# Nuclear collisions and energy

Question: If two radioactive sources are places together, one emitting alpha radiation, the other emitting beta...why do the two emitting particles join (due to the two equally opposing charges) to form atoms of Helium? I know that alpha radiation can be expressed as He2+, so why do the electrons not begin to form very simple s orbitals around the He2+ nucleus? This would infer that the energy in the beta radiation is greater than that of both the second ionisation energy and the attraction of the forces held in the two opposing charges combined.

Lets look at the energies involved.
The alpha particles emitted from a radioactive source typically have energies of around 5 MeV and a speed of 5% c. The beta particles emitted may have energies around 0.5 to 2 MeV and speeds of 90%c.

In the helium atom the electrons in the s orbital have energies of 54 eV, so yes, the radiated beta particles have energies far in excess of the orbital electrons. This is probably to be expected because they come from energy transitions within the nucleus – in the case of the beta minus a neutron decays within the nucleus to form a beta particle (emitted) and a proton. Looking at it from a quark point of view beta minus emission means a down quark forming an up quark with the emission of an electron.

The particles will also surely only combine if they are able to interact with each other. Even with the numbers emitted chances of a collision are rare. They must get close enough for long enough for the electrostatic forces to draw them together. Remember also that we are dealing with particles that have wave properties and treating them as purely classical ball like objects may not always be sufficient.

On a very simple classical theory equating the centripetal force in the electron in orbit to the electrostatic attraction between a proton and an electron (this would be hydrogen of course) then the kinetic energy for the electron in orbit is almost 300 times less than that of a beta particle.