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lec24 - 24 Lecture 24 24.1 Nuclear Physics 24.1.1...

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24. Lecture 24 24.1 Nuclear Physics 24.1.1 Constituents and binding energy The atomic nucleus has a typical size of 10 15 m and therefore is much smaller than the typical atomic size 10 10 m . Using the uncertainty principle we expect then that the energies associated with the nucleus are much larger, of the order of MeV. The nucleus is composed of protons which are positively charged and neutrons which are electrically neutral. The total number of protons and neutrons is called the mass number and denoted by an A. The number of protons is called the atomic number and is denoted by a Z. The number of protons determines the charge and therefore the number of electrons of the corresponding atom and with that its chemical properties. Therefore Z gives the “name” to the nucleus. For example Carbon has six protons as depicted schematically in fig.126. However the number of neutrons in Carbon can vary. In the picture we depicted Carbon fourteen written usually as 14 6 C . For example there is also Carbon twelve (the most common one). These are called isotopes, they have the same of protons but di ff erent number of neutrons. The mass of the proton and neutron is approximately similar and equal to m p m n 1 . 6 × 10 27 Kg . Thus, the mass of the nucleus is given by the mass number A . One important fact is that if one measures the mass of the nucleus M nucleus with precision one finds what is called a mass defect: M = Zm p + ( A Z ) m n M nucleus (24.1) namely a di ff erence between the mass of a corresponding number of protons and neu- trons and the actual mass. To do this computation we should use more precise values for the mass of the proton and neutron: m p c 2 = 938 . 272 MeV m n c 2 = 939 . 566 MeV (24.2) where we used the more convenient mass equivalent values given by Einstein’s formula E = mc 2 . In fact Einstein formula gives us the clue to understand the mass defect. Since mass and energy are equivalent, when protons and neutrons form the nucleus, the total system has less energy and therefore less mass than the separate components. Therefore E b = Mc 2 is precisely the binding energy of the nucleus. If we want to split it back in its components this is the energy that must be supplied. This happens for any physical system but in the nucleus the binding energy is large enough that the mass defect can actually be measured. Although they form a bound state not all nuclei are stable. They can decay into other nuclei as discussed in the next section.

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lec24 - 24 Lecture 24 24.1 Nuclear Physics 24.1.1...

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