3. A beam of protons, each with energy E = 20 MeV, falls on a potential step of 40 MeV. Graph the probability of finding protons at values of x> 0, for x = 0 at x = 5 fm (Assume | A|^2 = 1).

2. Protons with energy 1.0MeV scatter off a fixed spherical potential whose range is known to be a = 10-¹3 cm. The total elastic scattering cross section o and the differential cross section do/d are measured to a precision of about one percent. (a) Assuming that the energy is not near any resonance of the potential, show that the only phase shifts that can be reliably determined from the data are do and 6₁. (b) Given the experimental value o = = (10.5 ± 0.1) × 10-26 cm² and the values for do/dn listed in the table (one percent accuracy), determine do and 8₁. (Do not worry about the errors in your values for do or $₁. (deg) | dold_2 (10-26 cm²) O 1.232 45 90 135 180 1.103 0.823 0.585 0.499

An alpha particle reaches 28 fm in a gold foil experiment before it lost all of its kinetic energy. Estimate the kinetic energy of the alpha particle

Electrons are fired at a rectangular potential energy barrier, once every 149 ms. If the barrier is 2.55 nm thick and has a height that exceeds the energy of the incident electrons by exactly 712 meV, how long on average would you expect to wait for one electron to pass through the barrier? 8.57 x105 average wait: Incorrect