SEMMELWEIS UNIVERSITY PÁZMÁNY PÉTER CATHOLIC UNIVERSITY Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework** Consortium leader PÁZMÁNY PÉTER CATHOLIC UNIVERSITY Consortium members SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund *** **Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben ***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg. 2011.10.06.. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 1
WORLD OF MOLECULES (Molekulák világa) PROPERTIES OF ATOMS (Az atomok tulajdonságai) KRISTÓF IVÁN 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 2
Previously - Periodic system of elements 1. History of elements 2. Rutherford s scattering experiment 3. Bohr-Sommerfeld model 4. Elementary particles 5. Fundamental interaction 6. Periodic system/table of elements [an interactive periodic table is available at www.ptable.com] 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 3
Previously - Rutherford s atom model (He) http://http://en.wikipedia.org/wiki/file:helium_atom_qm.svg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 4
Previously - Elementary particles Elementary particles Fermions Quarks Leptons Bosons Gauge bosons Fundamental interactions strong nuclear force weak nuclear force electromagnetic force gravitational force http://en.wikipedia.org/wiki/file:standard_model_of_elementary_particles.svg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 5
Previously Periodic table of elements http://en.wikipedia.org/wiki/periodic_table 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 6
1. Nucleus 2. Isotopes 3. Tables of isotopes 4. Radioactivity 5. Decay modes 6. Bohr-Sommerfeld model 7. Quantum numbers 8. Electron structure 9. Examples Table of Contents 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 7
Nucleus Nucleus is made up of protons and neutrons Atomic number (Z) number of protons Number of neutrons (N) Mass number (A) Sum of protons and neutrons A=Z+N 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 8
Isotope Same chemical element Atomic number (Z) is the same Different number of neutrons (N) Mass number (A) different! e.g.: Carbon A 12 6 C 13 6 C 14 6 C Z 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 9
number of protons (Z) vs. neutrons (N) all isotopes of the same element are present at constant Z (atomic number) different representations half-life decay mode Table of isotopes table of nuclides Checker board for following radioactive decay chains 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 10
Isotopes stability number of neutrons number of protons http://en.wikipedia.org/wiki/file:isotopes_and_half-life.svg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 11
Isotopes Types of decay http://commons.wikimedia.org/wiki/file:table_isotopes_en.svg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 12
Table of isotopes (half life representation) National Nuclear Data Center, information extracted from the Chart of Nuclides database, http://www.nndc.bnl.gov/chart/ 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 13
Table of isotopes (decay mode representation) National Nuclear Data Center, information extracted from the Chart of Nuclides database, http://www.nndc.bnl.gov/chart/ 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 14
Isotopes of Carbon 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 15
Isotopes of Carbon Carbon-12 ( 12 C) is used as atomic mass unit: 1 atomic mass unit is 1/12th of 1 mole 12 C. Or 1 mole is the amount of atoms in 12grams of 12 C. It is the Avogadro number: 6.022 10 23 mol -1 Different isotopes of the same chemical element have different nuclear stabilities. 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 16
Radioactivity Main decay modes of unstable nuclei Alpha decay The release of 2 protons and 2 neutrons (i.e. a 4 He nucleus), A 2 =A 1-4; Z 2 =Z 1-2 Beta decay Release of an electron from the nucleus, Z 2 =Z 1 +1 Gamma decay High energy X-rays 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 17
Main decay modes http://en.wikipedia.org/wiki/file:alfa_beta_gamma_radiation.svg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 18
Radioactivity Other decay modes Proton emission, neutron emission, double proton emission, spontaneous fission Positron emission (β + ), electron capture, double beta decay, double electron capture, double positron emission, electron capture + positron emission 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 19
Decay modes on the table of nuclides http://en.wikipedia.org/wiki/file:radioactive_decay_modes.svg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 20
Radioactive decay chains half life: time required for half of the amount to decay t 1/2 Decay constant λ t = 1 2 ln(2) λ N ( t) = N 0 e λ t 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 21
Radioactive decay chains Decay chains occur when the resulting nucleus is also unstable. Decay chains have different decay modes and rates dependent on the properties of the unstable nuclei. Decay stops at a stable nucleus 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 22
Decay chain of Uranium-238 from 238 U (uranium) to 206 Pb (lead) http://en.wikipedia.org/wiki/file:decay_chain%284n%2b2,_uranium_series%29.png 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 23
Table of isotopes (decay mode representation) Z N National Nuclear Data Center, information extracted from the Chart of Nuclides database, http://www.nndc.bnl.gov/chart/ 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 24
http://en.wikipedia.org/wiki/table_of_nuclides 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 25
Electron configuration of atoms http://en.wikipedia.org/wiki/file:electron_configuration_table.jpg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 26
Bohr-Sommerfeld model http://en.wikipedia.org/wiki/file:bohr_atom_model_english.svg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 27
Bohr-Sommerfeld model http://en.wikipedia.org/wiki/file:sommerfeld_ellipses.svg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 28
Bohr-Sommerfeld model The electrons can only travel in special orbits at discrete distances from the nucleus with specific energies The electrons do not lose energy as they travel on these orbits in contrast with classical electrodynamics The angular momentum of electrons are integer multiples of the reduced Plack s constant (h/2π) 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 29
Bohr-Sommerfeld model Angular momentum and wavelength h mv n r n = n, where n 2π h h 2π rn λ = = p mv n Radius of orbits n = 1,2, h 2π r n nλ n = = mv The circumference of orbits are integer multiples of the electron s wavelength n 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 30
Bohr-Sommerfeld model 4 quantum numbers uniquely represent the state of the electron inside an atom n - principal quantum number describes the electron shell (n=1, 2,..., 6) l - azimuthal q. n. or angular momentum describes the subshell (l =0, 1..., n-1) m - magnetic quantum number describes the subshell s shape (m= -l,..., 0,..., l) s - spin quantum number (s =-1/2 or +1/2) 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 31
Bohr-Sommerfeld model name symbol meaning Value Principal quantum number Azimuthal quantum number Magnetic quantum number n Shell (distance from nucleus) n=1,2,3...,6 l Subshell (shape of orbital) l=0,1,..., n-1 m energy shift (orientation of the subshell's shape) Spin quantum number s Spin of the electron m=-l,...,0,..., l s = 1 2 or + 1 2 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 32
Bohr-Sommerfeld model value name of shell number of electrons in shell Principal quantum number (n) 1 K 2 2 L 2+6=8 3 M 2+6+10=18 4 N 2+6+10+14=32 5 O 2+6+10+14+18=50 6 P 2+6+10+14+18+22=72 7 Q 2+6+10+14+18+22+26=98 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 33
Bohr-Sommerfeld model value name of subshell number of electrons Azimuthal quantum number (l) 0 s (sharp) 2 1 p (principal) 6 2 d (diffuse) 10 3 f (fundamental) 14 4 g 18 5 h 22 6 i 26 Shells g, h, i are not occupied in naturally occuring elements due to their high orbital energy levels. (see Aufbau principle) 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 34
Bohr-Sommerfeld model Filling up the atomic orbitals with electrons Pauli s (exclusion) principle: no two electrons can have the same four quantum numbers (n, l, m, s) Hund s rules: for a given electron configuration, the maximum multiplicity has the lowest energy pairing of electrons is an unfavorable process 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 35
Atomic orbitals http://en.wikipedia.org/wiki/atomic_orbital 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 36
The electron structure of Hydrogen 1s 1 n=1 l=0 (s orbital) m=0 s =-1/2 or +1/2 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 37
The electron structure of Helium 1s 2 n=1 (closed shell) l=0 (s orbital) m=0 s =-1/2 and +1/2 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 38
The electron structure of Carbon 1s 2 2s 2 2p 2 example: n=2 l=1 (p orbital) m=0 s =-1/2 or +1/2 http://en.wikipedia.org/wiki/file:p2m0.png 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 39
The electron structure of Nitrogen 1s 2 2s 2 2p 3 example: n=2 l=1 (p orbital) m=1 s =-1/2 or +1/2 http://en.wikipedia.org/wiki/file:p2m1.png 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 40
The electron structure of Oxygen 1s 2 2s 2 2p 4 example: n=2 l=1 (p orbital) m=-1 s =-1/2 or +1/2 http://en.wikipedia.org/wiki/file:p2m-1.png 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 41
The electron structure of Neon 1s 2 2s 2 2p 6 n=2 (closed shell) all atomic orbitals of shells 1 and 2 are filled http://en.wikipedia.org/wiki/file:neon-glow.jpg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 42
The electron structure of Radium 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 5d 10 6p 6 7s 2 n=7 l=0 (s orbital) m=0 s =-1/2 and +1/2 http://en.wikipedia.org/wiki/file:s7m0.png 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 43
Periodic table electron configurations http://en.wikipedia.org/wiki/periodic_table_%28electron_configurations%29 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 44
Electron configurations 1. H 1s 1 2. He 1s 2 3. Li (He)2s 1 4. Be (He)2s 2 5. B (He)2s 2 2p 1 6. C (He)2s 2 2p 2 7. N (He)2s 2 2p 3 8. O (He)2s 2 2p 4 9. F (He)(2s) 2 (2p) 5 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 45
Electron configurations 10. Ne (He)2s 2 2p 6 11. Na (Ne)3s 1 12. Mg (Ne)3s 2 13. Al (Ne)3s 2 3p 1 14. Si (Ne)3s 2 3p 2 15. P (Ne)3s 2 3p 3 16. S (Ne)3s 2 3p 4 17. Cl (Ne)3s 2 3p 5 18. Ar (Ne)3s 2 3p 6 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 46
Electron configurations 19. K (Ar)4s 1 20. Ca (Ar)4s 2 21. Sc (Ar)4s 2 3d 1 22. Ti (Ar)4s 2 3d 2 23. V (Ar)4s 2 3d 3 24. Cr (Ar)4s 1 3d 5 25. Mn (Ar)4s 2 3d 5 26. Fe (Ar)4s 2 3d 6 27. Co (Ar)4s 2 3d 7 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 47
Electron configurations 28. Ni (Ar)4s 2 3d 8 29. Cu (Ar)4s 1 3d 10 30. Zn (Ar)4s 2 3d 10 31. Ga (Ar)4s 2 3d 10 4p 1 32. Ge (Ar)4s 2 3d 10 4p 2 33. As (Ar)4s 2 3d 10 4p 3 34. Se (Ar)4s 2 3d 10 4p 4 35. Br (Ar)4s 2 3d 10 4p 5 36. Kr (Ar)4s 2 3d 10 4p 6 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 48
Electron configurations 37. Rb (Kr)5s 1 38. Sr (Kr)5s 2 39. Y (Kr)5s 2 4d 1 40. Zr (Kr)5s 2 4d 2 41.... The filling of atomic orbitals is not in numerical order... but by energy levels. 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 49
Aufbau principle The orbitals of lower energy are filled in first with the electrons Madelung s rule (Klechowski) Orbitals are filled in the order of increasing n+l if equal, then the one with lower n is filled first This results in the order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, and 7p 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 50
Aufbau principle filling of orbitals http://en.wikipedia.org/wiki/file:klechkowski_rule_2.svg 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 51
Next - Dual nature of electrons 1. Dual nature of light 2. Particle nature of electron 3. Wave nature of electrons (de Broglie) 4. Particle-wave duality of electrons 5. Schrödinger equation 6. The wave functions of the electron in 1D 7. The wave functions of the electron in a harmonic oscillator 8. The wave functions of the electron in 3D 9. The wave functions of the electron in the Hydrogen atom 10. Short introduction to complex numbers 2011.10.06. TÁMOP 4.1.2-08/2/A/KMR-2009-0006 52