According to classical electromagnetic theory, an accelerating electron radiates energy at a rate where a is the acceleration, e is the electronic charge, c is the velocity of light, and K is a constant with value of 6 X 109 N m2 C-2. Suppose that the motion of the electron can be represented by the expression during one cycle of its motion.
(a) Show that the energy radiated during one cycle is .
(b) Recalling that the total energy of a harmonic oscillator is where m is the mass, show the the quality factor Q is .
(c) Using a typical value of for a visible photon, estimate the 'lifetime' of the radiating system (e = 1.6 X 10-19C, mass of an electron = 9.1 X 10-31kg).
According to classical electromagnetic theory, an accelerating electron radiates energy at a rate where a is...
3. The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Consider an electron trapped by a one-dimensional harmonic potential V(x)=-5 mo?x” (where m is the electron mass, o is a constant angular frequency). In this case, the Schrödinger equation takes the following form, **...
Review Constants Electromagnetic radiation is emitted by accelerating charges. The rate at which energy is emited from an accelerating charge that has charge 2 and acceleration a is given by = no where c is the speed of light. Part A If a proton with a kinetic energy of 5.1 MeV is traveling in a particle accelerator in a circular orbit with a radius of 0.720 m, what fraction of its energy does it radiate per second? IV AE +...