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Lesson6 - Lesson 06 Structure of the Nucleus MP200...

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Unformatted text preview: Lesson 06 Structure of the Nucleus MP200 Radiation Physics - 2010 Duke Medical Physics Graduate Program 1 Introduction In this lesson, we will study, • Basic Structure and the stability of the nucleus. • Binding Energy. • Liquid Drop Model (Semi-Empirical Mass Formula). • Shell Model. Nucleus: The nucleus is composed of two types of particles: • protons(p) and, • neutrons(n) These particles are collectively referred to as nucleons. Some of the basic properties of protons and neutrons are given in the following table. proton neutron Charge 1 . 6 × 10- 19 C Rest Mass 1 . 6726231 × 10- 27 kg 1 . 6749286 × 10- 27 kg 938 . 271998 MeV 939 . 565330 MeV 1 . 007277 a.m.u 1 . 008665 a.m.u Spin 1 2 1 2 • Coulomb force: Force between two point charges q 1 ,q 2 separated by a distance r : F = k q 1 q 2 r 2 where k = 8 . 98755 × 10 9 Nm 2 .C- 2 • Potential energy of charges: PE = k q 1 q 2 r • Coulomb force is a long range force. • When nucleons are close together (10- 15 m = 1 fm ), they exhibit a strong nuclear force. 2 • Nuclear forces: – attractive; – charge independent - acts on neutrons and protons, p-p, p-n, n-n; – act over short distances ≈ 10- 15 m ; – can overcome Coulomb forces; The figure shows the potential energy(PE ) of a proton as a function of distance r , from the center of the nucleus and its center. Figure 1: Forces between a proton and the nucleus From the figure, • PE-→ 0 as r-→ ∞ • when r gets closer, work done against the Coulomb force and PE increases. • when r < R radius of the nucleus, the nuclear force is attractive and PE becomes negative. • the proton is in a bound state in the nucleus. 3 The neutron is uncharged, and there is no Coulomb force acting on it. The figure shows the PE curve for a neutron and a nucleus. Figure 2: Forces between a neutron and the nucleus • The nucleus itself is a quantum mechanical system of bound particles. • Protons and neutrons are spin 1 2 particles, and they obey the Pauli exclusion principle. • The nucleus has a finite number of bound excited states, whereas the atom has an infinite number of bound excited states. Nuclear Notation Any nucleus X can be designated as, A Z X , where Z = Atomic number (number of protons in the nucleus) A = Mass number ( sum of number of protons and neutrons in the nucleus) N = number of neutrons Then, A = Z + N . A Z X is also called a nuclide. For example: 16 8 O , A = 16 ,Z = 8 ,N = 8 4 The nuclei are grouped into three categories: • Isotopes -Nuclei with same Z , examples: 16 8 O , 17 8 O • Isotones - Nuclei with same N , examples: 13 6 C , 14 7 N • Isobars - Nuclei with same A , examples: 14 6 C , 14 7 N There are 90 natural elements. Elements with Z ≥ 93 are man-made, except Tech- netium Tc = 43 and Promethium Z = 61....
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This note was uploaded on 10/30/2010 for the course MP 200 taught by Professor Guna during the Fall '10 term at Duke.

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Lesson6 - Lesson 06 Structure of the Nucleus MP200...

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