22.101 Applied Nuclear Physics
(Fall 2004)
Due: Nov. 8, 2004
Problem Set No. 7
Problem 1
Give a derivation of the Rutherford scattering cross section
dσ 1 ⎛ zZe 2
=
⎜
2
dΩ 4 ⎜
⎝ mv
⎞
1
⎟⎟
4
⎠
sin (θ / 2)
Define all the quantities. State the physical meaning of this formula and its significance
regarding charged particle interactions with matter. (Note: You are expected to consult a
reference book for this problem. You should cite your reference and give enough details
in your derivation to demonstrate that you have worked through all the steps.)
Problem 2
The range-energy relationship for protons in air at 1 atm. and 15o C is given in Fig. 3.9 of
Meyerhof as well as in Lec14. From this curve deduce the energy loss (in Mev cm2/gm)
curve for the same energy range. Compare your result with Fig. 13.2 in the Lecture
Notes as well as analyze your result using the Bethe formula.
Problem 3
Estimate the contributions to the stopping power due to ionization and to radiation for the
passage of electrons with energy E in aluminum. Consider E = 0.1, 0.5, 1, 2, and 4 Mev.
Express your results in both Mev/mm and Mev cm2/gm, and compare your values with
those given in the Lec14. Discuss the significance of your results and the comparison.