Nuclear Structure

Nuclear Structure

The Nucleus During the past several decades, we finally have reliable observations of the nucleus. Three techniques are used: • Probed with high energy electrons. • EMR of orbital electrons interacting with the nucleus. • (+) particles bounce of the nucleus and transfer energy exciting the nucleus. Gamma radiation is given off when the nucleus returns to ground state. The nucleus through these means has been seen as a shifting structure of rapidly moving parts.

Isotopes Dalton proposed that atoms of the same element were identical. He was wrong, there are different kinds of each of the elements (some have 6 or 7 variations). Rutherford and F. Soddy traced the decay of uranium and thorium, two radioactive elements, until they ended up as lead. Came up with more daughter products than were empty places in the periodic table. Elements in the decay series appeared that were chemically identical to other elements but had different radioactive characteristics. The lead present had a mass of only 206.05 compared to ordinary leads atomic mass of 207.20.

Isotope Defined Soddy named these variations of a given element isotopes from the Greek isos meaning the same and topos for place or having the same place on the periodic table. Confirmation came in 1913 by J.J. Thomson and F.W. Ashton, they were the first to separate the isotopes of an element. They put neon into positively charged tube and tried to measure its atomic mass, however the beam separated into two beams of neon not one. Neon is a mixture of two gases, one with an atomic mass of 20 the other 22.

Properties of Nuclei Some useful quantities when describing specific nuclei: • Atomic number, Z, which equals the number of protons. • Neutron number, N, which equals the number of neutrons. • Mass or Nucleon number,called a nuclide, A, which equals the number of nucleons (protons and neutrons).

Nuclide Designation Species of nucleus with a specific Z number and A number is called a nuclide. There are about 1500 nuclides. To differentiate we will use the following designation: AX Z N I.e.: What is the nuclide notation for the two isotopes of Neon? Why on the table is the Atomic mass of Ne given as 20.1797?

Atomic Mass Originally atomic masses were relative with hydrogen being 1. Today masses of atoms are specified in unified atomic mass units where a neutral carbon atom, C-12, is defined as having a mass of 12.000 000 u. 1 u = 1.660 540 x 10-27 kg = 931.494 MeV/c2

Line of Stability • There are 280 isotopes of naturally occurring stable elements and around 1200 are radioactive and transient. • Light nuclei are stable if N=Z, heavier nuclei need more neutrons to shield the electrostatic repulsion of added protons (line deviates up) • and above Z=83 repulsion cannot be shielded so there are no stable isotopes, all are radioactive.

Separating Isotopes Isotopes of the same element behave nearly identically chemically (electron configuration determines chemistry not nuclear structure) so, they cannot be separated chemically. i.e.: Three isotopes of Hydrogen Protium, Deuterium and Tritium World War II and heavy water (Norg). Mechanical means are used to separate isotopes, heavy water boils at 101.4 oC, centrifuges separate U-235 from U-238. i.e.: Why we went to war in Iraq????

Nuclear Size R. Hofstadter in the 1950’s found most nuclei are fairly spherical, with most being ellipsoidal, but some come flattened or pear shaped. He used an electron scattering technique to probe the nucleus. The nuclear radius, R, is from the center to the half charge density point. Rutherford approximated the size of the nucleus using conservation of energy. The size is in the range of femtometers, also called a fermi, or 10-15 (baseball at 2rd base of dome is like a nucleus in an atom).

Nuclear Radius R = RoA1/3 Ro is equal to about 1.2 fermi The size of a nucleus is dependent on the number of nucleons as a water drop is dependent on the number of water molecules.

Nuclear Spin Neutrons and protons are fermions with spins of 1/2 and angular momenta of 1/2h. The nucleus has energy levels just as the electron cloud does and the Exclusion Principle applies. Unpaired nucleons produce a spin and a possible magnetic moment about 0.15% of an electrons. I.e.: Nuclear magnetic resonance and Magnetic resonance imaging.

Nuclear Force In 1925 it was realized that a new force was needed to hold together the cluster of positively charged particles that must repel each other with a force of 50 N. A nuclear force must be present that binds neutrons and protons together to form nuclei, suggested Heisenberg in 1932.

The nuclear force is a short range proton to neutron force that imparts potential energies of 100 MeV and acts only at about 1 fm and is repulsive at less than 0.5 fm. The nuclear force is a form of the strong force, the most potent of all known forces. The strong force acting between two protons at 2 fm is 100 times stronger than the EM force and 1034 times stronger than gravity. It takes 8 MeV to remove a nucleon and 13.6 eV an electron.

Nuclear Stability Lighter elements are stable if the Z=N and tends to be more stable if the nuclei has and even number of neutrons and protons (alpha particle). There are only about 20 naturally occurring radioactive isotopes most are artificially induced in the laboratory.

The Shell Model Nuclides that have a magic number of nucleons and N equals to Z are stable and abundant. I.e.: 2, 8, 20, 28, 50, 82, 126 E.g.: Double magic nuclides (He, O, Ca, Pb) These numbers suggest the electron configuration of the Noble Gases.

An appropriate model for the nucleus is not a tightly packed cluster of cannon balls but instead a cloud of flying pairs of bees, each with an attraction only to its nearest neighbors. Each nucleon has an accompanying de Broglie wave that fits into the nucleus. Each nucleon has a quantum orbital, this is the shell model of the nucleus.

Each shell can hold two protons and two neutrons. The levels fill up from the bottom to the top and the highest occupied level is the Fermi level. When the energy levels were computed quantum mechanically it was found that the nucleus had a system of closely spaced subshells in groups making up major shells.

Maria Goeppert Mayer showed in 1947 that the magic numbers corresponded to the number of states in the major shell and was awarded the Nobel prize in 1963. I.e.: Tin has a nucleus with 50 neutrons and 50 protons and has a filled shell. Tin as a result is very abundant in nature and has 10 stable isotopes.

Line of Stability Nuclides off of the line of stability spontaneously decay changing neutrons to protons or visa versa becoming more tightly bound and stable. As Z increases the line shifts towards the N (y) axis, however there are no pea sized nuclei so eventually Coulombs force takes over and large nuclei decay.

Binding Energy In forming a deuteron, the ramming together of the neutron and proton releases a 2.224 MeV gamma ray photon. In forming, the deuteron has lost mass. This lost mass, the mass defect, is the energy that must be supplied to pull the two particles apart. 1 u = 931.494 MeV/c2 (E = mc2)

Nuclear Fusion Looking at the binding energy per nucleon curve if nuclides at either end alter their structure so as to move towards the middle energy could be liberated. If two hydrogen nuclides are fused the resulting nuclide would have greater binding energy per nucleon and less mass. The resulting mass defect appears as liberated energy in the process nuclear fusion.

Nuclear Fission Splitting a large nucleus, from the right side of the curve, into two smaller fragments, in the center of the curve, transforms mass to energy. The binding energy per nucleon of the fragments is higher and copious amounts of energy are released in this process of nuclear fission.

Nuclear v. Coal • 60 tons of fuel burned every 18 months. • 60 tons of spent fuel every 18 months (fills a 5’ x 5’ area). • No Greenhouse gases. • 3,000 tons of coal / day (120 tons / car, 120 cars / train). • 450,000 tons of ash every 18 months (fills a 20 city block landfill).

Nuclear Structure