a) The stationary observer’s account is correct
(b) The moving observer is correct.
(c) Both points of view are equally valid.
(d) Both are incorrect, the universal rest frame is the only frame which gives correct
measurements.
[16] The hydrogen alpha line is the red line you measured in lab. A star moves past an
observer at 0.6c. As the observer watches the star move by, looking from the side, the
light will be
(a) red shifted.
(b) blue shifted.
(c) unchanged.
(d) changed to gray.
[17] Which of the following is not a valid uncertainty relation?
(a) Δx Δp ≥ħ
(b) Δx Δt ≥ħ
(c) ΔE Δt ≥ħ
(d) ΔL Δ ≥ħ
[18] A quantum system with a charged particle can absorb light
(a) if the frequency = (energy difference between 2 levels)/h.
(b) of any frequency.
(c) of any frequency > (the smallest energy difference between 2 levels)/h.
(d) in integer multiples of h.
[19] Which of the following is not a valid quantum relation?
(a) E = hf
(b) p = h/λ
(c) L = n ħ
(d) t = n 2mh/p2
[20] Which of the following are true of lasers? {Check all that apply}
(a) The light is in phase (coherent).
(b) The light is nearly monochromatic.
(c) The laser cavity uses interference to determine the phase of the light.
(d) The system which emits the light must have a metastable state
with a high probability of emission.
(e) Any system with 2 or more energy levels can be used to make a laser.
Long answer, points as noted.
[A] A system has three energy levels with energies 1eV, 3 eV & 5 eV.
(1) Draw an energy level diagram of the system, labeling the levels with the energy and
quantum number. [5 points]
(2) Calculate all wavelengths which can be emitted or absorbed by such a system.
hc = 1240 eV•Ǻ [5 points]
[B] An observer measures a cube which flies by her at 0.8c. The edges of the cube
perpendicular to the motion measure 2 meters in length. What is the length of the side in
the direction of motion according to this observer? [5 points]
[C] Stellar black bodies. {Black Body radiation, pp. 855-6}
(a) Rank the above stars in order of increasing temperature : [5 points]
_______
< _________
<
__________
<
_______
The light curve below is the spectrum of a star. The black curve is a crude sketch of the
black body curve for the
spectrum; subtracting this would
leave the atomic absorption lines
from the cooler outer atmosphere
of the star.
(b) Use your best estimate for the
blackbody curve to calculate a
temperature for this star.
[5 points]
(c) The apparent magnitude for this star is 4.93, which is equal to the luminosity divided
by the square of the distance to the star. This star is 64.3 light years away. Calculate the
star’s Luminosity. 1 light year = 0.46E15 m. [5 points]
(d) The luminosity you calculated above is the emissive power, which Stefan’s law
relates to the size of the emitting object and its temperature. Using 1 as the emissivity of
the star, calculate the radius of the star in meters.
Luminosity = σAeT4. [ 5 points]
[D] Redshift of a star.
A star containing hydrogen would have intense peaks of energy at 410.17 nm, 434.05 nm,
486.13 nm, and 656.28 nm. These hydrogen emission peaks would be in addition to the
ones associated with the other elements contained in the star. In the 1920's, Edwin
Hubble, while studying the stars of distant galaxies, found that for some, their emission
spectra had peaks at 411.54 nm, 435.50 nm, 487.75 nm, and 658.47 nm.
(a) Assuming these are the hydrogen lines and are red shifted, verify that they conform to
the correct pattern by comparing the difference in wavelength divided by the original
wavelength (such as (411.54 – 410.17)/410.17 ). Are your ratios about the same? What
does this say about the possibility that they are the red shifted hydrogen lines? [10 points]
(b) Calculate the velocity of the star from the red shift for each of the lines. Average
your results. [5 points]
[E] Showers of pion particles (πo, π+, π-) are commonly produced in high energy particle
collisions. The rest energy of a pion is 139.6 MeV. A pion moving at 0.6c is observed to
travel 5.74 meters before it decays into an electron and a neutrino.
(a) What is the lifetime of this pion in its rest frame? [10 points]
(b) What is the pion’s momentum in the observer’s frame? [5 points]
(c) Calculate the pion’s energy in the observer’s frame. [5 points]
(d) What is the pion’s wavelength in the observer’s frame? [5 points]
[F] The rotational energy levels for a molecule are as given below.
The energy  = 0.0013 eV
(a) Calculate the possible wavelengths
of light which can be absorbed by this
molecule. [10 points]
(b) Sketch the spectrum, assuming all lines are equally intense. [5 points]
[G] Waves and macroscopic objects.
(a) A sand grain has a diameter of about 10-4 meters. If we assume an uncertainty
of 2E-5 m for this measurement, what is the corresponding uncertainty in momentum?
[5 points]
(b) What uncertainty in velocity does this correspond to, using a mass of about 0.1 mg?
[5 points]
(c) What speed would the sand grain need to be moving so that its momentum was equal
to the uncertainty calculated in (a)? [5 points]
(d) For such a sand grain moving at 200 m/s, calculate the DeBroglie wavelength.
[5 points]
(e) For each of the objects below, calculate the speed it must move in order to have a
DeBroglie wavelength of .1 nm (1E-10 m) [3 points each]
A 1 mg sand grain
An Argon atom
A proton
An electron