The work of Thompson, Rutherford, and Millikan established the modern picture of the atom, consisting of a nucleus with Z protons and N neutrons. Z is the atomic number, while A = Z + N is the atomic mass number. The nucleus has a size equal to a few times 10^-15 m. The atom consists of the nucleus, which contains most of the mass and positive charge, surrounded by a cloud of Z electrons, which is negatively charged. Atoms are thus neutral. The electron cloud in an atom has a typical diameter of order 10^-10 m.
The Curies and Becquerel established that atoms were not always stable. Certain kinds of atomic nuclei can decay, as indicated in the text.
The scattering of a moving particle off of a stationary particle may be viewed quantum mechanically as a diffraction process. The diffraction pattern for a wave (belonging to the moving particle) off of the stationary particle looks much like the diffraction pattern for a wave impinging on a screen with a hole the diameter of the stationary particle. Thus, the spreading angle of the diffracted wave is related to the ratio of the wavelength to twice the diameter of the stationary particle as for the hole in the screen. Thus, the smaller the hole, the larger the spreading angle for a given incident particle wavelength.
Note that when we refer to the diameter of a particle, we mean the intrinsic diameter independent of quantum uncertainty effects, i. e., not the delta x from the uncertainty principle. Also, it is important that the intrinsic diameter of the moving particle be small compared to the diameter of the target particle -- otherwise the size of the moving particle must be included when computing the spreading angle.
Quantum calculations (which are too mathematically involved for us to do) yield probabilities for colliding particles of various types to scatter with a certain value of the momentum transfer q, P_point(q). (Don't confuse q with electric charge.) For small angle scattering the momentum transfer can be related to the scattering angle, theta = q/p, where p is the momentum of the moving particle. If the target particle has diameter d, the actual scattering probability is related to the point particle scattering probability by P_actual(q) = P_point(q)*F(q), where F(q) is called the form factor. If q/p = theta < alpha = lambda/2d, then F is approximately 1, whereas if theta > alpha, then F is approximately 0. By comparing actual scattering probabilities with point particle calculations for a range of momentum transfers, we can measure F(q) and see where its value drops off from near unity to near zero. From this we can estimate the size of the target particle, assuming that the moving particle has zero diameter. For a moving charged particle scattering off of a stationary charged particle, P_point is proportional to 1/q^4, but other types of scattering events have a different dependence of P_point on q.
The above technique can be used to find the diameter of target particles in all sorts of situations, from scattering of photons off of water droplets, to the Geiger-Marsden experiment, to Hofstadter's nuclear size measurements. Deep inelastic scattering of electrons from protons demonstrated that the proton had a diameter of order 10^-15 m, but that the proton itself was made up of a number of much smaller particles which Feynman called partons. These were later shown to be quarks, the fundamental building blocks of matter, and gluons, the intermediary particles of the strong force.
In order to understand the material in this chapter, it is important that you review the ideas and calculation techniques associated with relativistic energy and momentum conservation and virtual particles. In particular, forces act by the emission and absorption of intermediary particles which carry (among other things) energy and momentum. The total energy and momentum of particles coming into an emission or absorption event equals the total energy and momentum of particles going out. Sometimes particles involved in such events are forced by energy and momentum conservation to have a mass which is not equal to the real mass of the particle. This ``virtual mass'' can can be hidden by the uncertainty principle for only a limited spacetime interval or proper time. Particles with a virtual mass which is not equal to their real mass are called ``virtual particles'' because they have a very short range.
In doing the above calculations, it is convenient to represent momenta and mass in energy units, usually multiples of electron volts, such as KeV, MeV, GeV, and TeV. Thus, momentum in energy units is actually momentum times c, whereas mass in energy units is actually mass times c^2 -- i. e., rest energy. When this is done, all the c's vanish from equations like E^2 = p^2 + m^2.