# Problems for Chapter 7

7-1. Use the "Rutherford Simulation" Mathematica notebook to simulate the results of Rutherford's experiment. Test the plum pudding model by modifying the potential to correspond to 11 positive charges of +7e each, placed at the origin and y = + and - .15, .35, .55, .75, .95 Angstroms along the y axis. Your alpha particle should have an initial velocity of 1.92 x 10 7 m / s, with impact parameters evenly spaced between .1 and 1 Angstrom, for a total of 10 simulations. The initial x coordinate should be -1 nm. Measure the scattering angles for each value of the impact parameter. Total simulation time should be 10 - 16 s.

Then test the solar system model by modifying the potential so that the locations of the positive charges is in Fermis instead of Angstroms. Use impact parameters ranging from 5 to 50 F, and an initial alpha particle x coordinate of - 100 F. Total simulation time should be 10 - 20 s.

7-2. Verify the Thorium series by checking the changes in A, N and Z with each decay.

7-3. Construct the 238U 92 series. It includes the following intermediate isotopes: 210Bi, 214Bi, 234Pa, 210Pb, 214Pb, 210Po, 214Po, 218Po, 226Ra, 222Rn, 230Th, 234Th, 210Tl and 234U. It ends with 206Pb. In all of the beta decays Z -> Z + 1. There is a branch in this series.

7-4. 100 mCi of 198Au (which has a half life of 2.7 days) is given to a patient for cancer therapy. If none is eliminated biologically, how much is left in two weeks?

If you would like to do these problems without a calculator, choose approximations such that t / t is an integer.

7-5. 1g of 131I is administered to a patient. If, after 24 days, there is 1/8 g left, what is its half life?

If you would like to do these problems without a calculator, choose approximations such that D 0 / D is a power of two.

7-7. Compute the effective half lives of the following:

Isotopecollects inphysical half lifebiological half life
14Cfat5570 years35 days
32Pbone14.3 days1000 days
35Sskin88 days23 days
45Cabone164 days1900 days
59Feblood45 days65 days
131Ithyroid8.08 days120 days

7-8. Draw the Feynman diagram for beta decay with positron emission. Why do you think this is a relatively rare process?

7-9. What is the gauge boson involved in alpha decay? in gamma decay?

7-10. Beta decay is usually written as

d -> u + e + anti-n e.

Which is correct? Are both? How could you tell?