General and Inorganic Chemistry I.

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1 General and Inorganic Chemistry I. Lecture 2 István Szalai Eötvös University István Szalai (Eötvös University) Lecture 2 1 / 44

2 Outline 1 Introduction 2 Standard Model 3 Nucleus 4 Electron István Szalai (Eötvös University) Lecture 2 2 / 44

3 Introduction Atoms Image of surface reconstruction on a clean Gold (Au(100)) surface, as visualized using scanning tunneling microscopy. The individual atoms composing the material are visible. István Szalai (Eötvös University) Lecture 2 3 / 44

4 Introduction Atoms A depiction of the atomic structure of the helium atom. István Szalai (Eötvös University) Lecture 2 4 / 44

Introduction Rutherford suggested that a large amount of the atom s charge and mass is instead concentrated into a very physically-small (as compared with the size of the atom) region, giving it a

5 Introduction Rutherford suggested that a large amount of the atom s charge and mass is instead concentrated into a very physically-small (as compared with the size of the atom) region, giving it a very high electric field. Outside of this central charge (later termed the nucleus), he proposed that the atom was mostly empty space. István Szalai (Eötvös University) Lecture 2 5 / 44 Rutherford experiment

6 Introduction Foundations of Chemistry Atoms: the smallest particle of an element that maintains its chemical identity. Structure of atoms: The diameter of an atom is m (0.1 nm). The nucleus contains protons and neutrons. The diameter of a nucleus is m. Particle Mass Charge proton kg C neutron kg none electron kg C m(p + ) m(e ) 1840 István Szalai (Eötvös University) Lecture 2 6 / 44

7 Standard Model Standard Model Model of fundamental particles and their interactions István Szalai (Eötvös University) Lecture 2 7 / 44

8 Standard Model Fundamental particles István Szalai (Eötvös University) Lecture 2 8 / 44

9 Standard Model Antiparticles Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron (e + ). Particle-antiparticle pairs can annihilate each other, producing photons; since the charges of the particle and antiparticle are opposite, charge is conserved. For example, the antielectrons produced in natural radioactive decay quickly annihilate themselves with electrons, producing pairs of gamma rays. e + e + 2γ István Szalai (Eötvös University) Lecture 2 9 / 44

10 Standard Model Fundamental particles 12 fermions (spin-1/2 particles): 6 quarks and 6 leptons They governed by the Pauli principles. generation quarks Q/e Leptons Q/e 1st d (down) -1/3 electron neutrino ν e 0 1st u (down) +2/3 electron e -1 2nd s (strange) -1/3 muon neutrino ν µ 0 2nd c (charme) +2/3 muono µ -1 3rd b (bottom) -1/3 tau neutrino ν τ 0 3rd t (top) +2/3 tau τ -1 István Szalai (Eötvös University) Lecture 2 10 / 44

11 Standard Model Fundamental particles Leptons: spin 1/2 They governed by the Pauli principles. 6 leptons and their corresponding antiparticles. They are structureless, point-like particles. They have nonzero magnetic and electric dipol moment. 1 MeV/c 2 = kg Leptons Q/e Mass (MeV/c 2 ) electron neutrino ν e 0 < electron e muon neutrino ν µ 0 < 0.27 muon µ tau neutrino ν τ 0 < 31 tau τ István Szalai (Eötvös University) Lecture 2 11 / 44

12 Standard Model Fundamental particles Quarks: spin 1/2 They governed by the Pauli principles. 6 quarks and their corresponding antiparticles. They are structureless, point-like particles. Quarks are never directly observed or found in isolation; they can be found only within hadrons. Quarks Q/e Mass (MeV/c 2 ) d (down) -1/ u (down) +2/ s (strange) -1/ c (charme) +2/ b (bottom) -1/ t (top) +2/ ± MeV/c 2 = kg István Szalai (Eötvös University) Lecture 2 12 / 44

13 Standard Model Fundamental particles Bosons: elementary particles with integer spin. They are not governed by the Pauli principles. A quantum state can be occupied by arbitrary number of bosons. Gauge bosons are mediators of the interactions. Graviton: (has not yet been detected experimentally): spin 2. Photon: spin 1, rest mass 0, charge 0. (Free photons are the energy quanta of light, virtual photons are the mediators of the electromagnetic interaction) W ±, Z 0 bosons: spin 1 (mediator of the weak interaction), mass 80 and 91 GeV/c 2. Gluons: (they bind the quarks together), spin 1, charge 0, mass 0. István Szalai (Eötvös University) Lecture 2 13 / 44

14 Standard Model Fundamental interactions Gravitation: is the only interaction that acts on all particles having mass; has an infinite range; cannot be absorbed, transformed, or shielded against; always attracts and never repels; the weakest of the four interactions. F g = G M1 M 2 r 2 G = Nm 2 /kg 2 István Szalai (Eötvös University) Lecture 2 14 / 44

15 Standard Model Fundamental interactions Gravitation: F g = G M1 M 2 r 2 G = Nm 2 /kg 2 Problem: Calculate the gravity force between two protons if the distance between them is m (m p = kg)! F g = Nm 2 /kg 2 ( kg) 2 (10 15 m) 2 F g = N (attraction) István Szalai (Eötvös University) Lecture 2 15 / 44

16 Standard Model Fundamental interactions Electromagnetism: acts between electrically charged particles; has an infinite range; can be attractive and repulsive; stronger than gravitation fundamentally determines all macroscopic, and many atomic level, properties of the chemical elements, including all chemical bonding. F c = k Q1 Q 2 r 2 k = Nm 2 /C 2 István Szalai (Eötvös University) Lecture 2 16 / 44

17 Standard Model Fundamental interactions Electromagnetism: F c = k Q1 Q 2 r 2 k = Nm 2 /C 2 Problem: Calculate the Coulomb force between two protons if the distance between them is m (Q p = C)! F c = Nm 2 /C 2 ( C) 2 (10 15 m) 2 F c = N (repulsion) István Szalai (Eötvös University) Lecture 2 17 / 44

18 Standard Model Fundamental interactions Gravity vs. Electromagnetism Problem: Calculate the ratio of gravity and Coulomb force between two protons if the distance between them is m! F g = N F c = N F g F c = N N F g F c = Lesson: on the atomic scale the gravity is negligible compare to the Coulomb force. István Szalai (Eötvös University) Lecture 2 18 / 44

19 Standard Model Fundamental interactions Weak interaction: acts between leptons and hadrons; its most familiar effect is radioactivity, beta decay (or the emission of electrons by neutrons or positrons by protons in atomic nuclei); has a finite range m; weaker than electromagnetism other than gravity, it is the only force affecting neutrinos. it is necessary for the buildup of heavy nuclei. István Szalai (Eötvös University) Lecture 2 19 / 44

20 Standard Model Fundamental interactions Strong interaction: acts between quarks; the residual strong force binds protons and neutrons together to form the nucleus of an atom; has a finite range m; stronger than electromagnetism (the force between quarks 10 5 N) István Szalai (Eötvös University) Lecture 2 20 / 44

21 Standard Model Fundamental interactions interaction type strength (rel.) range (m) field quanta strong gluons g electromagnetic 10 2 photons γ weak bosons W ±, Z 0 gravitation gravitons István Szalai (Eötvös University) Lecture 2 21 / 44

22 Standard Model Nucleons Proton mass (kg) mass (MeV/c 2 ) charge (C) lifetime year spin ( ) 1/2 magnetic moment µ K µ K = e /(2m proton ) p n + e + + ν e István Szalai (Eötvös University) Lecture 2 22 / 44

Standard Model Nucleons Neutron mass (kg) 1.675 10 27 mass (MeV/c 2 ) 939.

23 Standard Model Nucleons Neutron mass (kg) mass (MeV/c 2 ) charge (C) 0 lifetime 889 s spin ( ) 1/2 magnetic moment µ K µ K = e /(2m proton ) n p + e + ν e István Szalai (Eötvös University) Lecture 2 23 / 44

24 Standard Model Structure of atoms István Szalai (Eötvös University) Lecture 2 24 / 44

25 Nucleus The Nucleus The protons and neutrons are hold together by residual strong interaction in the nucleus. This force is effective over a very short range and causes an attraction between any pair of nucleons. The electrostatic repulsion between protons destabilizes the nucleus. István Szalai (Eötvös University) Lecture 2 25 / 44

26 Nucleus The Nucleus The isotopes have same number of protons and different number of neutrons. Radioactive isotopes are unstable nuclei. e.g. 12 6C stable, 13 6C stable, a 14 6C radioactive isotopes. Nuclei of all elements have approximately the same density: g/cm 3. The nuclear binding energy (mass deficiency): E nuclear binding = m c 2 E nuclear binding = (N p m p + N n m n m nucleus ) c 2 István Szalai (Eötvös University) Lecture 2 26 / 44

27 Nucleus Nuclear binding energy Example: Each atom of 35 17Cl contains 17 protons, and 18 neutrons. protons: amu = amu, neutrons: amu = amu calculated mass: amu, actual mass: , m = amu or g/mol E nuclear binding = m c 2 = kg/mol ( m/s) 2 = J/mol (for comparision the energy of covalent bonds is J/mol) István Szalai (Eötvös University) Lecture 2 27 / 44

28 Nucleus The Nucleus For low atomic numbers, the most stable nuclides have equal numbers of protons and neutrons (N = Z). Most naturally occurring nuclides have even numbers of protons and even numbers of neutrons. All nuclides with atomic number greater than 83 are beyond the band of stability. There are about 254 stable isotopes and thousands unstable ones. István Szalai (Eötvös University) Lecture 2 28 / 44

29 Nucleus Radioactive Decay There are many nuclear isotopes which are unstable and emit some kind of radiation. A decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide, transforms to an atom with a nucleus in a different state, or to a different nucleus containing different numbers of protons and neutrons. Either of these products is named the daughter nuclide. In some decays the parent and daughter are different chemical elements, and thus the decay process results in nuclear transmutation. István Szalai (Eötvös University) Lecture 2 29 / 44

30 Nucleus Radioactive Decay α-emission: for (N> 80) Po Pb He β -emission: neutron-rich nuclei 14 6 C 14 7 N + e + ν e β + -emission: neutron-poor nuclei 15 8 O 15 7 N + e+ + ν e electron capture: neutron-poor nuclei K + e Ar + ν e γ-emission: X X + γ István Szalai (Eötvös University) Lecture 2 30 / 44

31 Nucleus Radioactive Decay Problem: Predict the type of radioactive decay process that is likely for each of the following nuclides: U, 8 5B and 68 29Cu! U Th + 4 2He 8 5B 8 4Be + e + + ν e 68 29Cu 68 30Zn + e + ν e István Szalai (Eötvös University) Lecture 2 31 / 44

32 Nucleus Radioactive Decay N is the actual number of particles in the sample. N 0 is the initial number of particles in the sample. The half-life (t 1/2 ), is the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value. ln N 0 N = kt k = ln 2 t 1/2 István Szalai (Eötvös University) Lecture 2 32 / 44

33 Nucleus Radioactive Decay István Szalai (Eötvös University) Lecture 2 33 / 44

34 Nucleus Radioactive Decay Problem: A sample of sodium-24 was administered to a patient to test for faulty blood circulation by comparing the radioactivity reaching various parts of the body. What fraction of the sodium-24 nuclei would remain undecayed after 12.0 h? The half-life is 15.0h. If a sample contains 6.0 µg of 24 Na, how many micro- grams remain after 12.0 h? k = ln 2 t 1/2 = ln 2 15h = h 1 ln N 0 N = kt = h 1 12h =.5544 N N 0 = e = m = 6µg = 3.4µg István Szalai (Eötvös University) Lecture 2 34 / 44

35 Nucleus Nuclear Fission István Szalai (Eötvös University) Lecture 2 35 / 44

36 Nucleus Nuclear Fission Fission: U n U U Sm Zn n + energy U La Br n + energy U Ba Kr n + energy... István Szalai (Eötvös University) Lecture 2 36 / 44

37 Nucleus Nuclear Fission István Szalai (Eötvös University) Lecture 2 37 / 44

Nucleus Nuclear Fusion 2 1 H + 3 1 H 4 2 He + 1 0 n +

38 Nucleus Nuclear Fusion 2 1 H H 4 2 He n + energy István Szalai (Eötvös University) Lecture 2 38 / 44

39 Nucleus Nuclear Fusion The proton-proton chain dominates in stars the size of the Sun or smaller. István Szalai (Eötvös University) Lecture 2 39 / 44

40 Nucleus Nuclear Fusion The CNO cycle dominates in stars heavier than the Sun. István Szalai (Eötvös University) Lecture 2 40 / 44

41 Nucleus Nuclear Fission and Fusion István Szalai (Eötvös University) Lecture 2 41 / 44

42 Electron Electron The discovery of electrons: J. J. Thomson, 1897 (charge/mass ratio) Millikan oil-drop experiment, 1909 By applying a potential difference across the plates, a uniform electric field is created in the space between them. A fine mist of oil droplets was sprayed into a chamber above the plates. Some oil drops became electrically charged through friction with the nozzle as they were sprayed. István Szalai (Eötvös University) Lecture 2 42 / 44

43 Electron Electron Millikan oil-drop experiment F g = F e mg = EQ 4 3 r 3 π(ρ oil ρ air )g = V d Q Q = NQ e = d V 4 3 r 3 π(ρ oil ρ air )g (N is an integer number) István Szalai (Eötvös University) Lecture 2 43 / 44

44 Electron István Szalai (Eötvös University) Lecture 2 44 / 44

THE STANDARD MODEL OF MATTER

VISUAL PHYSICS ONLINE THE STANDARD MODEL OF MATTER The "Standard Model" of subatomic and sub nuclear physics is an intricate, complex and often subtle thing and a complete study of it is beyond the scope