26 pius augustine nucleus and radioactivity

1. 1 Nucleus and Radioactivity

2. Dr. Pius Augustine, SH College, Kochi

3. Can e-m radiation be used for seeing nucleus? Comment Hint: Can feel the presence of a bottle on a table in a dark room by making a large sound in the room? Dr. Pius Augustine, SH College, Kochi

4. Sir James Chadwick (1891 –1974)

5. Quark model of neutron Dr. Pius Augustine, SH College, Kochi

6. Neutron Neutral subatomic particle discovered by Chadwick Constituent of every atomic nucleus except ordinary hydrogen. It has no electric charge and a rest mass equal to 1.67493 × 10−27 kg Mass - marginally greater than that of the proton but nearly 1,839 times greater than that of the electron. Dr. Pius Augustine, SH College, Kochi

7. Neutron Discovered by James Chadwick, English physicist in 1932, was awarded Nobel prize. Produced by bombarding beryllium with α 2He4 + 4Be9 6C12 + 0n1 + Q. Zero charge and mass greater than proton Dr. Pius Augustine, SH College, Kochi

8. Neutron Collapsed H- atom At extreme temperature and pressure the electron of the H atom was forced towards proton. Before the electrons bangs into the proton, it was stopped close to proton by nuclear energy Dr. Pius Augustine, SH College, Kochi

9. Neutron Properties i. Fundamental particle in the atom except H- atom ii. No charge and not deflected in E and B iii. High penetrating power and low ionizing power iv. In free state, it is unstable and decays n p + β + υ v. Spin ½ particles (Fermions–obey FD statistics)

10. Classification of Neutrons Based on Kinetic energy (velocity) i. Slow neutrons: 0 to 1000 eV . They are in thermal equilibrium with the medium through which they pass and are called thermal neutrons. Slow neutrons are used in nuclear reactors. When interact with 10B, will form 7Li and 4He. Hence B-is used as slow neutron absorber in reactors to control the fission. Dr. Pius Augustine, SH College, Kochi

11. Classification of Neutrons Based on Kinetic energy (velocity) ii. Fast neutrons : 0.5 to 10 MeV. When pass through material, slowed down by collisions with the nuclei of the material and lose a part of their energy. Moderators: Materials rich in hydrogen are very efficient in slowing down neutrons. (heavy water, graphite) Dr. Pius Augustine, SH College, Kochi

12. Isotopes Atoms of the same element whose nuclei have same atomic number Z, but differ in their mass number A Around 400 stable siotopes Eg. 1H1, 1H2 , 1H2 6C12 , 6C13, 6C14 Dr. Pius Augustine, SH College, Kochi

13. Isobars Atoms of different elements having the same mass number A, but different number of protons (atomic number Z) Eg: 18Ar40 and 20Ca40 12Mg24 and 11Na24 Dr. Pius Augustine, SH College, Kochi

14. Isotones Atoms of different element, but nuclei having equal no. of neutrons. Eg. 6C14 , 7N15, 8O16 14-6 = 15-7 = 16-8 = 8 neutrons Dr. Pius Augustine, SH College, Kochi

15. Isomeric nuclei or isomers Nuclei having same Z and A, but different from one another in their nuclear energy states and exhibits differences in their internal structure. Differ in the manner of radioactive decay They are distinguished by their different life times. Dr. Pius Augustine, SH College, Kochi

17. Isodiaphers Nuclides which have different atomic numbers and mass numbers but the same neutron excess Neutron excess - difference between numbers of neutrons and protons in the nucleus. 90TH234 and 92U238 Thorium – P=90 n = 144 n-p = 54 Uranium - P=92 n = 146 n-p = 54 Dr. Pius Augustine, SH College, Kochi

18. Is it a general behavior associated with alpha decay? Analyze a few more alpha emissions. Dr. Pius Augustine, SH College, Kochi

19. Mirror Nuclei Same A, but with proton and neutron number interchanged Eg. 4Be7 and 3Li7 Dr. Pius Augustine, SH College, Kochi

20. Nuclear size Alpha particle scattering experiments -Smallest value of distance of closest approach was found to be 10-14 m to 10-15m which is nuclear radius Nuclear radius R = roA1/3 ro = 1.3 fm Size of atom (10-10m) is 10,000 time nucleus Dr. Pius Augustine, SH College, Kochi

21. By what factor must the mass number of a nucleus increase to double its volume? To double it radius? Dr. Pius Augustine, SH College, Kochi

24. Atomic mass unit (a.m.u) or 1 u 1a.m.u is equal to 1/12th mass of one 6C12 atom. Atomic mass of 12C is 12u. 12 x10-3kg C contains 6.023 x1023atoms 1amu or 1u = 1.660 x 10-27kg 1u = (1/12) (12g/mol)(1mol/6.022x 1023) = 1.66 x 10-24 g Using E = mc2 1u = 931MeVDr. Pius Augustine, SH College, Kochi

26. Particle Mass (kg) Mass (u) Mass (MeV/c2) 1 amu 1.660540 x 10-27 kg 1.000 u 931.5 (MeV/c2) Neutron 1.674929 x 10-27 kg 1.008664 u 939.57 (MeV/c2) Proton 1.672623 x 10-27 kg 1.007276 u 938.28 (MeV/c2) Electron 9.109390 x 10-27 kg 0.00054858 u 0.511 (MeV/c2) Dr. Pius Augustine, SH College, Kochi

27. Mass of proton = 1.007276 amu Mass of neutron = 1.008665 amu mn > mp Dr. Pius Augustine, SH College, Kochi

28. Nuclear mass Expected mass of nucleus - sum of the mass of protons and neutrons present M = Zmp+ (A-Z)mn Experimental value of nuclear mass is less than this expected value Note: Atomic Mass is the mass of complete atom (Nucleus + electrons) Nuclear mass – mass of nucleus

29. Mass defect Δm Real nuclear mass < Zmp+ (A-Z)mn Difference between real mass of nucleus and expected mass is called mass defect Dr. Pius Augustine, SH College, Kochi

30. Nuclear density (ρN ) Nuclear mass = A mn A – mass no. Mass of nucleon (mn) = 1.67 x 10-27kg Nuclear volume = (4/3) πR3 = (4/3) π {roA1/3}3 ρN = MN / (4/3) πro 3 = A mn /(4/3) π ro 3A = 1.816 x 1017kg/m3.(≈ white dwarfs) Dr. Pius Augustine, SH College, Kochi

31. The most common kind of iron nucleus has a mass number of 56. Find the radius, aproximate mass, and aproximate density of the nucleus. R = roA1/3 = 4.6 fm ro = 1.2 fm. Mass = 56 x 1.66 x 10-27 = 9.3 x 10-26 kg. Density = M/V = 2.3 x 1017 kg/m3. Dr. Pius Augustine, SH College, Kochi

32. Nuclear spins Electons, protons and neutrons are spin ½ particles. Spin angular momentum of nucleon S = [½ (½ +1)]1/2 h/2π Z- component of angular momentum Sz = ±½ h/2π Nucleons have orbital motion in addition to spin motion and hence there is total angular momentum (J) called nuclear spin Dr. Pius Augustine, SH College, Kochi

33. Nuclear spins and magnetic moments Like electrons magnetic moments (Bohr magneton μB = eh/4πme), nucleons also have magnetic moment due to this angular momentum (Nuclear magneton μN = eh/4πmP= 5.05079 x 10-27 J/T mp – proton mass (1836 times me) μN = μB/1836 Z component of magnetic moments of proton = 2.7928 μN Z component of magnetic moments of neutron = -1.9130 μN Dr. Pius Augustine, SH College, Kochi

35. Binding energy Energy equivalent to mass defect. When nucleus is formed mass defect is converted into energy (= Δmc2) (Released) To disrupt a stable nucleus into its constituent protons and neutrons, minimum energy required = B.E. ie. if B.E is more, nucleus is more stable

36. B.E /nucleon (BEN) and Packing fraction B.E / nucleon = B.E / mass number Packing fraction = mass defect per nucleon Packing fraction = Δm / A Dr. Pius Augustine, SH College, Kochi

37. Calculate the mass defect and binding energy of deuteron. The mass of deuteron mD = 3.34359 x 10-27 kg or 1875.61 MeV/c2 Z = 1 A = 2 ∆m = mp + mn - mD mn = 939.57 (MeV/c2) mp = 938.28 (MeV/c2) mD = 1875.61 MeV/c2 ∆m = 2.24 MeV/c2. B.E = ∆m x c2 = 2.24 MeV Note: More than two million (2.24 MeV) electron volts are required to separate simplest deuteron into proton and neutron. This very large value shows the strength of nuclear force. Dr. Pius Augustine, SH College, Kochi

38. Calculate the binding energy per nucleon of an alpha particle from the given data. Z = n = 2 A = 4 B.E = [2mp + 2mn] – m(4He) c2 mp = 1.007825 u mn = 1.008665 u m(4He) = 4.002602 u 1 u = 931.5 MeV/c2 B.E = 28.3 MeV BEN = BE/4 = 7.07 MeV/nucleon For H-isotopes BEN is 2 to 3 Mev/nucleon. So He nuclei cannot be broken down to hydrogen isotopes without giving energy Dr. Pius Augustine, SH College, Kochi

39. 40 80 Max stabilityFusion Fission

41. Because it has the highest binding energy per nucleon of all nuclides, 28Ni62 may be described as the most strongly bound. Its neutral atomic mass is 61.928349 u. Find its mass defect, its total binding energy, and its binding energy per nucleon. Z = 28 mH = 1.007825 u n = 34, mn = 1.008665 u and M = 61.928349 u ∆m = mp + mn - M = 0.585361 u = 0.585361 x 931 = 545.3 MeV. This much energy is required to separate 62 nucleons B.E/nucleon = 1/62 = 8.795 MeV/nucleon ∆m = 0.585361 u is about 1% of the mass of the nucleus ie. B.E/nucleon will be about 1% of the rest mass energy of a nucleon. Which means it will be very stableDr. Pius Augustine, SH College, Kochi

42. Calculate the mass of an alpha particle. Given B.E = 28.2 MeV Alpha particle contains 2p and 2n mH = 1.007825 u mn = 1.008665 u MHe. = 2 x1.007825x 931 MeV + 2 x 1.008665 x 931 Mev –28.2 MeV = 28.2 MeV Dr. Pius Augustine, SH College, Kochi

43. If the nucleons of a nucleus are separated from each other, the total mass is increased. Where does this mass come from? Dr. Pius Augustine, SH College, Kochi

44. Discussion of graph i. B.E/A increases with A and after attaining a flat max, it decreases. ii. Max for intermediate (A) nuclei, (nucleons are most tightly bound) Dr. Pius Augustine, SH College, Kochi

45. Discussion of graph iii.At multiple of 4 (4,8,12,16 …) shows sudden rise. iv. B.E/A is 8 MeV for nearly all elements except very light (fusion)and heavier (fission) elements. Dr. Pius Augustine, SH College, Kochi

46. Reason for variation in B.E B.E is due to interaction of nucleons. Surface nucleons B.E is less. Surface to Volume ratio is greater for light nuclei [4πR2/(4/3)πR3] As R decrease, reduction in volume is more prominent than surface effect due to (R3) dependence ie. proportionately large surface area in light nuclei - surface nucleons more in number Dr. Pius Augustine, SH College, Kochi

47. Play by substituting various numbers (size of the nucleus!) Dr. Pius Augustine, SH College, Kochi

48. Reason for variation in B.E Electrostatic repulsion (p-p) introduce –ve BE (proportional to q1q2)which increases as the square of no. of protons, which is the reason for reduction in B.E of heavy nuclides A balance of the surface effect and electrostatic effect are seen in the middle range nuclei. Dr. Pius Augustine, SH College, Kochi

49. Significance of average B.E /nucleon = 8 MeV It explains saturation nature of nuclear force. One nucleon does not interact with all other nucleon but only with certain no which gives saturation Note: if a nucleon was interacting with all other nucleons, B.E/nucleon would have increased linearly with A. Dr. Pius Augustine, SH College, Kochi

50. Nuclear Force - a few points Force that binds p and n inside nucleus, despite the electrostatic repulsion of protons. It does not depend on charge (P-P, P-n and n-n forces) Short range of the order of nuclear dimensions 10-15 m. (Otherwise nucleus would grow pulling more nucleons in to it) Within the acceptable range, it is much stronger that electrostatic force. Dr. Pius Augustine, SH College, Kochi

51. Nuclear Force – a few points Nearly constant nuclear density and constant nuclear B.E/nucleon of large nuclides established that nuclear force exhibit saturation property. ie.a particular nucleon cannot interact with all other nucleons in the nucleus, but only with those in the immediate viscinity. (Electrical force is different from this – infinite range) Dr. Pius Augustine, SH College, Kochi

52. Nuclear Force – pairing up Nuclear force favors binding of pairs of p or n each having opposite spins. (Pauli’s principle) It shows pairs of pairs – interaction between pair of protons with pair of neutrons. Alpha particle is exceptionally stable in its mass number. Dr. Pius Augustine, SH College, Kochi

53. Nuclear Force – tensor force Nuclear force is a spin dependant force It is a non central force (tensor force) Consider two pairs of neutrons. In each pair, the separation between the neutrons is the same. Can the force between the neutrons have different magnitudes for the two pairs? Dr. Pius Augustine, SH College, Kochi

54. Nuclear Models Liquid Drop Model- Semiempirical mass formula Shell Model and Magic numbers Collective Model – collective rotation and vibration Will be discussed in the next PPT file. Dr. Pius Augustine, SH College, Kochi

55. Radioactivity Dr. Pius Augustine, SH College, Kochi

57. Radioactivity? Two radioactive substances? Phenomenon of spontaneous emission of powerful radiations from the nucleus of heavy elements. Radioactive elements: uranium, Thorium, Radium and Polonium Compare with definition of poetry – spontaneous overflow of powerful emotions recollected in tranquility. But radioactivity is dangerous!!! Dr. Pius Augustine, SH College, Kochi

58. Light atoms (eg. He) p = n Massive elements (U235 p = 92 n = 143) n >>p Particles below the line (see B) will decay by beta plus (positron) emission Particles above (see A) will decay by beta minus emission. Neutron number (n) vs Proton number (Z) Dr. Pius Augustine, SH College, Kochi

60. SegreChart 238Udecayseriesto206Pb Timesarehalflives

61. A radioactive substance is oxidized. What changes would you expect to take place in the nature of radioactivity? No change Radioactivity is a nuclear phenomenon Oxidation is electronic.Dr. Pius Augustine, SH College, Kochi

62. A small hole is drilled in a lead block and a piece of radioactive element is placed in it. Radiations emitted from the radioactive element can escape only through the hole and others are absorbed by the lead wall. Radioactivity Experiment Dr. Pius Augustine, SH College, Kochi

63. Radioactive radiations in electric field α – towards –ve plate β - towards +ve plate γ - undeflected Dr. Pius Augustine, SH College, Kochi

64. Radioactive radiations in magnetic field Alpha and Beta particles are oppositely charged. Beta particles bent more (semicircle) – lighter compared to alpha. Gamma is uncharged - undeflected Uniform B is applied perpendicular to plane of the screen. Radiations splitted into 3 parts Fleming’s Left Hand Rule Dr. Pius Augustine, SH College, Kochi

65. Range of α – particles The distance traveled within the medium before it gets stopped or loses ionizing power completely is called the range of the alpha particle in the medium Range depends on the nature of medium, pressure, ionization potential of the gas and initial energy of alpha particle. Dr. Pius Augustine, SH College, Kochi

66. A radioactive sample emit either an alpha or a beta at a time along with gamma radiation. How will you account for the formation of three dots on the photographic plate ? One radioactive nucleus undergoes a series of decays one after the other, will have different emissions, until a stable end product is formed. So many nuclei will do the same Along alpha or beta emission will be followed by gamma emission by the excited daughter nucleus Dr. Pius Augustine, SH College, Kochi

67. Nucleus of an atom does not contain electron. How will you account emission of electron (beta) from nucleus? Two possibilities Neutron changes to p, e- and antineutrino or proton changes to neutron, e+ and neutrino Accordingly, β- or β+ will be emitted from the nucleus. Dr. Pius Augustine, SH College, Kochi

68. Properties of α, β and γ radiations Dr. Pius Augustine, SH College, Kochi

69. Sl. No. PROPE RTY α- PARTICLE β-PARTICLE γ - RAYS 1. Identifi cation Nuclei of He4 Fast moving e- Electromagnetic waves of short wavelength 2. Electric charge Positive charge(+2e) Negative charge(-e) No charge 3. Rest mass Equal to that of He4 nucleus Equal to rest mass of electrons Zero rest mass 4. Speed About (1/10)th velocity of light (C) 0.99 c Equal to c Dr. Pius Augustine, SH College, Kochi

71. 5. Penetrating power Smaller than that of β – particle 100 times that of α- particle 100 times that of β –particle 6. Ionizing power Higher than that of β – particle (1/100)th of that of α- particle (1/100)th of that of β – particle 7. Behavior in E and B fields Deflected in electric and magnetic fields Deflected Not deflected (electromagn etic) 8. Photographic plate Affect photographic plate Affect Affect 9. Fluorescence Produce fluorescence Produce Produce Dr. Pius Augustine, SH College, Kochi

72. What is the nature of alpha, beta and gamma radiations? State four properties of each. Refer previous slides An alpha particle captures an electron. What does it change to ? Singly ionized helium He+ Dr. Pius Augustine, SH College, Kochi

73. Which radiation suffer maximum deflection in magnetic field? Ans: β (lowest mass) State one difference between a chemical change and a nuclear change. Chemical change – due to change in orbital electrons. Nuclear – change in nucleons inside nucleus. Dr. Pius Augustine, SH College, Kochi

74. State the penetrating range of α ,β and γ α – 2.7 cm to 8.62 cm of air β – 5mm of Al or 1mm of Pb γ – 30cm of iron Dr. Pius Augustine, SH College, Kochi

75. How do IR and gamma rays differ in wavelength and penetrating power? Both are em radiations Wavelength of gamma rays is much shorter (10-13 m aprox) and IR(10-6 m aprox) IR is heat rays Gamma rays are high energetic and much more penetrating Dr. Pius Augustine, SH College, Kochi

76. Electromagnetic Spectrum Gamma rays-extremity of the spectrum, have high-energy photons. High penetrating power Can ionize other atoms Very dangerous if you are directly exposed to them.Dr. Pius Augustine, SH College, Kochi

77. Why do we usually use isotopes emitting gamma radiations as radioactive tracers (diagnose brain tumours, blood clots)in medical use? Gamma radiations are most penetrating (high energetic) Why are alpha particles not used in radio therapy ? Penetrating power is very low and cannot penetrate through human skin. Dr. Pius Augustine, SH College, Kochi

78. State two similarities and two dissimilarities between the γ rays and X rays Similarities : i. both are em radiations. ii. Equal velocity in vacuum Dis : i. wavelength difference ii. γ is higher penetrating than X Dr. Pius Augustine, SH College, Kochi

79. State three properties common to beta and cathode rays i. Negative charge ii. Deflected by E and B iii. Cause fluorescence Dr. Pius Augustine, SH College, Kochi

80. State three properties which are different for beta and cathode rays i. Cathode rays are extranuclear electrons. Beta comes from nucleus ii. Velocity of cathode ray depend on p.d between anode and cathode (beta rays very high depending on the source nucleus) iii. Cathode rays - mass constant, beta – relativistic variation of mass Dr. Pius Augustine, SH College, Kochi

81. 92U238 decays to 82Pb206. How many α and β particles are emitted ? 238 – 206 = 32 [reduction in A] 92 – 82 = 10 [reduction in Z] No. of α = 32 / 4 = 8 Corresponding reduction in Z is 16. But given case - only 10. (difference is 6 compensated by β ) No. of β = 6Dr. Pius Augustine, SH College, Kochi

82. 90Th234 decays to 82Pb206 . Find number of alpha and beta particles emitted ? Ans: 7α and 6β Dr. Pius Augustine, SH College, Kochi

83. A radioactive sample is kept at the centre of large evacuated sphere. How safe will it be? What changes do you suggest for more safety ? α – less penetrating and may be stopped by walls. β – since evacuated, no absorption within. No. of beta reaching surface/ area will be minimum if area is large. γ - thick lead walls will be good to absorb. (ie. safety - large lead sphere should be used, should not be evacuated) Dr. Pius Augustine, SH College, Kochi

84. A mass of lead is embeded in a block of wood. Radiations from a radioactive source incident on the side of block produce a shadow on a fluorescent screen placed beyond the block. The shadow of wood is faint , that of lead is dark. Explain. If block of wood is replaced by a block of Al, will there be any change in the shadow? Wood blocks only alpha. Lead stops all the three radiations. Hence dark. Al or light metal will not stop gamma , hence shadow will be faint. Dr. Pius Augustine, SH College, Kochi

85. Radio activity is a nuclear phenomenon. comment Emission of radiation from a fixed mass of radioactive substance is unaffected by chemical change or physical change like heating ,cooling, finely dividing etc. ie. electrons outside nucleus has no role in radioactivity or it is nuclear phenomenon. Dr. Pius Augustine, SH College, Kochi

86. Parent nuclei and Daughter nuclei A nucleus which undergo radioactive disintegration is called parent nucleus and the product nucleus formed is called daughter nucleus Dr. Pius Augustine, SH College, Kochi

87. Alpha Decay All nuclei with A>210 undergoes alpha decay. Nucleus will be unstable due to Coulomb repulsive force α-emission cause reduction in mass number and moves to stability Dr. Pius Augustine, SH College, Kochi

88. Nuclei which are unstable due to low B.E/ nucleon • To achieve greater stability by reducing size • Emit alpha which has a high value of binding energy • When alpha particles are emitted the B.E/ nucleon increases • Becomes more stable. Dr. Pius Augustine, SH College, Kochi

89. Q-value of nuclear decay or reactions The difference between the rest mass energy of the initial constituents (Ui) and that of the final products (Uf) is called Q-value of the process. Q = Ui – Uf. Applicable for any type of nuclear reactions Alpha decay Q = [m(zXA) – m(z-2YA-4) – m(2He4)]c2 Dr. Pius Augustine, SH College, Kochi

90. Beta Decay unstable due to higher or lower neutron to proton ratio, than that of a stable nucleus. Emits β-particles and thus the neutron to proton ratio is decreased. Dr. Pius Augustine, SH College, Kochi

91. No electron in the nucleus. How will you account for β emission ? Neutron is converted into a proton and an electron. When a parent nucleus X emits a β-particle, the daughter nucleus produced will have the same mass number but the atomic number will be increased by 1 0n1 → 1p1 + -1eo + υ Dr. Pius Augustine, SH College, Kochi

92. β – decay and neutrino theory β emission can be represented as, z X A  z+1 Y A + -1 e 0 + Q where Q is the energy released. According to this eqn, all β particles emitted must have same energy Magnetic spectrograph study shows continuous β – spectrum (energy ranging from 0 to a max ?). Max energy of spectrum is characteristic of the radioactive atom emitting β Dr. Pius Augustine, SH College, Kochi

93. β - spectrum Dr. Pius Augustine, SH College, Kochi

94. β – spectrum and confusions ??? 1. All particles from a particular radioactive sample should emit β particles having same energy. But only a few β particles are emitted with the maximum value of energy. What about remaining energy? Dr. Pius Augustine, SH College, Kochi

95. β – spectrum and confusions ??? 2. Conservation of angular momentum . How ? How is it possible for a nucleus of even mass number and therefore integral spin give daughter of same mass and integral spin and emit electron of spin ½ h/2π ? (Similarily for odd nuclei) 3. Also apparent failure of coservation linear momentum? Dr. Pius Augustine, SH College, Kochi

96. β – spectrum and neutrino theory In 1930 Pauli proposed that if an uncharged particle of zero mass and spin ½ is emitted in β – decay together with electron, above discrepancies can be settled. Particle was named neutrino. (which carries difference in energy) Two type of β (negatron and positron) and hence neutrino and antineutino. Dr. Pius Augustine, SH College, Kochi

97. Neutrino is lacking charge and mass Neutrino is not electromagnetic in nature Neutrino can pass unimpeded through vast amounts of matter. Neutrino has to pass through over 100 light years of solid iron on the average before interacting. (can pass through earth) Dr. Pius Augustine, SH College, Kochi

98. Neutrino theory – by Fermi Both β and neutrino are created in the nucleus and ejected simultaneously Total energy of these particles is a constant, which is the end point energy observed in the spectrum. Dr. Pius Augustine, SH College, Kochi

99. Neutrino theory – by Fermi β carry max energy when energy of the neutrino is zero, and other cases less than maximum Total energy may be shared in any proportion which is the reason for continuous spectrum Dr. Pius Augustine, SH College, Kochi

100. Q-value for beta decay In beta decay N/Z ratio will be altered If parent nucleus is having higher number of neutrons, then neutron will be converted into proton or vice versa, to move to stability. This is possible through weak nuclear interactions associated with beta decay Dr. Pius Augustine, SH College, Kochi

101. Q-value for beta decay β- decay z XA z+1YA + β- + ν Q = Ui-Uf = [m(zXA) – m(z+1YA)]c2 Note that rest mass energy of the created electron (β-) is not subtracted here. Because of the large mass, the residual nucleus (z+1YA) will not share appreciable kinetic energy. So energy is shared between antineutrino and beta particle (beta spectrum) Dr. Pius Augustine, SH College, Kochi

102. Q-value for beta decay β+ decay z XA z+1YA + β+ + ν Q = Ui-Uf = [m(zXA) – m(z-1YA) – 2me]c2 Can an isolated proton decay to a neutron emitting a positron and a neutrino? Mass of neutron is larger than the mass of a proton and hence the Q-value will be negative. So an isolated proton will not. (inside nucleus, it would be possible, as there is associated mass variations of the rest of the particles) An isolated neutron can. Dr. Pius Augustine, SH College, Kochi

103. Q-value for beta decay Electron capture z XA + e z-1YA + ν Q = Ui-Uf = [m(zXA) – m(z-1YA)]c2 When an electron is captured, vacancy will be filled from outer electrons and an X-ray photon will be emitted following the electron capture. Dr. Pius Augustine, SH College, Kochi

104. Gamma Decay

105. Nucleus can exist in different energy states. When a radioactive nucleus emits and α-particle or a β- particle, after the emission, the nucleus will be in the excited state. The nucleus can return to the ground state by the emitting γ-rays, which are e.m. waves of short wavelength. For example 27Co66 emits a β-particle and is converted to 28Ni60 which is in excited state. 28Ni60 returns to it’s ground state by emitting two γ-rays. Gamma Decay Dr. Pius Augustine, SH College, Kochi

106. A daughter nucleus formed after α or β decay may not be stable. More decay may continue until a stable end product is formed. α, β and γ dacays are collectively called radioactive decay and the materials capable of undergoing radioactive decay are called radioactive material. α, β and γ are collectively called nuclear radiations. Dr. Pius Augustine, SH College, Kochi

107. How much energy is released in the following reaction? 7Li + p α + α Atomic mass of 7Li = 7.0160 u 4He = 4.0026 u Energy released = 7Li + p - 2α = 7.0160 u + 1.007825 u - 2 x 4.0026 u = 16.83 Mev Dr. Pius Augustine, SH College, Kochi

108. Does a nucleus loose mass when it suffers gamma decay? In beta decay, an electron or a positron is emitted by a nucleus. Does the remaining atom get oppositely charged? Dr. Pius Augustine, SH College, Kochi

109. Gamma-ray burst (GRB) is a high-energy explosion that occurs in space. Most powerful blasts in the cosmos, and the dazzling flash of gamma rays fills up our sky at least once every day. An artist’s illustration of a gamma-ray burst

110. Energy for Earthquakes comes from radioactive energy in Earth's mantle. Radioactive decay produces heat that causes convection in the mantle. When the rock breaks, the stored energy is released suddenly. This energy is then carried outwards from the break by seismic waves, a form of energy radiation. Radioactivity and earthquake? Dr. Pius Augustine, SH College, Kochi

111. A combined analysis of the concentrations of radon and one of its radioactive isotopes called “thoron” may potentially allow for the prediction of impending earthquakes, without interference from other environmental processes, according to new work done by researchers from Korea. Radioactivity and earthquake-holy grail of geophysics? Dr. Pius Augustine, SH College, Kochi

112. In radioactive transformations either an alpha or beta particle is emitted by the atom at one time. Never both or more than one. When a radioactive atom emits an alpha particle, the mass no. of the new element will be less by 4 units and atomic no. less by 2 units than those of the parent atom. When a radioactive atom emits a beta particle, the new atom formed has the same mass no. but the atomic no. increases by 1 Soddy Fajan’s Displacement Law Dr. Pius Augustine, SH College, Kochi

113. Radioactive decay law states that the probability per unit time that a nucleus will decay is a constant, independent of time. The radioactive decay of certain number of atoms (mass) is exponential in time. It is a universal law – describes statistical behavior of large number of nuclides. Radioactive decay law or Rutherford and soddy theory Dr. Pius Augustine, SH College, Kochi

114. Radioactive decay law or Rutherford and soddy theory States that rate of disintegration is directly proportional to the total number of atoms present at that time. Consider a sample contains N un decayed nuclei. Let dN nuclei disintegrate in dt second. dN/dt α – N -ve sign signifies that number of nuclei decreases with time Dr. Pius Augustine, SH College, Kochi

115. dN/dt = -λN dN/N = -λdt Let at time t = 0, no. of undecayed nuclei be N0.and at time t, no. is N ∫ dN/N = -λ ∫ dt logeN – logeNo = – λt. Loge(N/No) = – λt. N = No e-λt N0 N 0 t Dr. Pius Augustine, SH College, Kochi

116. Time → ↑ N Dr. Pius Augustine, SH College, Kochi

117. Definition for decay constant dN/dt = -λN λ = -dN/dt N Decay constant of a radioactive substance is defined as the ratio of its instantaneous rate of disintegration to the number of atoms present (N = No e-λt )at that time . If t = 1/λ, N = No e-λ1/λ = No/e = No/ 2.718 = 0.368 No. Radio active decay constant λ may be defined as the reciprocal of time when the number of atoms of radioactive substance decreases to 0.368 of the number present

118. Half life T1/2 Time at which undecayed nuclei falls to half of its original number. T = T1/2 N = No/2 N = No e-λt Loge(N/No) = – λt. loge No/2No = -λ T1/2 loge 2 =λ T1/2 T1/2 = 0.693 /λ Half life of some elements are shorter than 10-15s and some as long as 1010years ≈ age of universeDr. Pius Augustine, SH College, Kochi

119. Half life T1/2 loge 2 =λ T1/2 λ = loge 2/T1/2 T1/2 = 0.693 /λ N = No e-(log 2/T1/2)t = No e-(log 2)(t/T1/2) = No = No e(log 2)(t/T1/2) 2(t/T1/2) Following the same argument Activity at time t will be A = Ao 2(t/T1/2)

120. Radioactive 131I has a half life of 8.0 days. A sample containing 131I has activity 20μCi at t = 0. a)what is its activity at t = 4.0 days? b) what is its decay constant at t = 4.0 days. a) t = 4.0 days λ = 0.693/T1/2 A0 = 20 x 10-6 Ci Activity A =Ao e-λt = 14 μ Ci b) λ = 0.693/T1/2 = λ = 0.693/(8 x 24 x 3600) = 1.0026 x 10-6 Dr. Pius Augustine, SH College, Kochi

121. The half life of a radioactive nuclide is 20 hrs. What fraction of original activity will remain after 40 hrs? t/T1/2 = 40 hr/20hr = 2 A = Ao 2(t/T1/2) A/A0 = 1/22 Dr. Pius Augustine, SH College, Kochi

123. Average or Mean life τ The mean of the ages of the atoms of the radioactive element is called average or mean life it is equivalent to reciprocal of decay constant λ. τ = Total lives of all the atoms Total no. of atoms τ = 1 / λ T1/2 = 0.693 /λ = T1/2 / loge2 = T1/2 /0.693 = 1.44 T1/2 Dr. Pius Augustine, SH College, Kochi

124. Mean life τ = τ1 + τ3 + ... + τ2 / n Where τ1, τ2,....... τn represent the observed lifetime of the individual nuclei and n is a very large number. Calculated as a weighted average: τ = (τ1N1 + τ3N2 + ... + τ2Nn) / (N1 + ... + Nn) Where N1 nuclei live for time τ1, N2 nuclei live for time τ2....... and so on. Dr. Pius Augustine, SH College, Kochi

125. T1/2 = τ 0.693 T1/2 and τ vary drastically for different substances. Eg. T1/2 of Po212 is less than 1 μs, while for Th232, T1/2 it is more than 1 billion years. Dr. Pius Augustine, SH College, Kochi

126. Let N0 be the total no. of radioactive atoms in the beginning and N after a time t. Let dN disintegrate between t and t+δt. (if δt is very small , each of these atoms had a life of t) Total life of dN atoms = (dN)t Total life of No atoms T = ∫t(dN) 0 ∞ Dr. Pius Augustine, SH College, Kochi

127. Total life of No atoms T = ∫t(dN) N = No e-λt dN/dt = λNoe-λt omitting –ve sign as it merely indicates the decrease dN = Noe-λt dt (-λ) Mean life = τ = T/N0. = λ∫ te-λt dt Integrate by parts will give result τ = 1/λ 0 ∞ 0 ∞ Dr. Pius Augustine, SH College, Kochi

128. Using calculus |dN| = λN0e–λtdt Mean life τ= 1/λ.

129. Cascade Decays: A nucleus ‘A’ decays into another nucleus ‘B’, which again decays into ‘C’, and so on until the series ends in a stable nuclide. These are known as cascade decays. Dr. Pius Augustine, SH College, Kochi

130. Activity of radioactive substance Is the rate of decay of the nucleus. If N is the number of radioactive nuclei present in a sample, out of which a small fraction dN decays in a small interval dt, Activity A = -dN/dt =λN = λ No e-λt = Ao e-λt Dr. Pius Augustine, SH College, Kochi

131. Units of Activity SI unit – Becquerel (Bq) 1Bq = 1 disintegration /second(small unit) Activity of a radioactive sample is said to be 1Bq , if it undergoes one disintegration in 1sec. Non SI units 1 curie (Ci) = 3.7 x 1010 Bq (number of disintegrations that one gram of radium-226 will undergo in one second.) 1Ci = 37 GBq. (is the activity of 1g radium) 1Rutherford (Rd) = 106 Bq. Dr. Pius Augustine, SH College, Kochi

132. The decay constant of a radioactive nuclide 64Cu is 1.516 x 10-5 s-1. Find the activity of a sample containing 1 μg of 64Cu. Atomic weight of copper = 63.5g/mole. Neglect the mass difference between the given radioisotopes and normal copper. 63.5 g of copper has 6 x 1023 atoms. (N)No. of atoms in 1 μg of 64Cu ? = 9.45 x1015. Activity = λN = 1.43 x 1011 disintegrations/sec 1.43 x 1011/3.7 x 1010 = 3.86 Ci Dr. Pius Augustine, SH College, Kochi

133. A measure of radioactivity (activity) is based on counting of disintegrations per second. The SI unit of activity is the becquerel (Bq), equal to one reciprocal second. Activity depends on the number of decays per second. Independent of type of decay, the energy of the decay products, or the biological effects of the radiation. Dr. Pius Augustine, SH College, Kochi

134. Specific activity is the activity per quantity of a radionuclide, (activity per quantity of atoms) of a particular radionuclide. It is usually given in units of Bq/g or Ci/g. Dr. Pius Augustine, SH College, Kochi

136. Isotopes of elements with atomic number less than 82, which are radio active are called radioisotopes. They are prepared artificially. Artificial radioactivity was discovered by I.Curie and F.Joliot. Eg. 27Co60, 6C14 , 19K40, 15P32 Radioisotopes Dr. Pius Augustine, SH College, Kochi

137. Al after bombarding with α particles showed continuous emission of radiations. (even after source of alpha particles was taken away). 2He4 + 13Al27 → 15P30 + on1 15P30 → 14Si30 + 1e0 Radio active phosphorous differ from the normal phosphorous only in the mode of preparation Such isotopes prepared artificially and are radioactive are called radioisotopes. Dr. Pius Augustine, SH College, Kochi

139. 1. They are chemically identical with stable isotope. Eg.11Na23 and 11Na24 are identical in chemical process. No one can distinguish, if 11Na24 is in dining table salt. 2. They can be easily detected 11Na24 is β emitter and its progress in the system can be detected. Thus role of stable isotope can be traced by the presence of radio isotope. 3. The masses of even small amount of radioisotopes may be accurately determined. Properties of radioisotopes which make them useful Dr. Pius Augustine, SH College, Kochi

140. Radioactive tracers In this process an atom in a chemical compound is replaced by another atom, of the same chemical element. This process is often called radioactive labeling. Used because, radioactive decay is much more energetic than chemical reactions. Dr. Pius Augustine, SH College, Kochi

141. Tracer technique or tagging Process of deliberately adding a small quantity of radio isotope with the substance to be investigated and tracing the path of radio isotope by means of radioactive detector is known as tracer technique. Used in medicine and agriculture Dr. Pius Augustine, SH College, Kochi

142. Medical i. radiation therapy (Co-60 ) - to kill cells in a tumour (inhibition of growth) ii. Diagnosis (radio Nacl, radio Fe, radio I) - used as tracers to detect suspected brain tumour and blood clots before become dangerous. iii. Radio cardiology (radio Nacl) to test blood circulation iv. Sterilisation (gamma rays) Uses of Radioisotopes Dr. Pius Augustine, SH College, Kochi

143. Gamma from Co-60

144. 27Co60 emits a β – particle and transforms into 28Ni60 which in turn emits a gamma radiation (energy 1.17 MeV ) which is used in the treatment of cancer. Cobalt therapy Dr. Pius Augustine, SH College, Kochi

145. Radio iodine for goitre treatment Dr. Pius Augustine, SH College, Kochi

146. I131 has half life 8 days. If fed to a patient, carried by blood and collected by thyroid. Rate at which it is collected can be detected by radiation detectors. Rate of accumulation depend on the condition of the gland. Dr. Pius Augustine, SH College, Kochi

147. Scientific i. Projectiles for nuclear reactions (α). ii. Radioactive tracers in agriculture iii. Age of rocks, fossils (Carbon dating) Uses of Radioisotopes Dr. Pius Augustine, SH College, Kochi

148. Industrial i. Locate obstruction in gas, oil or water pipes ii. Control the thickness of paper, plastic sheet etc (manufacture) iii. Radiography : γ from Co60 used to Check crack in welding, pipes etc. Uses of Radioisotopes Dr. Pius Augustine, SH College, Kochi

149. Radio carbon dating When a plant is alive, though C14 present in it decays, ratio of C14 to C12 remains constant due to the uptake from atmosphere. When plant dies C14 start disintegration and ratio decreases with time exponentially. By noting the % of C14 in a sample age can be determined (half life of C14 = 5760 years) Dr. Pius Augustine, SH College, Kochi

150. Rock dating Half life of U238 – 5 x 109 years End product of series is Pb.(intermediate elements have short lives) In a rock after billions of years only major elements present in appreciable quantity will be U238 and Pb. Relative proportion of the two in a sample enables to estimate how long back the rock contained only U238, gives age of rock. Dr. Pius Augustine, SH College, Kochi

151. Radiation measurement – 3 types i. Source activity – curie (Ci) = 37GBq. ii. Exposure - rontgen ( R) : one R is the quantity or exposure of radiation that produce 1.61 x 1015 ion pairs in 1kg of dry air at STP. iii. Absorbed dose(rad): one rad is that amount of radiation absorbed in a material which increases its energy by 0.01joule /kg. Dr. Pius Augustine, SH College, Kochi

152. rad / day 0 - 25 25 – 50 50 - 100 100 – 200 200 – 400 400 – 600 600 and more. Effect No observable effect. Possibility of slight blood changes. Vomiting, fatigue, loss of apetite, moderate blood changes etc. Vomiting, severe blood changes accompanied by hemorrhage etc Chances of permanent damage in the body 50% chance of death. Survivors to suffer permanent damage. 100% death !!!....... Dr. Pius Augustine, SH College, Kochi

153. Biological effects of nuclear radiations – 2 types 1. Somatic effects. (short term recoverable and long term irrecoverable) 2. Genetic effects (later generations) Radioactive radiations (α, β and γ) cause ionization and excitation of atoms of living cells due to which living cells are altered or destroyed. Dr. Pius Augustine, SH College, Kochi

154. Safety precautions at Nuclear plants. i. Reactors in thick concrete walls to prevent gamma or neutrons. ii. Nuclear materials in thick lead containers with narrow mouth (plug). iii. Lead lined aprons and gloves. iv. Handle with mechanical tongs. v. Wear badges and periodic checking. vi. Periodic compulsory check up Dr. Pius Augustine, SH College, Kochi

156. An object can be seen with a signal if the wavelength of the wave is smaller than the size of the object. If not wave will bent around the edge. Wavelength of electron wave depends on the velocity of the electron. Higher the velocity lower the wavelength. Hope you will be able to answer the opening question now. Dr. Pius Augustine, SH College, Kochi

157. For my youtube videos: please visit - SH vision youtube channel or xray diffraction series SH Vision Dr. Pius Augustine, SH College, KochiDr. Pius Augustine, SH College, Kochi

158. 160 Appeal: Please Contribute to Prime Minister’s or Chief Minister’s fund in the fight against COVID-19 Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara we will overcome Thank You http://piusaugustine.shcollege.ac.in https://www.facebook.com/piustine Please share Dr. Pius Augustine, Asst. Professor, Sacred Heart College, Thevara, Kochi.

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