Lecture 24-1 The Hydrogen Atom According to the Uncertainty Principle, we cannot know both the position and momentum of any particle precisely at the same time. The electron in a hydrogen atom cannot orbit the nucleus in a circular orbit or any other kind of orbit; otherwise, both the position and momentum would be exactly known! Instead, the probability to find an electron is given by a 3D standing wave. Standing waves of different shapes for different states (and different energy levels). Ground state wave function
Lecture 24-2 Quantum Numbers The Bohr model quantum number which specifies the energy level turns out to be only one of several such quantum numbers that specifies the quantum state of the hydrogen atom: E n 13.6eV n 2 n 1,2,3,... principal quantum number There are other quantum numbers: l for L m l for L z s for s m s for s z orbital angular momentum the z-component of L spin angular momentum the z-component of s
Lecture 24-3 Nuclear Structure A nucleus is at least O(10 3 ) times more massive than an electron and is positively charged. A nucleus is actually NOT a point charge. It has a size that is O(1) fm (1 femtometer = 10-15 m). A nucleus is composed of protons and electrically neutral neutrons (i.e., nucleons). The number of protons, Z, is called the atomic number. The atomic number determines what type of element the atom is. A Z N Atomic mass number (or nucleon number) Number of neutrons
Lecture 24-4 Nuclear Structure Each element has a fixed number Z of protons, but the number of neutrons, N, can vary. These are called isotopes. A Z N Shorthand notation for isotopes: e.g., Oxygen 18 has 8 protons (because it is Oxygen), the atomic mass number 18, and the neutron number N=10 (because A=Z+N). A 18 8O Z Element Symbol Other examples: O, H, H, C, C 16 2 3 12 14 8 1 1 6 6 Some isotopes are stable, others are unstable and radioactive.
Lecture 24-5 Physics 219 Question 1 April 11, 2012. Isotopes of an element have the same number of but different number of. Fill the blanks with the correct particle names. A. electrons, protons B. neutrons, electrons C. protons, electrons D. neutrons, protons E. protons, neutrons
(*for two u quarks separated by 0.03 fm) Lecture 24-6 The Strong Force How are the protons (positive charge) and neutrons (neutral) held together in the nucleus? The answer is: by the strong force! The strong force is one of nature s 4 fundamental forces: Force Relative Strength* Range (m) Strong 1 10-15 Electromagnetic 10-2 Weak 10-6 10-17 Gravitational 10-43 The strong force holds a nucleus of multiple nucleons together as well as the individual nucleons by themselves. It competes with the electromagnetic repulsion among the protons.
Lecture 24-7 How large is a nucleus? Mass of Nuclei 1 atomic mass unit (u) = 1/12 of a neutral 12 C atom = 1.660539 x 10-27 kg Mass of a nucleon is approximately 1 u. That of an electron is approximately 0.00055 u. 1 mole of nucleons 6.02 x 10 23 u 10-3 kg = 1 g Size of Nuclei A Mass M volume V. So the density ρ is roughly independent of A. r r A 0 1/3 where 4 3 3 M r A 15 r0 1.2 10 m 1.2 fm fermi
Lecture 24-8 Binding Energy The mass of a nucleus is less than the sum of the masses of its parts! The mass defect, m, is the difference between the sum of the masses of the protons and neutrons, and the mass of the nucleus. m m(z protons N neutrons) m(nucleus) The binding energy of the nucleus EB m c 2 represents the energy required to separate the nucleus into individual nucleons. Generally, a binding energy is the energy required to separate a composite object into its constituent parts.
Lecture 24-9 How to find the binding energy m c m( Z protons N neutrons) m( nucleus) 2 2 c Mass of neutral atoms can be found in a table (e.g., NIST table posted on the course home page under Lectures). (Relative Atomic Weight in that table gives the atomic mass in u.) To find the mass of the nucleus, you must subtract the mass of the electrons contained within the neutral atom. (But what about the binding due to electromagnetic forces?) Example: 14 N nuclear binding energy?
Lecture 24-10 Example: 14 N nuclear binding energy? Neutral 14 N atom = 14.003074 u Mass of 7 electrons = 7 x m e = 7 x 0.0005486 u = 0.003840 u So 14 N nuclear mass = 13.999234 u Mass of 7 individual protons and 7 neutrons = 7 x m p + 7 x m n = 7 x 1.0072765 u + 7 x 1.0086649 u = 14.111589 u So the mass defect m = (14.111589 u) (13.999234 u) = 0.112355 u 2 EB m c 0.112355u 931.494 MeV / u 104.659 MeV c 2
Lecture 24-11 Nuclear Energy Levels The nucleus has energy levels just like the electrons in an atom. Protons and neutrons have separate energy levels. They obey the exclusion principle and two of them can occupy each level (one with spin up, one with spin down), like the electron. The energy is lowest with 6 protons and 6 neutrons, if A=Z+N=12.
Lecture 24-12 Physics 219 Question 2 April 11, 2012. Which description of the isotope 14 6? is correct? A. O (oxygen) with 8 protons and 6 neutrons B. C (carbon) with 6 protons and 8 neutrons C. Si (silicon) with 14 protons and 6 neutrons D. Ca (calcium) with 6 protons and 20 neutrons E. C (carbon) with 6 protons and 14 neutrons Atomic numbers of the above elements are: carbon 6, oxygen 8, silicon 14, calcium 20.
Lecture 24-13 Composition of Nuclei For smaller nuclides, N=Z is most stable. For bigger nuclides, the Coulomb repulsion of protons favor more neutrons than protons to be in the nucleus. Some nuclides are unusually stable: e.g., He, O, Ca, Ca, Pb 4 16 40 48 208 2 8 20 20 82
tighter Lecture 24-14 Binding Energy Per Nucleon Curve For smaller nuclides, binding gets tighter as the mass number increases (as the nucleons gain more neighbors to bind with). For larger nuclides, the Coulomb repulsion among the protons begins to make them less tightly bound. The maximum binding occurs around A=60.
Lecture 24-15 Radioactive Decay There are stable nuclides and unstable ones. An unstable nuclide decays by emitting particles and/or radiation. radioactive decay Most (~80%) of nuclides are radioactive, including all those with Z > 83. There are 3 types of decays: alpha, beta, and gamma decays Radioactive decays occur with a probability which depends on the isotope and the type of decay. Decays are random events, i.e., they don t occur at predicted times.
Lecture 24-16 Conservation Laws in Radioactive Decay 1. The number of nucleons must remain the same (though the types may change). 2. The total electric charge must remain the same. 3. The total energy must remain the same. Energy here includes both the rest mass energy and the kinetic energy. 2 E 0 mc The sum of the masses of the decay products must be less than the mass of the original nucleus in order for a spontaneous decay from the nucleus at rest to be possible. Disintegration energy is the name for that part of rest mass energy of the original nucleus that is converted into other forms of energy (such as kinetic energy or EM radiation).