[ 499 ] 



LVIII. Collision of ex. Particles with Light Atoms. By 0. G. 

 Darwin, M.A., .Reader in Mathematical Physics, University 

 of Manchester *. 



1. TX order to account for the fact that a particles arc 

 X sometimes deflected through large angles, Ruther- 

 ford f put forward the hypothesis that the positive electricity 

 in an atom carries its mass and is concentrated in an 

 excessively small region. The experiments of Geiger and 

 Marsden \ fully confirmed this theory, and they succeeded 

 in calculating the nuclear charge for a few substances. 

 They found it to be about half the atomic weight multiplied 

 by the electronic charge. Rutherford's calculations apply 

 to the case where an a particle collides with a heavy atom, 

 and, for simplicity, he assumes that the collision does not 

 set the atom in motion. His work requires modification to 

 include the fact that the nucleus of the atom is set in 

 motion, and it is this question that is treated in the present 

 paper. 



2. We first require the result of a single collision. In 

 finding this we may neglect the effects of the electrons in 

 the atom on account of their small mass. Let E M be the 

 charge and mass of the a particle, em of the nucleus. 

 Let V be the initial velocity of the a particle. The nucleus 

 starts from rest. There are four unknown quantities to be 

 determined by the collision, the velocity v and deflexion <fi of 

 the a particle, and the, velocity u and direction of motion of the 

 nucleus. The latter is in the plane determined by the initial 

 and final motions of the a particle. Let it be at angle 6 from 

 the initial direction. For convenience 6 is measured in the 

 opposite direction from <£. When one of these quantities 

 is known the other three can be determined by the principles 

 of momentum and energy. To find the frequency of a given 

 set of values of v &c. we must calculate the orbits. 



The equations of momentum and energy are : — 



MV = Mv cos '</> + mu cos #, "j 



=Mvsm0-??iwsin0, 5- (1) 



MV 2 = Mi> 2 + wu< 2 . J 



* Communicated by Sir Ernest Rutherford, F.K.S. 

 t Rutherford, Phil Mao-, vol. xxi. p. (369 (1911;. 

 $ Geiger and Marsden, Phil. Mag-. 



