PHYS 342 Class Info

This page contains links to information for the PHYS 342 course (Modern Physics).

Class will be cancelled on Thurs Mar 10.

IMPORTANT: In addition to office hourse, I will be available to answer questions whenever I'm not in meetings. You can try your luck by just dropping in or you can email for a specific meeting time.

IMPORTANT: The tests will be in the classroom at the usual class time. If you miss a test, an excused absence needs to be verified through the Office of the Dean of Students: https://www.purdue.edu/advocacy/students/absences.html See the syllabus for  the grading policy for excused absences. Unfortunately, an unexcused absence will count for 0 points.

TEST 1 will be Thurs. Feb 27 and will cover Chaps 2, 15, 3, 4, 5.2 and 5.3 (the first 1 1/2 pages of Chap 5). Bring a nongraphing, dumb calculator (can only do logs, trig functions, exponentials, powers, roots; one or two line TI-30X and TI-36X models; if you are uncertain, ask me; similar to this rule) and a writing device. The test will have all of the end of chapter equations exactly as in the book "Chapter Summary" sections (for example, page 65 for Chap 2).

TEST 2 will be Thurs. Apr 17 and will cover Chaps. 5 (material not on Test 1), 6, 7, 8, and 12. Bring a nongraphing calculator and a writing device. All of the rules will be the same as Test 1.

FINAL will be Wed May 7 from 1-3 pm in room PHYS 203. The final will be comprehensive. Bring a nongraphing calculator and a writing device.


The text book for the class is Modern Physics 4th Edition by Kenneth S. Krane.

We will cover most of Chaps 2-7 and a wide variety of contemporary results.

Syllabus

Office hours: Wednesday 2:00-3:00, Thursday 2:00-3:00 (Contact me by email if you want to arrange a special time.)



Chap 2; Chap 2 slides.pdf; Chap 15; Chap 15 slides.pdf; Chap 3; Chap 3 slides.pdf; Chap 4; Chap 4 slides.pdf; Chap 5; Chap 5 slides.pdf; Chap 6; Chap 6 slides.pdf; Chap 7; Chap 7 slides.pdf; Chap 8; Chap 8 slides.pdf; Chap 12; Chap 12 slides.pdf; Standard Model Chart; Chap 14; Chap 14 slides.pdf; Chap QIS; Chap QIS slides.pdf; QIS_urls.txt


HWK 1 (Due Thu Jan 16, 5 problems total): Chap 2: Problems 2 (for part (c) only find the time to go from the end of the sidewalk back to the package), 4 but for this problem change the speed of light, c, to 330 m/s (if you get their speed is larger than this c then you're doing something wrong), 10, 14, 22

HWK 2 (Due Thu Jan 23, 5 problems total):
Prob 1: (a) An electron is accelerated in a uniform electric field of  -10⁶ V/m. It starts at the origin with 0 velocity. Using relativity, how far does the electron travel before it's speed is 0.09 c? 0.9 c? 0.99 c? 0.999 c? (Hint: What is the potential energy for a charge in a uniform electric field? Hint²: Can you use a conservation law to solve?) (b) Repeat (a) but using non-relativistic equations.
Prob 2: Chap 2 prob 44
Prob 3: Low mass stars have a stage where three ⁴He atoms combine into one ¹²C. Using the data in Appendix D "Table of Atomic Masses". Calculate how much energy is released for each ¹²C  formed.
Prob 4: Jun Ye's group have made some of the most accurate atomic clocks. For example, they used them to measure the effects of General Relativity. Here, they claim a relative clock accuracy of 3.1 X 10^-18. Suppose they have two of these clocks that are at different heights in their lab. Can they measure the difference in the rate that the two clocks tick when the vertical separation between the clocks is 10 cm? 1 cm? Roughly, what is the smallest vertical distance where they can measure the effects of General Relativity?
Prob 5: According to the interwebs, the most massive black holes are over 10 billion solar masses while the black hole at the center of the Milky Way is a measly 4.3 million solar masses. Calculate the Schwarzschild radius of the black hole at the center of Holmberg 15A and the black hole Sagittarius A* using the masses here. Compare these to the radius of the sun and the orbital radius of (say) Neptune.

HWK 3 (Due Thu Jan 30, 5 problems total):
Prob 1: Chap 15 prob 2
Prob 2: From Fig. 15.9 of the textbook (the right figure on pg 10 of Chap 15 slides.pdf): a) At 30 kpc, estimate the actual tangential velocity (dots) and the tangential velocity expected from visible matter (blue line). b) Use these numbers to estimate the fraction of matter that is visible and the fraction that is "dark". (For the universe, from NASA https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy
there is approximately 5X more dark matter than visible matter).
Prob 3: You have a light source of 700 nm wave length that emits 60 W of light uniformly in all directions. Assume nothing absorbs the light. a) What is the intensity 1 meter from the source? 100 meters from the source? (Hint: What is the average power through the surface of the sphere and what is the surface area of the sphere?) b) What is the average electric field (square root[E²₀]) 1 meter from the source? Repeat for 100 m from the source? c) The sun outputs 3.8X10²⁶ W. What is the intensity of the light at the orbital radius of the earth? at the distance to Alpha Centauri? d) What is the average electric field for both distances in part c)?
Prob 4: A light beam pulse is moving in the x-direction and has 10 J of energy. a) What is the momentum of the pulse? b) Suppose a stationary grain of dust in space (M = 2 X 10^-9 kg) completely absorbs the light pulse. What velocity will it have? c) Repeat b) but for a pulse with energy of 2.1 eV absorbed by an initially stationary atom with mass of 23 amu.
Prob 5: In a recent calculation, we simulated the effect of an X-ray pulse hitting an electron. The photon energy was 9.0 keV and the peak intensity of the X-ray pulse was 3X10²¹ W/cm² (be careful of the intensity units which are not SI).  a) What is the wave length of a photon in this pulse? b) At the peak intensity, what is the rate that these photons hit a circular area with a radius of 2X10^-10 m?

HWK 4 (Due Thu Feb 6, 5 problems total):
Prob 1: Use the book's table of work functions. Cobalt is illuminated with light. (a) What is the largest wavelength that will cause photoelectrons to be emitted? (b) What is the largest kinetic energy for ejected electrons when you shine light of 150 nm on Cobalt?
Prob 2: When you shine light of 241.257 nm on a gas composed of sodium atoms, electrons are ejected and you make positive sodium ions. When you shine light of 241.274 nm on a gas composed of sodium atoms, the light is not absorbed and no electrons are ejected. From these numbers you can calculate a fairly accurate work function for gaseous sodium which is completely different from solid sodium (solid sodium 2.28 eV). (a) What happens when you shine light of 700 nm on the sodium atoms? (b) What happens when you shine light of 200 nm on the sodium atoms? Make sure to give their kinetic energy if electrons are ejected in one of these cases.
Prob 3: (a) Chap 3 prob 23(a) (don't do 23(b)). (b) At what wavelength does the Sun emit its peak intensity?
Prob 4: Chap 3 prob 26
Prob 5: Hydrogen atoms absorb photons with a wavelength of 121.6 nm. Approximately 10 nanoseconds after absorbing a photon, the hydrogen atom will emit a photon of the same wavelength in a random direction; it will then be ready to absorb another photon. Suppose a hydrogen atom with a velocity of 50 m/s is flying at you. You are shooting 121.6 nm photons at it in pulses of light separated by 0.1 seconds. About how many photons would need to be absorbed before its speed is approximately 0? (For what it's worth, this is essentially the method we use to cool the antimatter version of hydrogen atoms. CERN press release, Purdue press release, various news reports)

HWK 5 (Due Thu Feb 13, 5 problems total):
Prob 1: 13.598 eV is required to change a hydrogen atom into a free electron and proton. A photon of energy 20.000 eV is travelling in the +x direction. It is absorbed by an initially stationary hydrogen atom. (a) After the photon is absorbed, what is the total kinetic energy (the sum of kinetic energies of the proton and electron)? (b) After  the photon is absorbed, what is the total momentum (the sum of the momentum vectors for the proton and electron)? (c) Give a quadratic equation that will determine the electron (or proton) momentum. You don't need to solve it because round-off errors make getting actual numbers somewhat tricky.
Prob 2: The Sunyaev-Zeldovich effect leads to higher energy photons from fast electrons scattering from the cosmic microwave background. In the lab frame, an electron is traveling in the +x direction with speed 0.99 c and a photon with energy 2.3 X 10^-4 eV is traveling in the -x direction. After the photon scatters off of the electron, it is traveling in the +x direction. (a) In the frame of the electron, what is the wavelength of the photon? (b) If a photon with this wavelength Compton scatters by 180 deg, what is the resulting wavelength of the photon? (c) In the lab frame, what is the wavelength and energy of this photon?
Prob 3: C₆₀ molecules with a velocity of 220 m/s go through a pair of horizontally separated slits with a separation of 100 nm. How far is the screen if the interference maxima are at the position in the figure on pg 10 of Chap 4 slides.pdf (estimate the maxima from figure a)?
Prob 4: For some of the higher energies, you will need the relativistic momentum for the electron. (a) For photons, calculate the wavelength for energies 10, 10³, 10⁵, 10⁷,10⁹ eV. (b) For electrons, calculate the wavelength for kinetic energies 10, 10³, 10⁵, 10⁷,10⁹ eV. (c) Why do the wavelengths become approximately the same as energy increases?
Prob 5: For complex numbers, i²= -1. (a) Write the Taylor series of sin(x), cos(x), and e^x (you can look these up). (b) Use the result in (a) to find the Taylor series of e^{i x}. (c) Use the result in (a) and (b) to get a relationship between e^{i x} and cos(x) and sin(x).

HWK 6 (Due Thu Feb 20, 5 problems total):
Prob 1: Chap 4 prob 20
Prob 2: Chap 4 prob 34
Prob 3: This is a relativistic quantum problem. a) What is the classical relativistic kinetic energy of a particle as a function of momentum? (The equation for energy as a function of momentum is in the textbook, Chap 2; from the energy, you can get the kinetic energy.) b) Determine angular frequency, omega, as a function of wave number, k, for a relativistic quantum particle. c) What is the phase velocity and what is the group velocity as a function of momentum? d) Compare the group velocity to the classical relationship for the velocity as a function of momentum (for velocity as a function of momentum see pg 4 of Chap 2). (Hint: you should find they are the same.)
Prob 4: For an electron between two walls (one at x=0 and the other at x=L), the wave function for 0<x<L is
Psi(x,t) = A [sin(pi x/L) e^{- i w1 t} + sin(2 pi x/L) e^{- i w2 t}]
For x<0 or x>L, the wave function is zero. The w1 and w2 are real numbers. Determine A (choose A to be positive and real). For this problem, you can get Mathematica (or similar) to do the necessary integral but make sure you clearly write out the integral you had it do. (As a sanity check, make sure Psi has the correct units.)
Prob 5: For the previous problem, a) what is the probability for finding the electron between x=0 and x=L/2 as a function of time? b) What is the maximum and the minimum for this probability? c) Give this maximum and minimum as a number with 3 significant digits (for example, max = 0.753 and min = 0.291). For this problem, you can get Mathematica (or similar) to do the necessary integral but make sure you clearly write out the integral you had it do.

HWK 7 (Due Thu Mar 6, 5 problems total):
Prob 1: The potential energy, U(x), is finite everywhere. An energy eigenstate is
For x<0, psi(x) = sin(2 pi x/lambda).
For x>0, psi(x) = A sin(pi x/lambda) + B cos(pi x/lambda)
Use the continuity conditions to determine A and B.
Prob 2: For 0<x<L, psi(x) = A x (L - x) and psi(x) = 0 for x<0 or x>L. a) Determine A. b) What is the probability for finding the particle between 0 and L/2? c) What is the probability for finding the particle between 0 and L/4? You can have Mathematica (or something like) do all of the integrals you need.
Prob 3: Chap 5 prob 9
Prob 4: Repeat the previous problem but with psi(x) = C exp(-a x²). The exp( ) function I mean exp(b) = e^b.
Prob 5: One of the energy eigenstates of a potential has the form
psi(x) = C x exp(-a x²)
for all x with C and a being positive constants. Which state is it? (lowest energy state, first excited state, etc) Explain how you know. You might plot the psi(x) and look at pages 44-48 of Chap 5 slides.pdf.


HWK 8 (Due Thu Mar 13, 5 problems total):
The first two problems revisit Prob 4 of HWK 6. You can use Mathematica to do any integrations you need.
Prob 1: For an electron between two walls (one at x=0 and the other at x=L), the wave function for 0<x<L is
Psi(x,t) = A [sin(pi x/L) e^{- i w1 t} + sin(2 pi x/L) e^{- i w2 t}]
For x<0 or x>L, the wave function is zero. a) Give the values for w1, w2, and A.  b) Compute <H>(t).
Prob 2: For the wavefunction in Prob 1, compute <p_op>(t). For the definition of the momentum operator, see the bottom of pg 4 of Chap 5.
Prob 3: Chap 5 prob 28
Prob 4: Chap 5 prob 32
Prob 5: a) Using the wave function in Eqs. 5.57, estimate how far into the classically unallowed region (x>0) can a particle go. For the sake of this problem, call a decrease in the wave function by a factor of e to define how far it can go. b) For U₀-E = 0.1 eV, calculate this distance for an electron, a proton, a C₆₀ molecule, and a nanosphere with a mass of 10^-18 kg.


HWK 9 (Due Thu Mar 27, 5 problems total):
Prob 1: For Eq. (5.37) with the potential Eq. (5.38), show that the solution can not have the form psi(x,y) = f(x) + g(y). (Hint: can you satisfy the boundary conditions psi(0,y) = 0, psi(x,0) = 0, psi(L,y) = 0, psi(x,L) = 0?)
Prob 2: For Eq. (5.37), determine the allowed energy levels if
U(x,y) = (1/2) k (x² + y²).
Prob 3: For the situation in Figure 5.26
For x<0,       psi(x) = A e^{i k x} + B e^{- i k x}
For 0<x<L,  psi(x) = C e^{a x} + D e^{- a x}
For L<x,      psi(x) = F e^{i k x} + G e^{- i k x}
a) Determine k and a in terms of E, U₀, .... b) Write down the 2 equations that relate A,B to C,D. c) Write down the 2 equations that relate C,D to F,G. d) For particles sent in from the left, which (if any) of A, B, C, D, F, G are 0? Explain why.
Prob 4: Chap 6 prob 6.
Prob 5: a) Chap 6 prob 19. b) Repeat but for a muon in place of the electron. For b), don't include the effect of a finite proton mass (just swap in the mass of the muon for the mass of the electron).

HWK 10 (Due Thu Apr 3, 5 problems total):
Prob 1: For l=0, substitute R(r) = A e^{-b r} into Eq. (7.12). (a) Find the only allowed value for b. (b) Compute the energy and compare to Eq. (7.13) to determine the value for n.
Prob 2: (a) For an electron in a 2 T magnetic field in the z-direction, find the two energies that come from the internal magnetic dipole moment of the electron. For this problem take the g-factor (middle of pg 4 of Chap 7) to be exactly 2 or use the treatment in Eqs. (7.30-7.32). (b) What would be the photon frequency and wavelength that would cause a transition between these two energies?
Prob 3: For the n=8, l=3, m=1 state, Determine the number of nodes in the r part of the wavefunction, the theta part of the wavefunction, and the phi part of the wavefunction.
Prob 4: Use the hydrogen atom. (a) For l=0, what is the smallest and largest r that is classically allowed for the state n? (b) Give a numerical value for n=10, n=100, and n=1000.
Prob 5: For a hydrogen atom in it's ground state, almost all of its magnetic dipole moment is from the electron. Suppose the hydrogen atom is in a magnetic trap in its ground state (see discussion on pgs 4 and 5 of Chap 7). (a) How large must the change in magnetic field be to trap a hydrogen atom that has a speed of 50 m/s when it is at the magnetic field minimum? (As in Prob 2, take g=2.) (b) The ALPHA trap has a change in magnetic field of 0.9 T. Will this hydrogen atom be trapped? What is the maximum speed a hydrogen could have at the magnetic field minimum and be trapped?

HWK 11 (Due Thu Apr 10, 5 problems total):
Prob 1: For Fig. 8.4(b) of the text, the Na atom starts in the 5p state. The atom emits a single photon. List all of the dipole allowed states the atom could be in.
Prob 2: Chap 8 prob 4
Prob 3: For the short pulse laser described here, the photons have a large spread in energy. Roughly, what is this spread in energy in eV?
Prob 4: Use the Weizsacker formula on pg 7 of Chap 12 slides.pdf to calculate the binding energy of ⁶²Zn and ⁶³Zn. Use the data in Appendix D to calculate the actual binding energy (be careful that Appendix D is the mass of the atoms). (Hint: you've done something wrong if the Weizsacker masses differ by more than 5 MeV from the experimental masses. A common mistake is not to use enough significant digits in the masses or in the conversion factors from 1 u to MeV.)
Prob 5: Radioactivity can cause a sample to be warmer than the surrounding temperature. Use the data in Table 12.2. Suppose you have 1 gram of ²⁴¹Am. (a) What is the rate that energy is generated due to the alpha decay? (b) After 1000 years, what is the rate that energy is generated due to the alpha decay? (c) What does this isotope decay into? Do we have to worry about the decay of this product over the time scale of this problem? Explain. (Hint: Appendix D might also be useful for part c.)

I've added very short HWK solutions under the content button in brightspace. These are short and are the steps I used to solve. There are not a lot of intermediate steps, but it might help with understanding what you did incorrectly.

HWK 12 (Due Thu Apr 24, 5 problems total)
For Probs 1-3, the data on the Standard Model Chart might be useful.
Prob 1: An electron and the antimatter electron (positron) can form a bound state (called positronium). Suppose the positronium is stationary. The electron and positron annihilate (they both disappear) and two photons come out in exactly opposite directions. a) Use conservation laws to get the energies of each photon. b) What wavelength(s) is this? c) What type of photon(s) is this? Infrared, UV, X-ray, etc.
Prob 2: A proton and an anti-proton form a bound state that is stationary. When they annihilate a bunch of pions come out. If 4 pions come out, what is the total amount of kinetic energy released? For this problem, approximate the mass of all pions to be the same.
Prob 3: In a bottom box of the chart, they describe the collision of 2 protons giving 2 Z⁰ bosons. a) If the protons do a head on collision with equal speeds and opposite directions, what is the minimum kinetic energy they each must have to make Z⁰ bosons? b) What fraction of the speed of light does this correspond to?
Prob 4: Two states, |psi> and |phi>, are orthogonal to each other if <phi|psi>=0. For Qubits, given |psi>, then |phi> is determined except for an irrelevant overall phase. |psi> is defined by a₀ and a₁. a) Determine |phi> if a₀ = a₁ = 1/sqrt(2). b) Determine |phi> if a₀ = 1/sqrt(2) and a₁ = i/sqrt(2).
Prob 5: Using Chap QIS Eqs. (11) and (12), a) do the intermediate steps to show Eqs. (13) and (14). b) For the case of q₀=0, determine the 2X2 matrix you get from QQ (that is multiply Q by itself).