# 6805: 1094 Activities 5

Write your name and answers on this sheet and hand it in at the end.

1. 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?

2. 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?

3. 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.

1. 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.
2. 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"?

3. 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?

4. 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?

5. 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
1. There are exactly two bound states.
2. The probability of finding the particle in the excited state at position 1 nm is 1/2 the peak probability.
What height and width did you find?

6. How does the last exploration relate to halo nuclei?

Goal: Think about some of the physics illustrated by the nuclear astrophysics figures in "Decadal survey slides on Astrophysics". Ask questions if you get stuck!!

1. 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 point" nucleus?

2. 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.]

3. 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 off energy!)? [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 10.

1. Why is gravity not usually included in the SEMF? Support your answer with a (very rough) numerical estimate.

2. Why do we neglect Coulomb, surface, and pairing energies?

3. Why do we solve for B=0?

4. 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?