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Introduction to

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Introduction to

  1. 1. Introduction to Nuclear Physics CHAPTER 2
  2. 2. Contents  1- Introduction  4- a) Alpha , b) Beta and c) Gamma Decay  2- Some Nucleus Properties  3- Radioactive Decay  5- Natural radioactive decay series  6- Induced Nuclear reactions (nuclear fission and nuclear fusion)  7- Radioactive Dating  8- Measuring Radiation Dosage
  3. 3. 1/ INTRODUCTION:  By accident, becquerel discovered that uranium salts spontaneously emit a penetrating radiation that can be registered on a photographic plate.  Rutherford showed that the radiation had three types: Alpha, Beta and Gamma 1896
  4. 4. 1/ INTRODUCTION:  Rutherford fired a beam of alpha particles at foil of gold leaf  The results of the experiment are : 1) Most of alpha particles Passed without deflection. 2) some of alpha particles are deflected at small angles. 3) few of alpha particles are deflected at large angles. 1911 Rutherford scattering experiment
  5. 5. 1/ INTRODUCTION:  The conclusions of the experiment are : 1) Most of the space inside the atom is empty 2) The positive charge of the atom occupies very little space 3) That all the positive charge and mass of the atom were concentrated in a very small volume within the atom 1911 Rutherford scattering experiment
  6. 6. 1/ INTRODUCTION:  Rutherford's Nuclear Model Of Atom : 1) There is a positively charged Centre in an atom called the nucleus. Nearly all the mass of an atom resides in the nucleus. 2) The electrons revolve around the nucleus in well- defined orbits. 3) The size of the nucleus is very small as compared to the size of the atom.  Nucleus of an atom is positively charged ,very dense , hard and very small 1911 Rutherford scattering experiment
  7. 7. 2/ Some Nuclear Properties The materials are made of atoms The atom is composed of a nucleus and electrons orbiting around the nucleus. The nucleus is a very small dense object made up of two kinds of nucleons [Protons (p), Neutrons (n)]. Atom Nucleus Protons Neutrons Electrons
  8. 8. 2/ Some Nuclear Properties 𝑚𝑝 ≅ 𝑚𝑛 𝑚𝑝 ≅ 1840 𝑚𝑒 Number of protons is equal to the number of the electrons in the neutral atom.
  9. 9. 2/ Some Nuclear Properties Numbers that characterize the nucleus Z, N and A Z = Atomic number N = Neutron number Number of nucleons in the nucleus. Number of protons in the nucleus. The number of neutrons in the nucleus. A = Mass number 𝐴 = 𝑁 + 𝑍 a) Nuclear Terminology
  10. 10. 2/ Some Nuclear Properties Example Find the number of protons, neutrons and electrons a) Nuclear Terminology Representation of a nucleus
  11. 11. 2/ Some Nuclear Properties Examples a) Nuclear Terminology 1) Isotopes The atoms of an element which have the same number of protons (𝑍1 = 𝑍2) and different number of neutrons are called Isotopes.
  12. 12. 2/ Some Nuclear Properties Example a) Nuclear Terminology 2) Isobars The atoms which have the same mass number (𝐴1 = 𝐴2) but different atomic numbers are called isobars.
  13. 13. 2/ Some Nuclear Properties Example a) Nuclear Terminology 3) Isotones Atoms which have different atomic number (𝑍1 ≠ 𝑍2) and different atomic masses (𝐴1 ≠ 𝐴2) but the same number of neutrons 𝑁1 = 𝑁2 are called Isotones.
  14. 14. Isotopes Isotones Isobars 𝑍1 = 𝑍2 𝑁1 = 𝑁2 𝐴1 = 𝐴2
  15. 15. 2/ Some Nuclear Properties 2) The Volume (V) of the nucleus is given by the formula : Most nuclei are spherical b) Nucleus Radius and Volume 1) The Average radius is given by the formula : 𝑟 = 𝑟0 𝐴1/3 ; 𝑟0 = 1.2 𝑋 10−15 m The unit used for measuring distance on the scale of nuclei is femtometer : 1 𝑓𝑚 = 10−15 𝑚 V = 4 3 𝜋(𝑟0 𝐴 1 3)3 V = 7.24 𝑋 10−45 (A) 𝑚3
  16. 16. Radius depends on 𝐴1/3 Volume depends on 𝐴
  17. 17. 2/ Some Nuclear Properties The Mass can also be expressed in 𝑀𝑒𝑉/𝑐2 The SI-unit of mass is Kg but in subatomic particles It is convenient to use atomic mass units ( 𝑢 ) to express masses. c) Atomic Mass Based on definition that the mass of one atom of C is exactly 12 𝑢 1 𝑢 = 1.660 539 x 10−27 kg 𝑚𝑝 = 1.0073 𝑢 , 𝑚𝑁 = 1.0087 𝑢 , 𝑚𝑒 = 5.486 ∗ 10−4 𝑢 𝑚𝑝 = 938.25 𝑀𝑒𝑉/𝑐2 , 𝑚𝑁 = 939.57𝑀𝑒𝑉/𝑐2 , 𝑚𝑒= 0.511𝑀𝑒𝑉/𝑐2 1 𝑢 = 931.494 𝑀𝑒𝑉/𝑐2
  18. 18. 2/ Some Nuclear Properties ρ = 𝑚 𝑉 = 𝑍∗𝑚𝑝+𝑁∗𝑚𝑁 4 3 𝜋(𝑟0 𝐴 1 3)3 (𝑚𝑝≅ 𝑚𝑛) ≅ 𝐴∗𝑚𝑝 4 3 𝜋(𝑟0 𝐴 1 3)3 = 𝐴∗𝑚𝑝 4 3 𝜋 𝑟0 3 𝐴 = 1.673∗10−27 7.238∗10−45 ≅ 2.3 ∗ 1017 Τ 𝐾𝑔 𝑚3 d) Nucleus Density That’s mean all nuclei have the same Density
  19. 19. 2/ Some Nuclear Properties 2) Electrical force: smaller in magnitude, but they become progressively more important as the number of protons in the nucleus increases. 1) Nuclear force: the force responsible of nuclei stability, which overcome the electrical force (repulsion between protons). e) Forces in the nucleus Properties of Nuclear force: strong, short range and attraction between nucleons.
  20. 20. 2/ Some Nuclear Properties p-p: electric repulsion and nuclear attraction. e) Forces in the nucleus p-n: nuclear attraction. n-n: nuclear attraction
  21. 21. 3/ Radioactive Decay Radioactivity : is the spontaneous emission of radiation. Radioactivity : is the result of the decay, or disintegration, of unstable nuclei. Radioactive nuclei can emit 3 types of radiation in the process: a) Definitions
  22. 22. 3/ Radioactive Decay  Alpha particles (𝛼): consists of 2 protons and 2 neutrons, and they are positively charged (+2e), have low speed and short range in matter. [2 4 𝐻𝑒]  Beta particles (𝛽): they could be 𝛽− (electrons) or 𝛽+ (positrons) , have high speed (near speed of light) and longer range in matter. [positrons are positively charged electrons]  Gamma ray (𝛾): It is electromagnetic wave (photon) carrying a high energy away from the nucleus, has speed of light and it is the most penetrating radiation . [have no mass or charge]
  23. 23. 3/ Radioactive Decay The number of particles that decay in a given time is proportional to the total number of particles in a radioactive sample. b) The Decay Constant λ is called the decay constant and determines the probability of decay per nucleus per second. 𝑑𝑁 𝑑𝑡 = −𝜆𝑁 𝑔𝑖𝑣𝑒𝑠 𝑁 = 𝑁0𝑒−𝜆𝑡 N is the number of undecayed radioactive nuclei present. No is the number of undecayed nuclei at time t = 0 (original number of nuclei).
  24. 24. 3/ Radioactive Decay The decay rate R of a sample is defined as the number of decays per second. c) The Decay Rate 𝑅0 = 𝜆𝑁0 is the decay rate at t = 0. R = 𝑑𝑁 𝑑𝑡 = 𝜆𝑁 = 𝜆𝑁0𝑒−𝜆𝑡 = 𝑅0𝑒−𝜆𝑡 The decay rate is often referred to as the activity of the sample.
  25. 25. 3/ Radioactive Decay The decay curve follows the equation: d) Decay Curve and Half-Life 𝑁 = 𝑁0𝑒−𝜆𝑡 Half life 𝑇1/2 is defined as the time required for half the nuclei present to decay. 𝑇1/2 = 𝐿𝑛2 𝜆 = 0.693 𝜆
  26. 26. 3/ Radioactive Decay c) Decay Curve and Half-Life t N 0 𝑁0 T 𝑁0/2 2T 𝑁0/4 3T 𝑁0/8 nT 𝑁0/(2𝑛)
  27. 27. 3/ Radioactive Decay Activity (R) in term of decay constant (λ) e) Activity (R) of a given mass 𝑁𝐴 = 6.023 𝑋1023 𝑚𝑜𝑙−1 is Avogadro’s Number 𝑛 = 𝑚𝑎𝑠𝑠 𝐴 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 ; 𝐴 is Mass number 𝑅 = 𝜆𝑛𝑁𝐴 𝑅 = 𝜆 𝑚𝑎𝑠𝑠 𝐴 𝑁𝐴
  28. 28. 3/ Radioactive Decay Activity (R) in term of Half life T e) Activity (R) of a given mass 𝑅 = 0.693 𝑇 𝑛𝑁𝐴 Remark Activity R must have a unit Bq ( Becquerel) Half life T must have a unit s ( Second) Constant decay λ must have a unit 𝑠−1
  29. 29. 3/ Radioactive Decay The SI unit of activity is the becquerel (Bq) f) Activity Units 1 Bq = 1 disintegration/s Remark The curie (Ci) is another unit of activity, 1 Ci = 3.7 X 1010 disintegration/s 1 Ci = 3.7 X 1010 Bq
  30. 30. 4/a Alpha Decay 𝑍 𝐴 𝑋 → 𝑍−2 𝐴−4 𝑌 + 2 4 𝐻𝑒 or 𝑍 𝐴 𝑋 → 𝑍−2 𝐴−4 𝑌 + 2 4 𝛼 X is called the parent nucleus Y is called the daughter nucleus Example : 92 238 𝑈 → 90 234 𝑇ℎ + 2 4 𝐻𝑒 84 234 𝑃𝑜 → 82 230 𝑃𝑏 + 2 4 𝛼 Alpha particle ( 2 4 𝐻𝑒 , 2 4 𝛼 ) is emitted leaving behind a residual nucleus that has lost 2 protons and 2 neutrons; 𝛼- decay is usually observed in heavier unstable nuclei (𝑍 > 82).
  31. 31. 4/a Alpha Decay Alpha particle (2 4 𝐻𝑒) is emitted leaving behind a residual nucleus that has lost 2 protons and 2 neutrons; 𝛼-decay is usually observed in heavier unstable nuclei (𝑍 > 82).
  32. 32. 4/b Beta Decay In Beta decay, an electron (𝑒− ) or a positron (𝑒+ ) is emitted by nucleus  When a nucleus emits an electron, the nucleus loses a neutron and gains a proton.  When a nucleus emits an positron, the nucleus loses a proton and gains a neutron.
  33. 33. 4/b Beta Decay 9 18 𝐹 → 8 18 𝑂 + 1 0 𝑒 + 𝜈 6 14 𝐶 → 7 14 𝑁 + 𝛽− + ҧ 𝜈 6 14 𝐶 → 7 14 𝑁 + −1 0 𝑒 + ҧ 𝜈 9 18 𝐹 → 8 18 𝑂 + 𝛽+ + 𝜈
  34. 34. 4/c Gamma Decay  Gamma rays are given off when an excited nucleus decays to a lower energy state.  The decay occurs by emitting a high energy photon called gamma-ray photons Example: 18 40 𝐴𝑟∗ → 18 40 𝐴𝑟 + 𝛾 The 𝑿∗ indicates a nucleus in an excited state.
  35. 35. 5/ Natural radioactive decay series  Decay series : The sequence of radioactive daughter nuclides that are formed by the radioactive decay of a parent nuclide to a final stable daughter nuclide.  There are three natural decay series that include the heavy elements 1) Thorium series : begins with 90 232 𝑇ℎ and end with 82 208 𝑃𝑏 ( its emits 6 𝛼 and 4 𝛽− in decay prosses) 90 232 𝑇ℎ → 82 208 𝑃𝑏 + 6 2 4 𝐻𝑒 + 4 −1 0 𝑒 + 4ഥ 𝜈 2) Uranium series : begins with 92 238 𝑈 and end with 82 206 𝑃𝑏 ( its emits 8 𝛼 and 6 𝛽− in decay prosses) 92 238 𝑈 → 82 206 𝑃𝑏 + 8 2 4 𝐻𝑒 + 6 −1 0 𝑒 + 6 ҧ 𝜈 3) Actinium series : begins with 92 235 𝑈 and end with 82 207 𝑃𝑏 ( its emits 7 𝛼 and 4 𝛽− in decay prosses) 92 235 𝑈 → 82 207 𝑃𝑏 + 7 2 4 𝐻𝑒 + 4 −1 0 𝑒 + 4 ҧ 𝜈 Each of the three series ends with an isotope of lead
  36. 36. 5/ Natural radioactive decay series Thorium series Uranium series Actinium series
  37. 37. 6/ Induced Nuclear reactions 1) Nuclear fusion : is a reaction in which two or more light nuclei are combined to form one or more heavy nuclei and subatomic particles (neutrons or protons). The fusion process releases a large amount of energy (Nuclear fusion occur inside the center of stars)
  38. 38. 6/ Induced Nuclear reactions 2) Nuclear Fission : is a reaction in which the heavy nucleus splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy
  39. 39. 7/ Radioactive dating Carbon-14 has half-life of 5730 years ; the production of C-14 is explained by the next nuclear equation: 7 14 𝑁 + 0 1 𝑛 → 6 14 𝐶 + 1 1 𝑝 Neutrons are produced in upper atmosphere by interaction of cosmic-ray with atomic nuclei Once an organism dies, the input of radiocarbon stops and the ratio of radiocarbon to ordinary carbon 6 12 𝐶 decreases steadily as the 6 14 𝐶 decays. Thus the quantity of 6 14 𝐶 remaining indicates the date of death 6 14 𝐶 → 7 14 𝑁 + −1 0 𝛽 + ҧ 𝜈 The decay of C-14 is explained by the next nuclear equation:
  40. 40. 8/ Measuring Radiation Dosage a) major categories of radiation 1. Positive ions (protons and alpha particles) 2. Electrons and Positrons (beta particles) 3. Photons (gamma rays and X-rays) 4. Neutrons
  41. 41. 8/ Measuring Radiation Dosage b) Absorbed dose This is a measure of radiation dose (as energy per unit mass) actually absorbed by a specific object, such as patient’s hand or chest. SI unit: gray (Gy). Other unit: rad, 1Gy =100 rad. 1Gy = 1 J/Kg
  42. 42. 8/ Measuring Radiation Dosage c) Dose Equivalent Although different types of radiation (gamma ray and neutrons…) may deliver the same amount of energy to the body, they do not have the same biological effect. The dose equivalent allows us to express the biological effect SI unit: Sievert (Sv)  Other unit: rem 1 Sv = 100 rem

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