Classical mechanics Lecture 9 of 16

October 26, 2011 by M. Fabbrichesi

M. Fabbrichesi , SISSA

In the first part of this lesson the professor continues the study of the two-body central force field problem, specifically the scattering in a central force field. He introduced the definition of the scattering cross-section in a given direction, and the scattering angle. The Impact parameter it is also introduced. The cross section it is calculated for the scattering Coulomb force field produced by a fixed charge –Ze on the incident particles having a charge –Z’e.

In the second part of this lesson the professor consider the problem of small oscillations in one dimension. He use the advantage that the solution to the harmonic oscillator problem is known to applied this solution to the problem of small oscillation around an equilibrium point of the total potential (a local minimum of the potential). He also consider the harmonic oscillator with an external force that depend on time of the form F = f Cos(?t+g) and the influence of a dissipative force that depend on the velocity of the particle F= -fv.

Compton Scattering experiment

<span>This video accompanies the Compton Scattering Experiment, providing students with an introduction to the theory, apparatus, and procedures.</span>

<span>When photons collide with electrons they give up energy, their wavelengths are increased, and they are scattered out of their original direction of travel. This phenomenon is the Compton Effect, described with an equation relating energy loss to scattering angle. In this experiment gamma rays from radioactive Americium are scattered by electrons in a target of aluminum. You will measure energy loss vs. angle to confirm the classical equation and the Klein-Nishina distribution. </span>

Rutherford's Alpha Scattering Experiment<span>Rutheford made a theoretical analysis of angles of scattering in accordance with Thomson's theory of atom and in accordance with his own theory. He assumed that atom consisted of positive charged nucleus and negative charged electrons circling around the nucleus. Then his theoretic calculations he compared with the experiment result. Alpha particles going through atom created in accordance with the "plum cake" model wouldn't be strong abberated because the electric field in that atom wouldn't be strong. In the model created by Rutheford the field is much stronger near to the nucleus, so some of alpha particles are much more abberated. The other going in the far distance to the nucleus are almost not at all abberated. The probability that any alpha particle will hit the nucleus is small but there is such a chance. The experiment showed that there are some not much abberated alpha particles but also some abberated of a very big angle (135-150 degree). That occurrence couldn't be explained by some small, added aberrations. Experimental data proved the "planetary" model of atom.</span>

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