| Never enter units in your answers. Be
sure to use the units indicated on the HW submission page.
Enter numbers without commas. 23,546 should be 23546 Always enter a * for multiplication. g(H+h) should be g*(H+h). |
| You are now obtaining input data for CID = |
|
Submitted Answers will be graded W
11/19, Th 11/20, F 11/21, and M 11/24 at 12:00 noon.
| Problem 10.1 | |||||||||||
| What you should learn: The first three questions are again reading questions. | |||||||||||
| Problem: Did you read Chapter 39 Sections 4:9? Type Y or N in the box. | |||||||||||
Results of previous submissions:
|
|||||||||||
| Submit HW answers. | |||||||||||
| Problem 10.2 | |||||||||||
| What you should learn: Reading... | |||||||||||
| Problem: Did you read Chapter 40 Sections 1:4? Type Y or N in the box. | |||||||||||
Results of previous submissions:
|
|||||||||||
| Submit HW answers. | |||||||||||
| Problem 10.3 | |||||||||||
| What you should learn: Reading... | |||||||||||
| Problem: Did you read Chapter 40 Sections 5:8? Type Y or N in the box. | |||||||||||
Results of previous submissions:
|
|||||||||||
| Submit HW answers. | |||||||||||
| Problem 10.4 | |||||||||
| What you should learn: Moving objects are contracted in the direction of their motion by a factor of γ, moving clocks run slow by a factor of γ, and the effective mass of objects increases by a factor of γ. | |||||||||
| Problem: A cube of rest mass
m has its edges
parallel to the x, y, and z directions. The length of each side is a. An observer sees the cube traveling in the z direction a speed of β. If the rest mass of the cube is m, what is the effective density of the cube as measured by the observer? The effective density is defined as
ρeff = meff / Volume.
Express the effective density, rho, in terms of a, m, and
beta. (Do not include gamma in your answer.) | |||||||||
| Hints:
What do I need to consider? |
|||||||||
Results of previous submissions:
|
|||||||||
|
Answer range:
Submit HW answers. |
|||||||||
| Problem 10.5 | |||||||||||
| What you should learn: The life of an elementary particle, as any other time interval, depends on the velocity of the particle. | |||||||||||
| Problem: A π+ meson decays with a mean lifetime of 2.60 x 10–8 s. Mesons are created in large numbers when high-energy protons collide into matter. In an experiment, it is found that the mean distance a π+ travels before it decays is d, given below. What is the value of β (beta) for the meson? | |||||||||||
| Constants and fixed variables:
Mean π+ lifetime: tmean = 2.60 x 10–8 s. |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
| Hints:
A useful identity. |
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range:
beta = 0.710 to 0.790 Submit HW answers. |
|||||||||||
| Problem 10.6 | |||||||||||
| What you should learn: Simultaneity is relative. Lorentz transformations can be used to transform events from one inertial frame to another. | |||||||||||
|
Problem: A spaceship of length L is traveling at speed β with respect to a platform in space. Lights on both ends of the spaceship blink simultaneously, as seen by observers on the spaceship. What is the time between flashes of light (Deltat) as observed on the platform? |
|||||||||||
| Constants and fixed variables:
Length of the spaceship: L = 20.0 m |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
| Hints:
You will need to use the Lorentz transformations here. Note that we can't think of the two lights as a single clock. What are the Lorentz transformation equations? |
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range:
Deltat = 65.0 to 138 ns Submit HW answers. |
|||||||||||
| Problem 10.7 | |||||||||||
| What you should learn: Any four-vector transforms in the same way as the space-time four-vector. | |||||||||||
| Problem: A laser on a spaceships shines at an angle θ ' (thetap) from the "forward" direction. The wavelength of the laser (lamba0) is 640 nm. What is the wavelength (lambda) of the laser measured on a platform where observers see the spaceship moving forward at a speed β. | |||||||||||
| Constants and fixed variables:
Speed of the spaceship: beta = 0.920 |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
| Hints:
Consider the spaceship to be in the S' frame. Remember to consider the components of the energy-momentum four vector. What is the four-vector I need to use and what are the transformation equations (This is the hint for 10.6, but it has the information you need for 10.7, too.) |
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range: lambda = 150 to 195 nm Submit HW answers. |
|||||||||||
| Problem 10.8 | |||||||||||
| What you should learn: The next problems relate to the kinematic variables of a high-energy particle. Note that we use units of MeV where 1 joule = 1.602 x 10–13 MeV. | |||||||||||
| Problem: A proton has kinetic energy of K. What is its total energy (E)? | |||||||||||
| Constants and fixed variables:
Rest mass of a proton: mp = 938 MeV/c2 |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
| Hints:
Total energy is rest energy + kinetic energy. Rest energy is mc2 |
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range:
1430 to 1750 MeV Submit HW answers. |
|||||||||||
| Problem 10.9 | |||||||||||
| What you should learn: This is another kinematics problem. | |||||||||||
| Problem: A proton has kinetic energy of K. What is its momentum (p) in units of MeV/c? | |||||||||||
| Constants and fixed variables:
Rest mass of a proton: mp = 938 MeV/c2 |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
| Hints:
Use the relativistic energy momentum relationship E2 = (pc)2 +E02 |
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range:
p = 1085 to 1465 MeV/c Submit HW answers. |
|||||||||||
| Problem 10.10 | |||||||||||
| What you should learn: Kinematic, continued. | |||||||||||
| Problem: A proton has kinetic energy of K. What is β (beta) for the proton? | |||||||||||
| Constants and fixed variables:
Rest mass of a proton: mp = 938 MeV/c2 |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
| Hints:
The easy way to do this is to use β = pc / E. |
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range:
beta = 0.750 to 0.845 Submit HW answers. |
|||||||||||
| Problem 10.11 | |||||||||||
| What you should learn: We can apply the Lorentz transformations on energy-momentum four-vectors. | |||||||||||
| Problem: In its rest frame, a πo meson of each photon is decays into two photons that come off in the +y and –y directions. The energy of each gamma ray is half the rest energy of the πo. In this frame, the angle between the two gamma rays is 180°. What is the angle between the two gamma rays (DeltaTheta) in the lab frame where the πo is seen to move with a velocity β (beta) in the x direction? | |||||||||||
| Constants and fixed variables:
Rest energy of the πo : Epi = 135.0 MeV |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
| Hints:
A gamma ray is a photon, so its rest energy is 0 and its momentum and energy are related by the expression E = pc. The πo's energy is shared equally by the gamma rays. You know then energy and momentum of the gamma rays, so you can construct an energy-momentum four vector. Call the rest frame of the πo S' and the lab S. What were the Lorentz transformations? |
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range:
DeltaTheta = 60.0 to 85.0 degrees Submit HW answers. |
|||||||||||
| Problem 10.12 | |||||||||||
| What you should learn: This is an application of the velocity addition formula. | |||||||||||
| Problem: A pitcher standing on top of a train car throws a ball at a velocity βb (betab) with respect to the train. The train in turn moves at a velocity βt(betat) with respect to the ground. What is the velocity of the ball β (beta) with respect to the ground? | |||||||||||
| Constants and fixed variables:
Velocity of the ball with respect to the train: betab = 0.85 |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
| Hints:
How do I use the velocity addition formula? |
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range:
beta = 0.890 to 0.990 Submit HW answers. |
|||||||||||
| Problem 10.13 | |||||||||||
| What you should learn: The problems on Chapter 40 will be quite basic. The first two involve aspects of the photoelectric effect formula hf = Kmax + φ. The formula says that when photons of a given frequency are incident on a metal surface, the photon energy goes to two places: energy to pull the electron off the surface, and kinetic energy of the electron. The minimum kinetic energy to pull any electron off the surface is called the work function. When such an electron is removed, it has the maximum possible kinetic energy. | |||||||||||
| Problem: What is the maximum wavelength of light (lambda) that can cause photoelectron emission from a metal that has the work function listed below? | |||||||||||
| Constants and fixed variables:
Planck's constant: h = 4.136 x 10–15 eV s |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
| Hints:
What is the cutoff frequency? |
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range:
lambda = 400 to 600 nm Submit HW answers. |
|||||||||||
| Problem 10.14 | |||||||||||
| What you should learn: This problem also uses the photoelectric effect formula hf = Kmax + φ. | |||||||||||
| Problem: When ultraviolet light of wavelength λ (lambda) is incident on zinc metal, what is the maximum kinetic energy (Kmax) of photoelectrons emitted from the zinc surface? | |||||||||||
| Constants and fixed variables:
Planck's constant: h = 4.136 x 10–15 eV s Work function of zinc: phi = 4.31 eV |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range:
Kmax = 1.88 to 8.09 eV Submit HW answers. |
|||||||||||
| Problem 10.15 | |||||||||||
| What you should learn: The de Broglie equation relates wavelength and momentum: p = h / λ | |||||||||||
| Problem: What is the the kinetic energy (K) of a proton which has a de Broglie wavelength (lambda) given below? Note that the radius of a proton is about 0.8 fm where 1 fm =10–15 m. | |||||||||||
| Constants and fixed variables:
Planck's constant: h = 4.136 x 10–21 MeV s (Note these units are convenient!) Mass of a proton: mp = 938 MeV/c2 |
|||||||||||
Variables that must be changed with each
submission:
|
|||||||||||
| Hints:
The steps are these: (1) find p from the de Broglie relationship, (2) find pc, (3) find E from E2 = (pc)2 +E02, (4) find K from K = E – E0 I'm really confused with units... |
|||||||||||
Results of previous submissions:
|
|||||||||||
|
Answer range:
K = 120 to 280 MeV Submit HW answers. |
|||||||||||
| Problem 10.16 | |||||||||
| What you should learn: This problem makes use of the uncertainty relationship of position and momentum: ΔxΔpx ≥ ħ/2. In this problem, we look at the radial position and radial momentum, so this becomes: ΔrΔpr ≥ ħ/2. | |||||||||
| Problem: An electron in a hydrogen atom has a kinetic energy (K) of 13.6 eV. Based on this value, calculate the momentum of the electron. Making the rather bizarre assumption (that may be correct to an order of magnitude or so) that Δpr = pr/2, estimate Δr (Deltar) for the electron in the hydrogen atom. Note that the average electron radius of a hydrogen atom is 0.0529 nm. | |||||||||
| Constants and fixed variables:
Planck's constant: h = 4.136 x 10–15 eV s Rest energy of an electron: E0 = 511 keV |
|||||||||
| Hints:
Note that relativistic kinematics are not necessary. You may use K = p2/(2m) = (pc)2/(2E0) I'm still confused with units... |
|||||||||
Results of previous submissions:
|
|||||||||
|
Answer range:
0.0200 to 0.0800 nm Submit HW answers. |
|||||||||
| Problem 10.17 | |||||||||
| What you should learn: Another uncertainty relationship relates uncertainties in space and time: ΔEΔt ≥ ħ/2 | |||||||||
| Problem: A Δ++ is an elementary particle with a rest energy of 1232 MeV. It decays with an average lifetime of 6 x 10–24 s. Taking this to be Δt, find the uncertainty in a measurement of the particle's rest energy (DeltaE) | |||||||||
| Constants and fixed variables:
Planck's constant: h = 4.136 x 10–21 MeV s Average lifetime of the Δ++: tave = 6 x 10–24 s |
|||||||||
Results of previous submissions:
|
|||||||||
|
Answer range:
DeltaE = 10 to 90 MeV Submit HW answers. |
|||||||||