6805: 1094 Activities 5
Write your name and answers on this sheet and hand it in at the
Work with others at your table on these activities. Argue about
the answers but work efficiently!
Radiation Dose Calculation
Goal: Think about your yearly dose of radiation
- Follow the link to the ANS radiation dose calculator. Fill in the
blanks, googling as needed (e.g., elevation of Columbus) and note
the relative size of different sources of radiation.
What is your annual dose in mrem?
- What is this in μSv (as used in the xkcd chart; look
up as needed)? Are you measuring activity, the absorbed amount of
energy, or the biological effect?
- Describe where and how you would live if you wanted to minimize
your exposure to radiation. Would it be worth it? :)
Exploration: quantum weakly bound states
Goal: Explore the conditions for a weakly bound state in a square-well potential.
- From the 6805 home page, go to the simulations page and find
the PhET simulation "Quantum Bound States". Start it with the right triangle ("Play").
You may get some warning dialogs; agree to everything.
- The simulation calculations the bound-state solutions to the Schrodinger equation for a square
well for the selected energy level (which is in red).
Why are these called "bound states"?
Describe what happens to the probability density as you change which energy
level is selected. For which level are you most likely to find the particle
outside the well?
- Let's figure out why this setup is called a "particle in a box".
Using that the classical force is related to the potential by
F(x) = -dV(x)/dx, what is the force inside the box? What is the force
at the walls?
Now we'll look at the probability density as we change the height and width of the well.
You can change the height and width with your mouse or more precisely by pressing
"Configure Potential...", entering numbers in the boxes, and pressing close to
recalculate. Your mission, should you decide to accept it, is to find a combination
of a height and width such that
What height and width did you find?
- There are exactly two bound states.
- The probability of finding the particle in the excited state at position
1 nm is 1/2 the peak probability.
- How does the last exploration relate to halo nuclei?
Discussion questions based on Decadal Study figures
about nuclear astrophysics
Goal: Think about some of the physics illustrated by the nuclear astrophysics
figures in "Decadal survey slides on Astrophysics". Ask questions if you get
- Figure 2.15 on slide 5 shows experimental data for several neutron-rich
r-process nuclei. Based on the nuclei shown,
what determines the energy loss? [Hint: what are N and Z for these nuclei?]
Speculate on what determines the "time of flight" for a given energy loss.
Locate 78Ni on the r-process shown in
Figure 2.11 (slide 2). Why do you think this is called a "waiting
- A cartoon neutron star is shown in Figure 2.19 on slide 6. Using that
mass = density times volume, estimate roughly how much denser than our sun is this
neutron star [Hint: write this equation for the neutron star and for the
sun and divide them.]
- Figure 2.14 on slide 4 shows the cross section (proportional to
the probability) for the fusion of helium-3 and helium-4 as a function
of the relative energy of the two nuclei. Why does this probability become
extremely small at low relative energies (after all, the fusion process gives
[Hint: How is this like Rutherford's scattering experiment? (Side note:
this experiment was carried out by Rutherford's two graduate students,
one of whom was Geiger!)]
Neutron star from SEMF
Goal: Explore the implications for neutron stars
of the liquid drop SEMF as given on slide 2 of
the Nuclear Masses 1 slides ("in class" links for 04-Sep).
Fill in the details for the estimate of the minimum size of a neutron star on slide
- Why is gravity not usually included in the SEMF? Support
your answer with a (very rough) numerical estimate.
Why do we neglect Coulomb, surface, and pairing energies?
Why do we solve for B=0?
Carry out the calculation using
the constants in the Mathematica notebook semi_empirical_mass_formula.nb
we used in Activities 3. How do
your answers for A, R, and M compare to those on the slide?
6805: 1094 Activities 5.
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