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

7-4. 100 mCi of ^{198}Au (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 ^{131}I 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.

7-6. ^{3}H (tritium) is one radioisotope used for whole body scans. Its physical half life is 12.3 years, and its biological half life is 19 days. What is its effective half life?

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

Isotope | collects in | physical half life | biological half life |
---|---|---|---|

^{14}C | fat | 5570 years | 35 days |

^{32}P | bone | 14.3 days | 1000 days |

^{35}S | skin | 88 days | 23 days |

^{45}Ca | bone | 164 days | 1900 days |

^{59}Fe | blood | 45 days | 65 days |

^{131}I | thyroid | 8.08 days | 120 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?

If you have stumbled on this page, and the equations look funny (or you just want to know where you are!), see the College Physics for Students of Biology and Chemistry home page.

©1996, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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