IPhO2011_Th_Q3

Theoretical Competition: 12 July 2011 Question 3 Page 1 of 2 3. To Commemorate the Centenary of Rutherford’s Atomic Nucleus: the Scattering of an Ion by a Neutral Atom An ion of mass m , charge Q , is moving with an initial non-relativistic speed 0 v from a great distance towards the vicinity of a neutral atom of mass M m and of electrical polarisability . The impact parameter is b as shown in Figure 1. The atom is instantaneously polarised by the electric field E of the in-coming (approaching) ion. The resulting electric dipole moment of the atom is p E . Ignore any radiative losses in this problem. 3.1 Calculate the electric field intensity p E at a distance r from an ideal electric dipole p at the origin O along the direction of p in Figure 2. [1.2 points] 2 ,p aq r a 0 v Ion, m,Q b Atom, M  FIGURE 1 Ion, m,Q v r min r q q p a a O r FIGURE 2 Theoretical Competition: 12 July 2011 Question 3 Page 2 of 2 3.2 Find the expression for the force f acting on the ion due to the polarised atom. Show that this force is attractive regardless of the sign of the charge of the ion. [3.0 points] 3.3 What is the electric potential energy of the ion-atom interaction in terms of ,Q and r ? [0.9 points] 3.4 Find the expression for min r , the distance of the closest approach, as shown in Figure 1. [2.4 points] 3.5 If the impact parameter b is less than a critical value 0 b , the ion will descend along a spiral to the atom. In such a case, the ion will be neutralized, and the atom is, in turn, charged. This process is known as the “charge exchange” interaction. What is the cross sectional area 2 0 A b of this “charge exchange” collision of the atom as seen by the ion? [2.5 points]