2. The Discovery of the Nucleus Rutherford's alpha scattering experiments were the first experiments in which individual particles were systematically scattered and detected. This is now the standard operating procedure of particle physics.

3. Alpha particles from a radioactive source were allowed to strike a thin gold foil. Alpha particles produce a tiny, but visible flash of light when they strike a zinc sulfide screen. Surprisingly, alpha particles were found at large deflection angles and some were even found to be back-scattered.

4. As expected, most alpha particles were detected at very small scattering angles Alpha particles Thin gold foilSmall-angle scattering

5. To their great surprise, they found that some alpha particles (1 in 20 000) had very large scattering angles Alpha particles Thin gold foil Small-angle scattering Large-angle scattering

6. The results suggested that the positive (repulsive) charge must be concentrated at the centre of the atom. Most alpha particles do not pass close to this so pass undisturbed, only alpha particles passing very close to this small nucleus get repelled backwards (the nucleus must also be very massive for this to happen). Remember on this scale, if the nucleus is 2 cm wide, the atom would be 200 m wide!

7. Rutherford calculated theoretically the number of alpha particles that should be scattered at different angles (using Coulomb’s law). He found agreement with the experimental results if he assumed the atomic nucleus was confined to a diameter of about 10 -15 metres.

8. Using the idea of energy conservation, it is possible to calculate the closest an alpha particle could get to the nucleus during a head- on collision. Alpha particle nucleus

9. Initially, the alpha particle has kinetic energy = ½mu 2 K.E. = ½mu 2

10. At the point of closest approach, the particle reaches a distance b from the nucleus and comes momentarily to rest. b K.E. = 0

11. All the initial kinetic energy has been transformed to electrical potential energy. K.E. = 0 b

12. Using the formula for electrical potential energy which is derived from Coulomb’s law Kinetic energy lost = Electrical potential ½mu 2 = 1 q 1 q 2 4πε o b K.E. = 0 b

13. Rearranging we get; b = 1 q 1 q 2 4πε o ½mu 2 K.E. = 0 b

14. For an alpha particle, m = 6.7 x 10 -27 kg, q 1 = 2 x (1.6 x 10 -19 C) and u is around 2 x 10 7 m.s -1. If the foil is made of gold, q 2 is 79 x (1.6 x 10 -19 C). b = 1 q 1 q 2 4πε o ½mu 2 b = 1 x (2 x 1.6 x 10 -19 C) x (79 x 1.6 x 10 -19 C 4π x 8.854 x 10 -12 Fm -1 ½ x 6.7 x 10 -27 kg x (2 x 10 7 m.s -1 ) 2 b = 2.7 x 10 -14 m

15.  The Rutherford scattering experiment was conducted in the early 1900s although the discovery of the neutron was not made until 1932.  James Chadwick made the discovery having used results from experiments that showed neutral emissions from alpha particle bombardment.