Modern Physics for Scientists and Engineers
Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 4, Problem 13P

(a)

To determine

The average scattering angle of an alpha particle from a gold atom for the positively charged part of the Thomson model.

(b)

To determine

Compare this value with the scattering from the electrons.

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Problem 1. Consider the following 1-dimensional model of negative ion photodetachment. Let m be the electron mass, and assume the electron-atom potential energy is an attractive delta function, V(x)= - V. 8(x) with coefficient -Vo. (b) Now suppose a weak time-dependent perturbing electric field is applied along the x-axis, equal to E(t)= E, exp(-i w t) +c.c.; Find the energy-normalized final state eigenfunctions for the unperturbed Hamiltonian, having odd parity. (c) Using the Golden Rule, calculate the photodetachment rate as a function of (hbar w) in these units, i.e. calculate the probability per unit time in these units for the electron to escape to infinity. Glve an analytic expression and plot it from 0 final state energy up to an energy|10 E(ground) |, i.e. for frequencies that reach up to a final state energy that is 10 times the absolute value of the ground state energy. For making a plot of these numerical values, use V. =0.03 and a field strength amplitude Eo=0.0002.
A 3.0 MeV proton is incident on a potential energy barrier of thickness 10 fm and height 10 MeV.What are (a) the transmission coefficient T, (b) the kinetic energy Kt the proton will have on the other side of the barrier if it tunnels through the barrier, and (c) the kinetic energy Kr it will have if it reflects from the barrier? A 3.0 MeV deuteron (the same charge but twice the mass as a proton) is incident on the same barrier.What are (d) T, (e) Kt, and (f) Kr?
What do we need to do to average over Θ and ф to get the probability that the electron is inside a shell of radius r and thickness dr?
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