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12.1 Discovery of the Neutron
12.2 Nuclear Properties
12.3 The Deuteron
12.4 Nuclear Forces
12.5 Nuclear Stability
12.6 Radioactive Decay
12.7 Alpha, Beta, and Gamma Decay
12.8 Radioactive Nuclides
The Atomic Nucleus
It is said that Cockroft and Walton were interested in raising the voltage of their equipment, its reliability, and so on, more and more, as so often happens when you are involved with technical problems, and that eventually Rutherford lost patience and said, “If you don’t put a scintillation screen in and look for alpha particles by the end of the week, I’ll sack the lot of you.” And they went and found them (the first nuclear transmutations).
- Sir Rudolf Peierls in Nuclear Physics in Retrospect
12.1: Discovery of the Neutron
Rutherford proposed the atomic structure with the massive nucleus in 1911. Scientists knew which particles compose the nucleus in 1932. Reasons why electrons cannot exist within the nucleus: 1) Nuclear size The uncertainty principle puts a lower limit on its kinetic energy that is much larger that any kinetic energy observed for an electron emitted from nuclei. 2) Nuclear spin If a deuteron consists of protons and electrons, the deuteron must contain 2 protons and 1 electron. A nucleus composed of 3 fermions must result in a half-integral spin. But it has been measured to be 1.
Discovery of the Neutron
The electromagnetic radiation (photons) are called gamma rays which have energies on the order of MeV. Curie and Joliot performed several measurements to study penetrating high-energy gamma rays. In 1932 Chadwick proposed that the new radiation produced by α + Be consisted of neutrons. His experimental data estimated the neutron’s mass as somewhere between 1.005 u and 1.008 u, not far from the modern value of 1.0087 u.
12.2: Nuclear Properties
The nuclear charge is + e times the number ( Z ) of protons. Hydrogen’s isotopes : Deuterium : Heavy hydrogen. Has a neutron as well as a proton in its nucleus. Tritium : Has two neutrons and one proton. The nuclei of the deuterium and tritium atoms are called deuterons and tritons. Atoms with the same Z , but different mass number A , are called isotopes.
Atomic masses are denoted by the symbol u. 1 u = 1.66054 × 10 − 27 kg = 931.49 MeV/ c 2 Both neutrons and protons, collectively called nucleons , are constructed of other particles called quarks.
Nuclear Properties
Sizes and Shapes of Nuclei
Rutherford concluded that the range of the nuclear force must be less than about 10 − 14 m. Assume that nuclei are spheres of radius R. Particles (electrons, protons, neutrons, and alphas) scatter when projected close to the nucleus. It is not obvious whether the maximum interaction distance refers to the nuclear size ( matter radius ), or whether the nuclear force extends beyond the nuclear matter ( force radius ). The nuclear force is often called the strong force. Nuclear force radius ≈ mass radius ≈ charge radius
Sizes and Shapes of Nuclei
If we approximate the nuclear shape as a sphere, The nuclear mass density is 2.3 × 10 17 kg / m 3 . The shape of the Fermi distribution
The proton’s intrinsic magnetic moment points in the same direction as its intrinsic spin angular momentum. Nuclear magnetic moments are measured in units of the nuclear magneton μ N. The divisor in calculating μ N is the proton mass mp , which makes the nuclear magneton some 1800 times smaller than the Bohr magneton. The proton magnetic moment is μp = 2.79μ N. The magnetic moment of the electron is μe = −1.00116 μ B. The neutron magnetic moment is μn = −1.91 μ N. The nonzero neutron magnetic moment implies that the neutron has negative and positive internal charge components at different radii. Complex internal charge distribution.
Intrinsic Magnetic Moment
The Deuteron
md + me is the atomic deuterium mass M ( 2 H) and mp + me is the atomic hydrogen mass. Thus Eq.(12.7) becomes Because the electron masses cancel in almost all nuclear-mass difference calculations, we use atomic masses rather than nuclear masses. Convert this to energy using u = 931.5 MeV / c 2 . Even for heavier nuclei we neglect the electron binding energies (13.6 eV) because the nuclear binding energy (2.2 MeV) is almost one million times greater.
The Deuteron
The binding energy of any nucleus = the energy required to separate the nucleus into free neutrons and protons. Experimental Determination of Nuclear Binding Energies Check the 2.22-MeV binding energy by using a nuclear reaction. We scatter gamma rays from deuteron gas and look for the breakup of a deuteron into a neutron and a proton: This nuclear reaction is called photodisintegration or a photonuclear reaction. The mass-energy relation is where hf is the incident photon energy. Kn and Kp are the neutron and proton kinetic energies.
12.4: Nuclear Forces
The angular distribution of neutron classically scattered by protons. Neutron + proton ( np ) and proton + proton ( pp ) elastic. The nuclear potential
Nuclear Forces
The internucleon potential has a “hard core” that prevents the nucleons from approaching each other closer than about 0.4 fm. The proton has charge radius up to 1 fm. Two nucleons within about 2 fm of each other feel an attractive force. The nuclear force ( short range ): It falls to zero so abruptly with interparticle separation. stable. The interior nucleons are completely surrounded by other nucleons with which they interact. The only difference between the np and pp potentials is the Coulomb potential shown for r ≥ 3 fm for the pp force.
12.5: Nuclear Stability
The binding energy of a nucleus against dissociation into any other possible combination of nucleons. Ex. nuclei R and S. Proton (or neutron) separation energy : The energy required to remove one proton (or neutron) from a nuclide. All stable and unstable nuclei that are long-lived enough to be observed.
Nuclear Stability
The line representing the stable nuclides is the line of stability. It appears that for A ≤ 40 , nature prefers the number of protons and neutrons in the nucleus to be about the same Z ≈ N. However, for A ≥ 40, there is a decided preference for N > Z because the nuclear force is independent of whether the particles are nn , np , or pp. As the number of protons increases, the Coulomb force between all the protons becomes stronger until it eventually affects the binding significantly. The work required to bring the charge inside the sphere from infinity is
