Tiêu đề 14. Nuclear Chemistry.pdf ✅

Nuclear Chemistry 235 14 Nuclear Chemistry QUICK LOOK Radioactivity refers to the particles which are emitted from nuclei as a result of nuclear instability. Because the nucleus experiences the intense conflict between the two strongest forces in nature, it should not be surprising that there are many nuclear isotopes which are unstable and emit some kind of radiation. The most common types of radiation are called alpha, beta, and gamma radiation, but there are several other varieties of radioactive decay. There are three primary types of radiation: Alpha: The nucleus releases an alpha particle (a helium-4 nucleus) consisting of two neutrons and two protons; these are fast moving helium atoms. They have high energy, typically in the MeV range, but due to their large mass, they are stopped by just a few inches of air, or a piece of paper. Beta: The nucleus ejects an electron (or a positron). Note: this is not the same as an electron being removed from orbital’s around the nucleus; these are fast moving electrons. They typically have energies in the range of a few hundred keV to several MeV. Since electrons are might lighter than helium atoms, they are able to penetrate further, through several feet of air, or several millimeters of plastic or less of very light metals. Gamma: The protons and neutrons within the nucleus rearrange into a more stable form, and energy is emitted as a gamma ray. These are photons, just like light, except of much higher energy, typically from several keV to several MeV. X-Rays and gamma rays are really the same thing; the difference is how they were produced. Depending on their energy, they can be stopped by a thin piece of aluminum foil, or they can penetrate several inches of lead. Nucleus consists of protons and neutrons. The number of electrons in every nucleus is zero Proton was discovered by Rutherford and neutron by Chadwick. Nuclear density is nearly 1017 kg/m3 and is independent of mass number of nucleus. Mass number of nucleus A = N + Z, Where N = neutron number, Z = proton number. Radius of nucleus 1/3 R R A = 0 where 5 R 1.2 10 m 1.2 0 − = × = Fermi Size of nucleus is of the order of 10–14m, Nuclear density: E=1017 kg/m3 (independent of mass number) 1 amu 27 1.66 10 kg 931 − = × = MeV Mass defect, ∆ = + − − m Zm (A Z)m M(Z, A) p m Packing fraction mass defect f mass number = M A f A − = Where M = mass of nucleus, A= mass number Figure: 14.1 N N N N N N N N Electric Nuclear N N α β γ Figure: 14.3 Magnetic field B Beta emission is Preferentially in The direction Opposite the Nuclear spin, in Violation of conservation of parity. Wu, 1957 60Co I Nuclear spin e – 60 60 Co Ni e v → + + e Figure: 14.2 Radioactive source α (alpha) γ (gamma) β (beta)
236 Quick Revision NCERT - CHEMISTRY Binding energy of nucleus Figure: 14.4 With increase of mass number the binding energy increase, becomes maximum and then it decreases. B [( m)in amu] 931MeV = ∆ × Binding energy per nucleon [( m)in amu] 931 B MeV A ∆ × Order of binding energy per nucleon = 8 MeV Naturally Radioactive Decay Chains: For the half life the following abbreviations are used: s = seconds, m = minutes, h = hours, d = days and a = years. In some cases there are several decays leading to the same isotope. In these cases the upper decay is more frequent than the one below, as indicated with dashed arrows. Nowadays the neptunium chain (A = 4n + 1) does not exist in nature. A = mass number, n = an integer. Thorium Chain (A = 4n) 232 228 228 228 90 88 89 90 14.0Ga 5.76a 6.15h 1.913a Th Ra Ac Th − → → → → α β− β α 224 220 216 212 88 86 84 82 Ra Rn Po Pb 3.66d 55.6s 0.1451s 10.64h − → → → → α α α β 212 224 1.009 h 0.298 s 84 88 208 25m 3.053m 81 Po Bi TI − β α μ α β     → →       → → Neptunium Chain (A = 4n +1) 241 241 237 233 94 94 93 91 13.2a 458a 2.14Ma 27.4d Pu Am Np Pa − − → → → → β α α β 233 229 225 225 92 90 88 89 U Th Ra Ac 162ka 7340a 14.8d 10.0d − → → → → → α α β α 213 221 217 213 47m 4.2 s 84 87 85 83 4.8m 0.0323 209 81 2.2m Po Fr At Bi TI − − − β α β α μ α β     → → → → →       → → 209 211 82 8 Pb Bi 5.014d 3 − → → β Uranium Chain (A = 4n + 2) 238 234 234 234 92 90 91 92 U Th Pa U 4.47Ga 24.10d 6.69h 0.246Ma − − → → → → α β β α 230 226 222 218 90 88 86 84 75.4 ka 1600a 3.8235d 3.10 m Th Ra Rn Po → → → → α α α α 214 214 214 210 19.9m 164 s 84 82 83 82 27 m 22.3a 210 81 1.30m Po Pb Bi Pb TI − − − − β α β β μ α β     → → → →       → → 210 210 206 83 84 82 Bi Po Pb 5.01d 138.4d − → → β α Actinium Chain (A = 4n + 3) 235 231 231 215 92 90 91 81 U Th Pa Ac 704Ma 1.603d 32.8ka 21.77a − − → → → → α β α β 223 227 219 215 1.78ms 90 86 84 18.72d 11.435d 3.96s 88 Th Ra Rn Po − α α α α β → → → →  → 211 207 82 81 36.1m 2.14m 4.77 m 211 207 215 83 82 211 85 0.10ms 84 0.516s Pb Po Bi Pb(stable) At TI − − α α β α β α → → →          →     → → Nuclear Fission: Breaking of heavy nucleus in two nuclei 235 1 1 92 0 0 U n X Y p( n ) 200 + → + + + (Slow neutron) where X and Y are any tow isotopes having mass number about 40% to 60% of original nucleus and p is number of neutron which may be 2 or 3. 235 U is fissioned by slow neutron. It may be pointed out that it is not necessary that in each fission of uranium, the tow fragments Ba141 and Kr92 are formed but they may be any stable isotopes of middle weight atoms. The most probable division is into two fragments containing about 40% and 60% of the original nucleus with the emission of 2 or 3 neutrons per fission. Most of energy released appears in the form of kinetic energy of fission fragments. The fission of U238 takes place by fast neutrons Nuclear Fusion: Synthesis of lighter nuclei into heavier ones. If takes at high temperature (2×107 K) and high pressure. Source of energy of sun and stars is nuclear fusion. 235U 236U 92Kr 141Ba Figure: 14.5 yield from nuclear fission Elements heavier than iron can yield energy by nuclear fission Average mass of fission fragments is about 118. The “iron group” of isotopes are the most tightly bound (most tightly bound) Have 8.8 MeV per nucleon binding energy Binding energy per nuclear particle (nucleon) in meV Mass number, A Fe yield from nuclear fission 62 28Ni 62 28Fe 56 26Fe 235U 8 6 4 2
Nuclear Chemistry 237 For the fusion to take place, the component nuclei must be brought to within a distance of 10–4 m. For this they must be imparted high energies to overcome the repulsive force between nuclei. This is possible when temperature is enormously high. The principle of hydrogen bomb is also based on nuclear fusion. To start a fusion bomb very high temperature is required. This is achieved by bombarding an atom bomb. The source of energy of sun and other stars is nuclear fusion of thermo-nuclear reactions. There are two possible cycles. Different Types of Nuclei The nuclei have been classified on the basis of the number of protons (atomic number) or the total number of nucleons (mass number) as follows: (i) Isotopes: These are the elements having same atomic number but different mass number. They have the same atomic number because the number of protons inside their nuclei remains the same. The difference in their mass number is due to the difference in their number of neutrons. Let us see some examples 1H 1 , 1H 2 , 1H 3 are all isotopes of hydrogen. The isotope can occur either naturally or can be produced artificially in the laboratory. (ii) Isobars: Isotopes are chemically same and physically different. But the converse is true in isobars. That is isobars are elements, which are chemically different but physically same. So, isobars are atoms of different elements having the same atomic mass but different atomic number. Since their number of electrons is different, their chemical properties are different. The light nuclei have unstable isobars. Heavy nuclei have stable isobars and these occur in pairs. Suppose the number of protons of one isobar matches with that of another they are called as mirror-nuclides of each other. Examples of isobars are 76 76 32 3 Ce, Se 4 and 58 58 26 2 Fe, Ni 7 (iii) Isotones: Isotones are elements having the same number of neutrons. Examples of isotones are Chlorine - 37 and Potassium – 39. Both have 20 neutrons in their nuclei. (iv) Mirror nuclei: Nuclei having the same mass number A but with the proton number (Z) and neutron number (A Z) − interchanged (or whose atomic number differ by 1) are called mirror nuclei for Example. 3 3 7 7 1 2 3 4 H and He , Li and Be (v) Magic Number: It is found that nuclei with even numbers of protons and neutrons are more stable than those with odd numbers. In particular, there are "magic numbers" of neutrons and protons which seem to be particularly favoured in terms of nuclear stability: 2,8,20,28,50,82,126. Nuclei which have both neutron number and proton number equal to one of the magic numbers can be called "doubly magic", and are found to be particularly stable. 4 16 40 48 208 2 8 2 He O Ca Ca Pb 0 20 82 Pair Production Figure: 14.7 When two high energy gamma-ray photons collide, an electron/ positron pair are produced (the energy is converted into mass E = mc2 ). γ e e → + + (Must occur near a nucleus) 2 e 0 nucleus k,e k,e 1 E E hv m c E 0 2 + + ≈ ≈ − ≈ 2 σ p ∝ hvZ when 2 2 0 hv 2m C > σ p = cross section of pair production Dose: R A 2 k CK t D d = KR = does rate from diagram C = strength of source D = distance kA = fraction penetrating a radiation shield Laws of radioactive disintegration: The no. of atoms present in the radioactive substance depends upon the rate of disintegration. dN N dt − ∝ (– sing is for disintegration) dN N dt = −λ where λ is decay constant e e 0 log N t log N = − + λ e 0 N log t N = −λ ; t 0 N e N −λ = ⇒ t N N e0 −λ = Gamma ray photon Pair production Electron Positron Gamma ray photon Figure: 14.6 Energy Tritium Neutron Deuterium Helium
238 Quick Revision NCERT - CHEMISTRY Half life: half life of a radioactive substance is defined as the time period during which half of the no. of atoms of the substance remains un-decayed. If N0 N 2 = and 1/ 2 t t = ; 0 t1/ 2 0 N N e 2 −λ = t1/ 2 a 1/ 2 2 e ; log 2 t ; λ = = λ 1/ 2 0.693 t = λ 1/ 2 1/ 2 0.693 t T 0.693τ λ = = = 1/ 2 1/ 2 t 0.693t T T N N 2 N 0 0 − = = θ t t N e N e 0 0 − −λ τ = = Table 14.1: Half Life Time and Number of Decayed Atoms Time (t) Number of un- decayed atoms (N) (N0 = Number of initial atoms) Remaining fraction of active atoms (N/N0) probability of survival Fraction of atoms decayed (N0 – N) /N0 probability of decay t = 0 N0 1 (100%) 0 t = T1/2 N0 2 1 2 (50%) 1 2 (50%) t = 2(T1/2) 0 0 2 1 N N 2 2 (2) × = 1 4 (25%) 3 4 (75%) t = 3(T1/2) 0 0 3 1 N N 2 (2) (2) × = 1 8 (12.5%) 7 8 (87.5%) t = 10(T1/2) 0 10 N (2) 10 1 0.1% 2     ≈   ≈ 99.9% t = n (N1/2) 2 N (2) 1 2 n       1 1 2 n         −         Mean lifetime: The decay of particles is commonly expressed in terms of half-life, decay constant or mean lifetime. The probability for decay can be expressed as a distribution function t decay f (t) NE−λ = where λ is called the decay constant. The average survival time is then the mean value of time using this probability function. The integral becomes: can be integrated by parts x x x 0 0 0 1 1 1 t xe e dx 0 e τ λ λ λ ∞ ∞ − ∞ − − = = − = − = + − =   ∫   1 T T 1/ 2 1/ 2 ln 2 0.693 τ λ = = ≈ The mean life and "probability per second" Figure: 14.8 Radioactive equilibrium: A state ultimately reached when a radioactive substance of slow decay yields a radioactive product on disintegration. This product also decay to give a further radioactive substance and so on to produce a radioactive series. The amount of any daughter radioactive product present, after equilibrium has been reached, remains constant, the loss due to decay being counter balanced by gain from the decay of immediate product A→B→C At equilibrium, rate of formation of B = rate of decay of B = rate of decay of B K .N K .N A A B B = or A B B A K N K N = ∴ A B B 1/ 2 B B A 1/ 2 A A K N t K N t τ τ = = = K is decay constant 1/ 2 1 1 K and K τ t     ∴ ∝ ∝   Parallel path decay: A radioactive element A decays to B and C in two parallel paths as: The average decay constant for the element A can be expressed as average αpath β path λ λ λ = + . . .(i) Eq. (i) can be expressed in Eq. (ii) and (iii) as: αpath λ = [Fractional yield of B] av. × λ . . .(ii) β path λ = [Fractional yield of C] av. × λ . . .(ii) Maximum yield of daughter element: A radioactive element A decays to given a daughter element B which further decays to another daughter element C and so on till a stable element is formed (A→B→C). Also if number of daughter atoms at t = 0 is zero and parent atom is much more lived than daughter A B ( ), i.e.,λ < λ where λA and λb are decay constant of A and B respectively, then number of atoms of daughter element B after respectively, then number of atoms of daughter element B after time t is A B 0 A λ t λ t B B A N λ N [e e ] λ λ − − = − − . . .(i) Maximum activity of daughter element can be expressed at max t : B max 10 B A A 2.303 λ t log λ λ λ   =   −   . . .(ii) B C A Say emission of α Say emission of β Figure: 14.9 Amount remaining Time 100 % 100 % T1/2 τ Probability, or amount of daughter present 1 τ Time 1/τ