l'.»li>] on Atomic Projectiles and their Collisions 56^ 



be simply illustrated by impact of two perfectly elastic balls of masses 

 proportional to the masses of the atoms. 



While the velocities of the recoil atoms can be easily calculated, 

 the distance which they travel before being brought to rest depends 

 on both the mass and the charge carried by the recoil atom. Experi- 

 ment shows that the range of H atoms, like the range of a-particles, 

 varies nearly as the cube of their initial velocity. .If the H atom 

 carries a single charge, Darwin showed that its range should be about 

 four times the range of the a-particle. This has been confirmed by 

 experiment. Generally, it can be shown that the range of a charged 

 atom carrying a single charge is nm^'R, where ))i is the atomic weight, 

 and u the ratio of the velocity of the recoil atom to that of the 

 a-particle, and R the range of the a-particle before collision. In 

 comparison of theory with experiment, the results agree better if the 

 index is taken as 2*9 instead of 3. If, however, the recoil atom 

 carries a double charge after a collision, it is to be expected that its 

 range would only be about one-quarter of the corresponding range 

 if it carried a single charge. It follows that we cannot expect to 

 detect the presence of any recoil atom carrying two charges beyond 

 the range of the a-particle, but we can calculate that any recoil 

 atom, of mass not greater than oxygen and carrying a single charge^ 

 should be detected beyond the range of the a-particle. For example, 

 for a single charge the recoil atoms of hydrogen and helium should 

 travel 4 R, lithium 2 • 8 R, carbon 1 * 6 R, nitrogen 1 • o R, and oxygen 

 1 • 1 R, where R is the range of the incident a-particles. We thus see 

 that it should be possible to detect the presence of such singly 

 charged atoms, if they exist, after completely stopping the a-particles 

 by a suitable thickness of absorbing material. This is a great 

 advantage, for the number of such swift recoil atoms is minute in 

 comparison with the number of a-particles, and we could not hope 

 to detect them in the presence of the much more numerous a-particles. 



In order to calculate the number of recoil atoms scattered through 

 any given angle from the direction of flight of the a-particles, it is 

 necessary, in addition, to make assumptions as to the constitution of 

 the atoms and as to the nature and magnitude of the forces involved 

 in the collision. Consider, for example, the case of a collision of an 

 a-particle with an atom of gold of nuclear charge 79. Assuming 

 that the nucleus of the a-particle and that of the gold atom behave 

 like point charges, repelling according to the inverse square law, it 

 can readily be calculated that, for direct collision, the a-particle from 

 radium 0, which is turned through an angle of 180", approaches 

 within a distance D = 3'6 x 10"^^ cm. of the centre of the gold 

 nucleus. This is the closest possible distance of approach of the 

 a-particle, and the distance increases for oblique colhsions. For 

 example, when the a-particle is scattered through an angle of 150°, 

 90°, 30°, 10°, 5°, the closest distances of approach are 1*01, 1*2, 2*4, 

 6 '2, 12 D respectively. 



2 Q 2 



