STRUCTURE OF MATTER AND NUCLEAR TRAMSFORMATIOMS

1. STRUCTURE OF MATTER AND NUCLEAR TRAMSFORMATIOMS 物理師 蕭安成 參考資料：1.The Physics of Radiation Therapy 2. Principles and Practice of RADIATION THERAPY

2. STRUCTURE OF MATTER

3. Structure of matter---The atoms • All matter is composed of individual entities called elements. Each element is distinguishable from the others by the physical and chemical properties of its basic components --- the atom • Each atom consists of a small central core, the nucleus, where most of the atomic mass is located and a surrounding "cloud" of electrons moving in orbits around the nucleus.

4. Structure of matter---The atoms

5. Structure of matter---The atoms • The radius of the atom (radius of the electronic orbits) is approximately 10-10 m • The nucleus has a much smaller radius, namely, about 10-14 m • Thus, for a particle of size comparable to nuclear dimensions, it will be quite possible to penetrate several atoms of matter before a collision happens

6. Structure of matter---The atoms • it is important to keep track of those particles that have not interacted with the atoms • --- the primary beam • and those that have suffered collisions • --- the scattered beam

7. Structure of matter---The nucleus • The properties of atoms are derived from the constitution of • their nuclei and • the number and the organization of the orbital electrons • The nucleus contains protons and neutrons. Whereas protons are positively charged, neutrons have no charge

8. Structure of matter---The nucleus • The number of protons in the nucleus is equal to the number of electrons outside the nucleus, thus making the atom electrically neutral • Atomic nomenclature X : atomic symbol A : atomic mass number Z : atomic number ＊ A = Z + N (質量數=質子數+中子數)

9. Terms used to describe a nucleus Ei-Ef

10. 原子的分類 • 1.同位素(isotope)：相同質子數，不同中子數 • 2.同中素(isotone)：相同中子數，不同質子數 • 3.同重素(isobar) ：相同質量數，不同中子數， • 不同質子數 • 4.同質異能素(isomer)：相同核種，不同核子能階

11. Structure of matter---The nucleus • Certain combinations of neutrons and protons result in stable (nonradioactive) nuclides than others • stable elements in the low atomic number • --- N = Z • as Z increases beyond about 20, the N/P ratio for stable nuclei becomes > 1 and increases with Z

12. Structure of matter---The nucleus combinations of neutrons and protons result in stable

13. Atomic mass and energy units • atomic mass unit (amu) • defined as 1/12 of the mass of a nucleus • Thus the nucleus of is arbitrarily assigned the mass equal to 12 amu

14. Masses and charges of the main subatomic particles

15. Atomic mass and energy units • mass defect ( binding energy) • the mass of an atom is not exactly equal to the sum of the masses of constituent particles • a certain mass is destroyed and converted into energy that acts as a "glue" to keep the nucleons together

16. THE NUCLEUS Binding Energy

17. THE NUCLEUS • Binding Energy • Mass defect • The difference between the atomic weight and the sum of the weights of the parts = W - M W = ZmH + ( A-Z )mn M = atomic weight BE = ( W – M )amu × 931 MeV/amu

18. Atomic mass and energy units • The basic unit of energy is the joule (J) • equal to the work done when a force of 1 newton acts through a distance of 1 m • Energy unit in atomic and nuclear physics • electron volt ( eV ), • defined as the kinetic energy acquired by an electron in passing through a potential difference of 1 V

19. Atomic mass and energy units

20. Distribution of orbital electrons • Rutherford’s atomic model (1911)

21. Distribution of orbital electrons • Bohr atomic model (1913)

22. Bohr’s postulates • 1.An electron in an atom moves in a circular orbit about the nucleus under the influence of the Coulomb attraction between the electron and the nucleus, and obeying the law of classical mechanics. • 2.Instead of the infinity of orbits which would be possible in classical mechanics, it is only possible for an electron to move in an orbit for which its orbital angular momentum L is an integral multiple of Planck’s constant h, divided by 2π. (L=nħ)

23. 3.Despite the fact that it is constantly accelerating, an electron moving in such an allowed orbit does not radiate electromagnetic energy. Thus its total energy E remains constant. • 4.Electromagnetic radiation is emitted if an electron, initially moving in an orbit of total energy Ei, discontinuously changes its motion so that it moves in an orbit of total energy Ef. The frequency of the emitted radiation ν is equal to the quantity (Ei - Ef) devided by Planck’s constant h. (hν= Ei - Ef)

24. ATOMIC ENERGY LEVELS • Energy level diagram of the tungsten atom

25. NUCLEAR FORCES • There are four different forces in nature, in the order of their strengths : • strong nuclear force • electromagnetic force • weak nuclear force • gravitational force

26. NUCLEAR FORCES • strong nuclear force • responsible for holding the nucleons together in the nucleus • electromagnetic force • force between charged nucleons is quite strong, but it is repulsive and tends to disrupt the nucleus

27. NUCLEAR FORCES • weak nuclear force • appears in certain types of radioactive decay • gravitational force • in the nucleus is very weak and can be ignored

28. NUCLEAR FORCES • The strong nuclear force is a short-range force that comes into play when the distance between the nucleons becomes smaller than the nuclear diameter

29. NUCLEAR ENERGY LEVELS • The shell model of the nucleus assumes that the nucleons are arranged in shells, representing discrete energy states of the nucleus similar to the atomic energy levels • If energy is imparted to the nucleus, it may be raised to an excited state, and when it returns to a lower energy state , it will give off energy equal to the energy difference of the two states.

30. NUCLEAR ENERGY LEVELS • Sometimes the energy is radiated in steps, corresponding to the intermediate energy states, before the nucleus settles down to the stable or ground state

31. PARTICLE RADIATION • Radiation • emission and propagation of energy through space or a material medium • particle radiation • energy propagated by traveling corpuscles that have a definite rest mass and within limits have a definite momentum and defined position at any instant

32. PARTICLE RADIATION • Besides protons, neutrons, and electrons , many other atomic and subatomic particles have been discovered • Interact with matter and produce varying degrees of energy transfer to the medium

33. ELECTROMAGNETIC RADIATION • Wave Model • in terms of oscillating electric and magnetic fields • the mode of energy propagation for such phenomena as light waves, radio waves, microwaves, ultraviolet rays, g-rays, and x-rays • with the speed of light ( 3 x 108 m/sec in vacuum)

34. Electromagnetic radiation • A. Wave model • λ= C/ν

36. ELECTROMAGNETIC RADIATION • Quantum Model • wavelength becomes very small or the frequency becomes very large, the dominant behavior of electromagnetic radiations can only be explained by considering their particle or quantum nature

37. Electromagnetic radiation • B. Quantum model • E = hν= hc /λ • h : Planck’s constant (6.62×10-34 J‧sec) • c：3×108 m/sec • E (keV) = 1.24 /λ(nm)

38. NUCLEAR TRAMSFORMATIOMS

39. NUCLEAR TRAMSFORMATIOMS • RADIOACTIVITY • Radioactivity, first discovered by Henri Becquerel in 1896, is a phenomenon in which radiation is given off by the nuclei of the elements • This radiation can be in the form of particles , electromagnetic radiation, or both.

40. NUCLEAR TRAMSFORMATIOMS • RADIOACTIVITY • a radioactive nucleus has excess energy that is constantly redistributed among the nucleons by mutual collisions • As a matter of probability, one of the particles may gain enough energy to escape from the nucleus, thus enabling the nucleus to achieve a state of lower energy

41. NUCLEAR TRAMSFORMATIOMS • RADIOACTIVITY • Also, the emission of a particle may still leave the nucleus in an excited state. In that case, the nucleus will continue stepping down to the lower energy states by emitting particles or g rays until the stable or the ground state has been achieved.

42. NUCLEAR TRAMSFORMATIOMS • DECAY CONSTANT • where l is a constant of proportionality called the decay constant

43. NUCLEAR TRAMSFORMATIOMS • ACTIVITY • The rate of decay is referred to as the activity of a radioactive material • where A is the activity remaining at time t, and A0 is the original activity equal to lN0

44. NUCLEAR TRAMSFORMATIOMS • ACTIVITY • The unit of activity is the curie (Ci) : • 1 Ci = 3.7 x 1010 disintegrations/sec (dps) • The SI unit for activity is becquerel (Bq). The becquerel is a smaller but more basic unit than the curie and is defined as: • 1 Bq = l dps = 2.70 x 10-11 Ci

45. NUCLEAR TRAMSFORMATIOMS • THE HALF-LIFE AND THE MEAN LIFE • The term half-life ( T1/2 ) of a radioactive substance is defined as the time required for either the activity or the number of radioactive decay to half the initial value

46. NUCLEAR TRAMSFORMATIOMS • THE HALF-LIFE AND THE MEAN LIFE • The mean or average life is the average lifetime for the decay of radioactive atoms

47. NUCLEAR TRAMSFORMATIOMS • Example • 1. Calculate the number of atoms in 1g of 226Ra. • 2. What is the activity of 1 g of 226Ra (half-life = 1,622 years)?

48. NUCLEAR TRAMSFORMATIOMS • specific activity • The activity per unit mass of a radionuclide is termed • One reason why cobalt-60 is preferable to cesium-137, in spite of its lower half-life (5.26 years for 60Co versus 30.0 years for 137Cs) is its much higher specific activity

49. NUCLEAR TRAMSFORMATIOMS • Example • 1) Calculate the decay constant for cobalt-60 ( T1/2 = 5.26 years) in units of month-1. • 2) What will be the activity of a 5,000-Ci 60Co source after 4 years?

50. NUCLEAR TRAMSFORMATIOMS • THE HALF-LIFE AND THE MEAN LIFE • When will 5 mCi of 131I (T1/2 = 8.05 days) and 2 mCi of 32P (T1/2 = 14.3 days) have equal activities?