• Structure of matter

There is an immense abundance of varieties of matter in the macroscopic world. How do we understand it, how did all this come about?

Matter comes in the form of solids, liquids, vapors, all made of molecules, which are made of atoms (see lectures 7,10). The quest for understanding the structure of matter dates back for at least a couple of millenia. The alchemists' efforts during the Middle Ages resulted in the science of chemistry which in turn led to the idea of the "elements", that is the atoms. Although it was thought at first that atoms are indivisible, we now know that there are many more layers of structure:
 

• layers of matter and their sizes: molecules, atoms, nuclei, protons & neutrons and other "elementary" particles, quarks & leptons,  ...  (strings?)
• In the subatomic world the laws of motion and the types of forces that govern Nature deviate from Newton's laws. Now we need Quantum Mechanics and Relativity, and three more forces in addition to Gravity (Electro-magnetic, Strong, Weak). QM applies to microscopic objects of subatomic size, Relativity applies to fast moving objects. The limit of QM for macroscopic objects and the limit of relativity for slow moving objects are in agreement with Newton's laws of motion.

 
• To get a rough big picture on how our understanding of matter evolved, see the video: Cosmic Alchemy (Stephen Hawking's Universe), starting with Mendeleev to the end. Read the narrative.
• Mendeleev and periodic table (electronic structure of the atom ---> chemistry).
• Pierre and Marie Curie : Radiation, radioactivity (rays: alpha= ⁴He, beta=electron, gamma=photon). See discovery of radioactivity.
• Rutherford : Transmutation of elements, bombarding the atom

---> most of the weight is at the center, a nucleus!
---> transformation of mass into energy E=mc² (Einstein) - occurs in FISSION, FUSION.
• Dirac: There must be antimatter. Matter and antimatter can annihilate into vacuum and can be created from vacuum  ( E=mc² again). Anderson finds antimatter (the positron = anti-electron)
• Cosmic rays and bubble chamber
• Particle accelerators and creation + annihilation of matter and antimatter
• At the Big Bang matter+antimatter is created from energy (E=mc² ),  asymmetry develops in favor of matter due to assymmetric interactions. Evolution continues to the present universe, as the following structures of matter form at various stages:  particles (1 second), nuclei (1-3 minutes), neutral atoms (300,000 years), then gravitational attraction dominates and formation of galaxies & stars occur (1 billions yrs) - heavier elements up to iron form at cores of stars, even heavier elements form at supernovae - solar-planetary systems develop, finally life and matter as we know it (15-20 billion years).

 
• The nucleus  (see Hewitt Ch.33, 34).  The size of the nucleus is about 10^-14  - 10^-15  meters, this is about 10,000 to 100,000 times smaller than the overall size of the atom. (See The ABC of Nuclear Physics and The Atomic Nucleus ).

• A nucleus contains positively charged protons and neutral neutrons. The charge of a proton (+) is exactly the opposite of the charge of an electron (-). Neutrons have no electric charge (0). Protons repel each other under electrostatic forces, but the attractive strong force is greater, and it binds the protons as well as the neutrons.
• Protons and neutrons weigh about 2000 times an electron. Therefore the mass of the atom is concentrated mostly at the nucleus (Rutherford's discovery).
• The number of protons (equal to the number of electrons of a neutral atom) in a nucleus is called the atomic number Z. The nucleus is also distinguished by its neutron number N. The total number of protons + neutrons is the atomic mass A. An element in the periodic table is labelled by a large number A and a small number Z, sometimes the third number  N is included (then ).







The number at the top left is the  # protons + # neutrons (A=Z+N) and the small number at bottom left is the number of protons. For example Oxygen ¹⁶₈O ,  Hydrogen  ¹₁H ,  Hydrogen isotopes  ²₁H ,  ³₁H , etc. This means ¹₁H has 1 proton and zero neutrons, and O has 8 protons and 8 neutrons, etc.

There exist many isotopes of the same chemical elements. These contain nuclei all with the same number of protons Z, but different numbers of neutrons N. For example heavy hydrogen isotopes occur in heavy water H₂O.
 

• Due to the Weak force, neutrons decay over time and they emit a proton (+ charge), an electron (- charge) and a anti-neutrino (0 charge)
¹₀n  ---> ¹₁p  +  ⁰_-1e  +  ⁰₀n




Electric charge is conserved in any reaction. Total charge before the reaction is the same as the total charge after the reaction (like energy or momentum or angular momentum). Also total number of protons+neutrons A is conserved in any reaction. The atomic numbers of e  or n  are both 0.

Total energy, including the mass equivalent (E=mc² ) is also conserved in any reaction. In neutron decay, the mass of n is larger than the total mass of (p,e, n) combined. The balance of mass is converted to kinetic energy of the products of the decay (E=mc² ).
 

• Nuclear reactions: see  The ABC of Nuclear Physics

• Alpha, beta, gamma decays. Nuclei have limited lifetime as measured by their half-life.

 

In alpha decay, the atomic number changes, so the original (or parent) atoms and the decay-product (or daughter) atoms are different elements and therefore have different chemical properties. This occurs mainly due to the electric repulsion among protons.

In beta decay, an excess neutron decays into a proton, an electron, and an antineutrino. The product nucleus is more stable. The number of protons change, therefore the product is a new chemical element.

In gamma decay, depicted in Fig. 3-6, a nucleus changes from a higher energy state to a lower energy state through the emission of electromagnetic radiation (photons). The number of protons (and neutrons) in the nucleus does not change in this process, so the parent and daughter atoms are the same chemical element.

• Fission, and Fusion reactions produce large quantities of nuclear energy.

 

 

There is natural fission and induced fission. In nuclear reactors fission is induced via energetic neutrons.  Some relevant nuclear reactions that lead to chain reactions can be written as follows: 235U + 1n --->  fission products + 2 to 4 neutrons + energy (~200 MeV) (1) 238U + 1n --->   239U + gamma rays (2) 239U   --->   239Np ---> 239Pu (a series of beta decays). (3) The "big three" readily fissionable nuclei are: 235U, 239Pu, and 233U.

To obtain fusion a lot of energy has to be pumped in to squeeze nuclei together to overcome the electric repulsion of charged protons.  Nuclear fusion is the source of energy in the sun and stars where high temperatures and densities allow the positively-charged nuclei to get close enough to each other for the (attractive) nuclear force to overcome the (repulsive) electrical force and allow fusion to occur. The basic reaction chain in the sun (86% of the  time) is the fusion sequence:                                1H + 1H ---> 2H + e+ + n e,                                2H + 1H --- > 3He + gamma,                                3He + 3He ---> 4He + 1H + 1H. Nuclear fusion reactors, if they can be made to work, promise virtually unlimited power for the indefinite future. This is because the fuel, isotopes of hydrogen, are essentially unlimited on Earth. Efforts to control the fusion process and harness it to produce power have been underway in the United States and abroad for more than forty years. Fusion plays an important role in the production of the elements during the evolution of the universe.


 
 
• Cosmic rays are showers of particles coming from all over the universe. They play a role in mutation and biological evolution.
• Radioactivity in Nature.
• There are numerous applications of nuclear science, from smoke detectors to medicine. One of them is extracting the  energy from the nucleus.

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