2) 35 points total] Consider an isolated neutral atom where the nucleus of the atom is
held fixed in place at the origin of some coordinate system. A plane, linearly polarized,
electromagnetic wave of angular frequency w impinges on the atom, exerting a force on the
electron cloud and causing it to oscillate. If r(t) denotes the center of mass of the electron
cloud with respect to the nucleus, the electron cloud moves under the influence of three
forces: (i) the force from the electromagnetic wave, (ii) a restoring force muzr pulling the
electron back to the nucleus, and (iii) a dissipative force -myv. Here m is the mass of
the electron cloud, -q its charge, and V = r the velocity of the electron cloud's center of
mass. You may approximate the electron cloud as a fixed rigid object moving in a classical
a) [20 pts] What is the total work done on the electron cloud by the electromagnetic wave
in one period of osciallation?
b) [10 pts] What is the total energy radiated away from the atom in electromagnetic radiation
in one period of oscillation?
c) [5 pts] If one wishes to interpret the dissipative force -myv as arising solely from the
radiated energy, what should be the value of the parameter Y? Do you see anything funny
about your answer? Is there a physical interpretation?
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.