THE NUCLEUS: A CHEMIST S VIEW Chapter 20
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1 THE NUCLEUS: A CHEMIST S VIEW Chapter 20 "For a long time I have considered even the craziest ideas about [the] atom[ic] nucleus... and suddenly discovered the truth." [shell model of the nucleus]. Maria Goeppert Mayer, Nobel Prize in Physics, 963 It follows from the theory of relativity that mass and energy are both different manifestations of the same thing a somewhat unfamiliar conception for the average man. Furthermore E = mc 2, in which energy is put equal to mass multiplied with the square of the velocity of light, showed that a very small amount of mass may be converted into a very large amount of energy... mass and energy were in fact equivalent. Albert Einstein, Nobel Prize in Physics, 92 Nuclei obey the laws of ) thermodynamics, 2) kinetics, 3) quantum mechanics Basics of the Atom small, dense world diameter of a nucleus, 0-4 m diameter of smallest atom, 0-0 m density of g cm -3 designation of a nuclide (nucleus) Z = atomic number (number of protons) N = neutron number (number of neutrons) A = mass number (sum of protons and neutrons) nucleus of nuclides consists of nucleons protons neutrons however leptons (e.g., electrons and neutrinos) and quarks are the true elementary particles of matter proton consists of 2 up quarks and down quark: 2u ( + 2 /3) + d ( /3) neutron consists of 2 down quarks and up quark: 2d ( /3) + u ( + 2 /3) Artist s conception of the structure of a helium nucleus that contains two protons and two neutrons. The protons each have two up quarks and one down quark, and the neutrons have two down quarks and one up quark. Neutron proton 20.3 Types of Radioactivity Nuclear stability can be discussed from the viewpoint of thermodynamics, kinetics, and quantum mechanics. One consequence of a lack of stability of a nucleus is its decomposition via radioactive decay. Wilhelm Röntgen Antoine-Henri Becquerel Marie Curie
2 Particles to be Encountered alpha (α) particle nucleus of helium atom, 2He 2+ beta (β) particle high energy electron gamma ( 0 0 γγ) radiation high energy radiation (photons) originating from nucleus proton: H + electron:, p 0 e (beta particle) neutron: 0 n usually omitted in nuclear chemistry, written as 0 positron: e (antielectron) neutrino/antineutrino: υ, ῡ required for conservation of angular momentum (can ignore) Some Rules for Nuclear Reactions NOTE: charge on the nucleus (such as 2+ in 2He 2+ ) 4 He. in balancing, charge (Z) and mass number (A) are conserved (sum on left = sum on right) 2. spontaneous nuclear reaction => ΔG < 0 (what is ΔG?) thermodynamics 3. fast reaction => small activation energy kinetics Modes of Radioactive Decay (β, positron emission, electron capture become more understandable once protons and neutrons are known to be composed of quarks) 4 2 0n p + 0 e + ῡ p 0 n e + υ p + 0 e 0 n + υ neutron emission proton emission fission remember that s electrons have a finite probability of being found at the nucleus
3 The Valley of Stability: FIG I. Neutron Number Versus Atomic Number for Predicting the Type of Nuclides Radioactivity Of approximately 3200 known nuclides, only 279 (288) are stable. Their stability is highly correlated with the ratio of neutrons to protons: nuclide nucleus N/Z =.5 Z > 83 isotopes nuclides with the same Z but different N Z = 20 (Ca) # n = # p 00nn N/Z too large pp + 00 ee + ῡ N/Z = Z > 20 # n > # p (# n ~.5 # p) p 00 nn ee + υ Z > 83 (Bi) all nuclides unstable with respect to radioactive decay pp + 00 ee 00 nn + υ N/Z too small The stability of a nuclide also appears to depend upon whether the number of neutrons and protons is even or odd, with an even number of both types of nucleons predominating. The question is why?
4 - 4 - Nuclei Obey the Laws of Quantum Mechanics Maria Goepert Mayer (shell model of the nucleus). Both protons and neutrons are spin /2 particles (like electrons) and consequently can pair up, protons with protons and neutrons with neutrons. Therefore just like electrons, protons and neutrons possess angular momentum values of 0 (s), (l), 2 (d), 3 (f), etc. Nuclear structure behaves like atomic shell structure for electrons with a magic number indicating a closed shell of protons or of neutrons. Especially stable are nuclides with an even number of both protons and neutrons, doubly magic. Closed Electron Shells and Closed Nuclear Shells magic number special electrons nucleons stability [He] He (2p, 2n) [Ne] O (8p, 8n) [Ar] Ca (20p, 20n) [Kr] Ca, 28Ni [Xe] Ni (28p, 50n) [Rn] Pb (82p, 26n) 8 (n) 26 omit Angular momentum magic numbers 20.8 Nuclei Obey the Laws of Thermodynamics In thermodynamics, spontaneity of a reaction is given by G = H T S < 0. What determines the spontaneity of a nuclear reaction such as the emission of radioactivity? Mass Energy Relationship Einstein's E = mc 2 from Einstein's special theory of relativity EX. What is the change in mass in a typical exothermic reaction of 00 kj mol -? Mass is not conserved in a chemical reaction!
5 Four Forces of Nature. gravitational 2. electromagnetic strong nuclear range, 0-5 m ~ diameter of medium sized nucleus; hold nucleus together 4. weak nuclear range ~ 0-8 m ~ 0.% diameter of proton; changes one quark into another => radioactive decay, sun burning Nuclear Binding Energy and the Strong Force (force that holds nucleus together) mass defect Δm measure of strength of strong force which holds nucleus together The binding energy is the negative of the energy change to form a nucleus from its constituent protons and neutrons: AA Z p + (A Z) 0n ZZ X FIG II. Nuclear Exothermic Reaction 2 p + 2 0n Needs activation energy to surmount barrier 2 4 He Energetics of the nuclear reaction of two protons 4 and two neutrons forming an alpha particle, 2He, displayed in a reaction energy diagram. EX 2. What is the binding energy of a helium nucleus? ( ΔE of forming nucleus from constituents no electrons)
6 - 6 - FIG III. Binding Energy of Nuclides Note stable nuclides with magic numbers (both the number of protons and the number of neutrons are even): 4 6 2He, 8 O and the dominance of even numbers of nucleons. Only consider the nucleus (and its mass) when working with nuclear equations. The change in the Gibbs free energy for nuclear reactions is dominated by the enormous energy released. So the chemical criterion of G < 0 for a chemical reaction is basically E < 0 for a reaction involving the nucleus. Determine why the following reactions are spontaneous. EX 3. beta decay: C 7 N e + ῡ ( 6 C = , 7 N = ) EX 4. positron emission: 6 C 5 B e + υ ( 6 C =.0433,, 5 B = )
7 - 7 - EX 5. electron capture: 23 U + e neutrino) ( = ,, Pa = ) U Pa + υ (nucleus captures one of its orbiting electrons and emits a 9 EX 6. alpha decay: Th + He ( U = ,, Th ) U Nuclei Obey the Laws of Kinetics Nuclear decay follows first order kinetics and the different half-lives reflect the different rate constants which ultimately comes down to the difference in activation energies for the decay. first order: rate ~ k [A] where the rate constant k is given by the Arrhenius expression: k = A e Ea/RT
8 - 8 - Origin of Universe. before "big bang"? (Sound waves cannot propagate in space!) 2. Planck time 0-43 s region of diameter 0-33 cm, density of 0 94 g/cm 3, and temperature of 0 32 K ( teaspoon would weigh 00 million trillion trillion trillion pounds) s region of 00 cm at 0 28 K 4. s universe expanding mixture of neutrons, protons, electrons, positrons, photons, and neutrinos at 0 0 K (0 billion degrees) in a region of cm 0n H + 0 e + ῡ s 2 H, 3 He, 4 He nuclei created from fusion reactions (all the H atoms in the universe are created) 0 9 K ( billion degrees) 6. in 0 minutes 25% of the mass of the universe was 4 He and about 0.025% 2 H ,000 years - universe rapidly expands and cools, still very hot, 3000 K, neutral H and He formed earliest light detected from this period (cosmic microwave background radiation) 8. billion years gravitational forces pull nuclei together into primitive contracting stars billion years solar system and sun form billion years the age of our universe, K, region at least 0 29 cm universe: 4.9% normal matter, 26.8% dark matter, 68.3% dark energy Elements Formed in the Life Cycle of a Star Nuclear Fusion and Nucleosynthesis. gravitational forces pull nuclei together heating core to 0 7 K where fusion H burning: 4 4 H 2He e + 2 υ + 2γ + energy after several billion years about 0% of H consumed (our sun consists of 73% hydrogen, 26% helium and % other elements) 2. star contracts further with hydrogen depleted, temperature about K, and starts burning He causing expansion (about 00 times) into a red giant in core unstable 8 Be forms initiating a chain of fusion reactions with α particles 2 4 He 8 Be [+ 4 He] 2 C [+ 4 He] 6 O [+ 4 He] 20 Ne [+ 4 He] 24 Mg consumed for about 0 million years with heavier elements forming a core 3. core contracts with depletion of lighter elements, heats, expands into a red supergiant in core (7 0 8 K) carbon and oxygen burn: 2 C + 2 C 23 Na + H 2 C + 6 O 28 Si + γ fusion reactions with α particles form nuclei through 40 Ca further contraction and heating to K ultimately leads to 56 Fe, 58 Fe, and 62 Ni, nuclei with highest binding energies 4. small and medium-sized stars: endothermic fusion process to form higher elements cannot furnish energy to sustain star which cools to a small, dense white dwarf; larger stars: when fuel of core consumed it implodes within a second - many Fe and Ni nuclei break down into neutrons and protons protons capture electrons to form an incredibly dense neutron star while outer layers explode into a supernova sending out debris which can eventually coalesce into a secondgeneration star neutron capture in supernova explosion forms heavier elements (all nuclei heavier than Fe thought to originate from supernova explosions); alternatively massive stars can form black holes after a supernova explosion.
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