33-211/213: Physics 3 - Modern Essentials
Homework Assignments and Solutions

Physics 33.211 Homepage.

WEEK 14 assignment

Finish reading Chapter 5 of Tipler and Llewellyn.

Problems: (due WEDNESDAY December 3, 9:30 am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Tipler & Llewellyn (Chapter-Problem):

TIP5-22 (electron double-slit experiment)
TIP5-23 (classical particle probability)
TIP5-25 (quantum probability)
TIP5-27 (photons from an excited state)
TIP5-28 (position uncertainty of a dust grain)
TIP5-29 (energy widths in radon)
TIP5-34 (neutron diffraction)
TIP5-35 (simple "uncertainty" calculation)
TIP5-44 (zero-point energy)

The following three problems are part of the assignment. You can download this file, if you wish, from: Rest of Assignment 14 (PDF) or Rest of Assignment 14 (postscript)

PROBLEM 14.A Basic complex number manipulation. Define two complex numbers z1 and z2. Let z1 = 3+i4 and z2 = 1-i2.
a) Compute z1 + z2 and z1*z2.
b) Convert z1 and z2 to the polar variables r and a, where r is the magnitude of the number and a is the phase. Then write z1 and z2 in complex exponential form.
c) Compute z1*z2 using the complex exponential results from Part (b). Verify that this answer is the same as what you computed without using complex exponentials in Part (a).

PROBLEM 14.B Write down Euler's formula (see class notes). Use it to show that for angle "a" we have
sin a = {exp(ia) - exp(-ia)}/(2i) and cos a = {exp(ia) + exp(-ia)}/2.

PROBLEM 14.C Define two rightward-moving waves in complex exponential form: psi1 = A exp{i(k1*x - omega1*t)} and psi2 = A exp{i(k2*x - omega2*t)}, where the k's are wavenumbers and the omega's are angular frequencies. A is the wave amplitude, x is position, and t is time. Using this notation, show that psi_tot = psi1 + psi2 can be written as
psi_tot = 2A cos((1/2)(delta_k*x - delta_omega*t)) cos(k*x - omega*t)
where k and omega are the average values of the k's and omega's, and delta_k = k2 - k1 and delta_omega = omega2 - omega1.

WEEK 13 assignment

Finish reading Chapter 5.3 of Tipler and Llewellyn.

Problems: (due TUESDAY November 25, 9:30 am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Tipler & Llewellyn (Chapter-Problem):

TIP5-7 (protons trapped between two walls)
TIP5-17 (phase and group velocity of a wave packet)
TIP5-19 (radar bandwidth)
TIP5-20 (tuning fork)
TIP5-21 (phone line bandwidth)
TIP5-40 (linearity of the wave equation)

WEEK 12 assignment

Read Chapter 5.1, 5.2, and 5.3 of Tipler and Llewellyn.

Problems: (due TUESDAY November 18, 9:30 am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Tipler & Llewellyn (Chapter-Problem):

TIP4-33 (Mosley plot)
TIP4-34 (Franck-Hertz using hydrogen)
TIP4-36 (Franck-Hertz using potassium)
TIP4-43 (reduced mass in hydrogen vs. deuterium)
TIP4-51 (sophisticated Mosley plot)
TIP5-2 (deBroglie wavelength)
TIP5-3 (electron microscope)
TIP5-5 (nitrogen at room temp)
TIP5-12 (scattering from MgO)
TIP5-13 (neutron scattering)
TIP5-14 (Davisson-Germer experiment)

WEEK 11 assignment

Read rest of Chapter 4 of Tipler and Llewellyn.

Problems: (due TUESDAY November 11, 9:30 am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Tipler & Llewellyn (Chapter-Problem):

TIP4-6 (Rutherford scattering: rates ratio)
TIP4-8 (impact parameter concept)
TIP4-10 (distance of closest approach concept)
TIP4-14 (units exercise; there is a typo: "h" should be "h-bar" in the problem statement)
TIP4-15 (Lyman wavelengths)
TIP4-16 (Earth's orbit if it were quantized)
TIP4-19 (muonic atoms)
TIP4-21 (energy level diagram)
TIP4-26 (K_alpha X-rays)
TIP4-31 (relativity problem)
TIP4-32 (effective nuclear charge)
TIP4-46 (using the full Rutherford formula)

WEEK 10 assignment

Finish reading Chapter 3 of Tipler and Llewellyn.
Read Sections 4.1 and 4.2 of Tipler and Llewellyn.

Problems: (due TUESDAY November 4, 9:30 am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Tipler & Llewellyn (Chapter-Problem):

TIP3-34 (dental X-rays)
TIP3-35 ('units' exercise)
TIP3-36 (Compton scattering)
TIP3-40 (Compton data problem)
TIP3-41 (Compton wavelength exercise)
TIP3-49 (recoil energy of electron)
TIP4-2 (Balmer transition)
TIP4-3 (checking data interpretation)
TIP4-5 (testing some data)

WEEK 9 assignment

Finish reading Chapter 3 of Tipler and Llewellyn.

Problems: (due WEDNESDAY October 29, 9:30 am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Tipler & Llewellyn (Chapter-Problem):

3-24 (black & white film) TIP3-24
3-26 (the stopping potential) TIP3-26
3-28 (photoelectric effect in Mo) TIP3-28
3-29 (wavelengths exercise) TIP3-29
3-32 (work function of Cesium) TIP3-32
3-45 (photoelectric effect) TIP3-45
3-46 (Special Relativity problem) TIP3-46
3-47 (Bragg scattering) TIP3-47

WEEK 8 assignment

Read Chapter 3 of Tipler and Llewellyn.

Problems: (due WEDNESDAY October 22, 9:30 am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Tipler & Llewellyn (Chapter-Problem):

3-1 (radius of curvature in B field) TIP3-1
3-3 (velocity selector) TIP3-3
3-5 (orbiting electrons) TIP3-5
3-6 (electron speeds) TIP3-6
3-8 (in Millikan's footsteps) TIP3-8
3-13 (Stefan-Boltzmann constant) TIP3-13
3-14 (calculus problem with distributions: use u(lambda)d_lambda = u(f) df) TIP3-14
3-15 (cosmic microwaves) TIP3-15
3-19 (radiating cavity) TIP3-19
3-21 (temperature of the Earth: think disks and spheres...) TIP3-21
3-48 (sailing with light) TIP3-48

WEEK 7 assignment

Read Chapter 9 of Taylor and Wheeler. It is mostly qualitative, but still important.

Problems: (due TUESDAY October 14, 9:30 am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Taylor & Wheeler (Chapter-Problem):

8-18 (the Doppler effect, revisited) TW_8.18
8-23 (expanding universe) TW_8.23
8-25 (application of Doppler formula) TW_8.25
8-29 (photon ("Compton") scattering) TW_8.29 (solution not included; was done in class)
8-30 (the computer calculation is optional) TW_8.30

Taylor & Wheeler (Chapter-Problem): we revisit a Chapter TWO for the next problem
2-13 (the "calculus proof" is optional but fun to try) TW_2.13 TW_2.13'

WEEK 6 assignment

Read Chapter 8 of Taylor and Wheeler. Don't miss the "Dialog: Use and Abuse of the Concept of Mass."

Problems: (orginally due Tuesday October 7, 9:30am)
POSTPONED until Wednesday October 8, 9:30am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Problem 6.A Consider a kaon (mass = 497.67 MeV/c^2) which decays into two pions (each with mass = 139.57 MeV/c^2). In the rest frame of the kaon the pions each have a momentum of 206 MeV/c. The kaon is moving at 0.9c in the lab frame.
a) What is the total energy of the kaon in the lab frame?
b) What is the momentum of the kaon in the lab frame?
c) What is the speed of the pions in the kaon rest frame?
d) If the pion goes forward in the kaon rest frame (at zero degrees with respect to the kaon's direction in the lab frame), what are its energy and momentum in the lab frame? Use the Lorentz Transformation you derived in Problem 7.5.
e) Verify your result for Part (d) by computing the mass of the pion from its energy and momentum in the lab frame.
f) Repeat Parts (d) and (e) for the other pion, the one that goes backwards in the kaon rest frame.

Taylor & Wheeler (Chapter-Problem):
7-8 (use the book's "units" for all quantities. Forget about keeping the factors of c.) TW_7.8
7-10 (in Figure 7.10, particle C is NOT at rest) TW_7.10
7-11(use z=-(v/c)^2) TW_7.11
8-1 (just turn the crank) TW_8.1
8-5 (rewrite the equations in Parts a, b, and c in energy units, with all factors of "c" included) TW_8.5
8-8 (an example from nuclear physics) TW_8.8
8-14 (an example from particle physics) TW_8.14, TW_8.14'

Five extra credit points: Locate the spot in the text where a well-known Pittsburgh institution is mentioned. Write the answer on your homework paper.

WEEK 5 assignment

Read Chapter 6 of Taylor and Wheeler.
Read Chapter 7 of Taylor and Wheeler.

Problems: (due WEDNESDAY October 1, 9:30am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Taylor & Wheeler (Chapter-Problem):

4-2 (one-way twin journey: who is younger?) TW_4.2
6-3 (spacelike and timelike intervals) TW_6.3, TW_6.3'
6-5 (detonator 'paradox') TW_6.5, TW_6.5'
7-5 (building an important bridge in our understanding) TW_7.5
7-6 (the mass of an electron is m=0.511 MeV/c^2) TW_7.6

WEEK 4 assignment

Read Chapter 5 of Taylor and Wheeler. Read this chapter first!
Read Chapter 4 of Taylor and Wheeler.

Problems: (due Wednesday September 24, 9:30am, neatly handwritten on paper, with multiple sheets stapled at top left corner)
When making spacetime diagrams, use a *ruler* and a *sharp pencil*!

Taylor & Wheeler (Chapter-Problem):

    5-2 (keep event 0 at the origin in S') TW_5.2
    5-6 (do this problem before trying 5.4a) TW_5.6
    5-4a (the famous "pole in the barn paradox"; does it fit or not? Do only part (a)) TW_5.4
    5-7 (reciprocity can be subtle: think carefully about which events are valid to use) TW_5.7 TW_5.7' TW_5.7''
    4-1 (make a space-time diagram for this problem) TW_4.1 TW_4.1'

WEEK 3 assignment

Finish reading Chapter 3 of Taylor and Wheeler.
Read Chapter "ST" in Taylor and Wheeler on the Lorentz Transformation.

Problems: (due Tuesday September 17, 9:30am, neatly handwritten on paper, with multiple sheets stapled at top left corner)
Do all parts of all problems, except as specifically noted.

Taylor & Wheeler (Chapter-Problem):

WEEK 2 assignment

Finish reading Chapter 2 of Taylor and Wheeler.
Read Chapter 3 of Taylor and Wheeler.

Problems: (due Tuesday September 9, 9:30am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Taylor & Wheeler, (Chapter-Problem):

WEEK 1: Assignments 0 and 1

Read all of Taylor and Wheeler Chapters 1 and 2. This is the longest reading assignment of the semester.

More Problems, Assignment 1: (due Tuesday September 2, 9:30am, neatly handwritten on paper, with multiple sheets stapled at top left corner)

Taylor & Wheeler, (Chapter-Problem):

WEEK 1 solutions (activated!)

Physics 33.211 Homepage.

Last updated on 12-1-03 by schumacher@cmu.edu.