PÁZMÁNY PÉTER CATHOLIC UNIVERSITY Consortium members SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER

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SEMMELWEIS UNIVERSITY PÁZMÁNY PÉTER CATHOLIC UNIVERSITY Development of Complex

framework** Consortium leader PÁZMÁNY PÉTER CATHOLIC UNIVERSITY Consortium members

the support of the European Union and has been co-financed by the European Social

fejlesztése konzorciumi keretben ***A projekt az Európai Unió támogatásával, az

1 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 TÁMOP /2/A/KMR

2 WORLD OF MOLECULES (Molekulák világa) PROPERTIES OF ATOMS (Az atomok tulajdonságai) KRISTÓF IVÁN TÁMOP /2/A/KMR

3 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 TÁMOP /2/A/KMR

Previously - Rutherford s atom model (He) http://http://en.wikipedia.

4 Previously - Rutherford s atom model (He) TÁMOP /2/A/KMR

Previously - Elementary particles Elementary particles Fermions Quarks Leptons Bosons Gauge bosons Fundamental interactions strong nuclear force weak nuclear force

5 Previously - Elementary particles Elementary particles Fermions Quarks Leptons Bosons Gauge bosons Fundamental interactions strong nuclear force weak nuclear force electromagnetic force gravitational force TÁMOP /2/A/KMR

Previously Periodic table of elements http://en.wikipedia.

6 Previously Periodic table of elements TÁMOP /2/A/KMR

7 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 TÁMOP /2/A/KMR

8 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 TÁMOP /2/A/KMR

9 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 TÁMOP /2/A/KMR

10 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 TÁMOP /2/A/KMR

Isotopes stability number of neutrons number of protons http://en.wikipedia.

11 Isotopes stability number of neutrons number of protons TÁMOP /2/A/KMR

12 Isotopes Types of decay TÁMOP /2/A/KMR

from the Chart of Nuclides database, http://www.nndc.

13 Table of isotopes (half life representation) National Nuclear Data Center, information extracted from the Chart of Nuclides database, TÁMOP /2/A/KMR

14 Table of isotopes (decay mode representation) National Nuclear Data Center, information extracted from the Chart of Nuclides database, TÁMOP /2/A/KMR

15 Isotopes of Carbon TÁMOP /2/A/KMR

16 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: mol -1 Different isotopes of the same chemical element have different nuclear stabilities TÁMOP /2/A/KMR

17 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 TÁMOP /2/A/KMR

18 Main decay modes TÁMOP /2/A/KMR

Radioactivity Other decay modes Proton emission, neutron emission, double proton emission, spontaneous fission Positron emission (β + ), electron capture,

19 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 TÁMOP /2/A/KMR

Decay modes on the table of nuclides http://en.wikipedia.

20 Decay modes on the table of nuclides TÁMOP /2/A/KMR

21 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 TÁMOP /2/A/KMR

22 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 TÁMOP /2/A/KMR

Decay chain of Uranium-238 from 238 U (uranium) to 206 Pb (lead) http://en.wikipedia.

23 Decay chain of Uranium-238 from 238 U (uranium) to 206 Pb (lead) TÁMOP /2/A/KMR

24 Table of isotopes (decay mode representation) Z N National Nuclear Data Center, information extracted from the Chart of Nuclides database, TÁMOP /2/A/KMR

25 TÁMOP /2/A/KMR

Electron configuration of atoms http://en.wikipedia.

26 Electron configuration of atoms TÁMOP /2/A/KMR

27 Bohr-Sommerfeld model TÁMOP /2/A/KMR

28 Bohr-Sommerfeld model TÁMOP /2/A/KMR

29 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) TÁMOP /2/A/KMR

30 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 TÁMOP /2/A/KMR

31 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) TÁMOP /2/A/KMR

32 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 TÁMOP /2/A/KMR

33 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 =18 4 N =32 5 O =50 6 P =72 7 Q = TÁMOP /2/A/KMR

34 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) TÁMOP /2/A/KMR

35 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 TÁMOP /2/A/KMR

36 Atomic orbitals TÁMOP /2/A/KMR

37 The electron structure of Hydrogen 1s 1 n=1 l=0 (s orbital) m=0 s =-1/2 or +1/ TÁMOP /2/A/KMR

38 The electron structure of Helium 1s 2 n=1 (closed shell) l=0 (s orbital) m=0 s =-1/2 and +1/ TÁMOP /2/A/KMR

39 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/ TÁMOP /2/A/KMR

40 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/ TÁMOP /2/A/KMR

41 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/ TÁMOP /2/A/KMR

42 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 TÁMOP /2/A/KMR

43 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/ TÁMOP /2/A/KMR

Periodic table electron configurations http://en.wikipedia.

44 Periodic table electron configurations TÁMOP /2/A/KMR

45 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) TÁMOP /2/A/KMR

46 Electron configurations 10. Ne (He)2s 2 2p Na (Ne)3s Mg (Ne)3s Al (Ne)3s 2 3p Si (Ne)3s 2 3p P (Ne)3s 2 3p S (Ne)3s 2 3p Cl (Ne)3s 2 3p Ar (Ne)3s 2 3p TÁMOP /2/A/KMR

47 Electron configurations 19. K (Ar)4s Ca (Ar)4s Sc (Ar)4s 2 3d Ti (Ar)4s 2 3d V (Ar)4s 2 3d Cr (Ar)4s 1 3d Mn (Ar)4s 2 3d Fe (Ar)4s 2 3d Co (Ar)4s 2 3d TÁMOP /2/A/KMR

48 Electron configurations 28. Ni (Ar)4s 2 3d Cu (Ar)4s 1 3d Zn (Ar)4s 2 3d Ga (Ar)4s 2 3d 10 4p Ge (Ar)4s 2 3d 10 4p As (Ar)4s 2 3d 10 4p Se (Ar)4s 2 3d 10 4p Br (Ar)4s 2 3d 10 4p Kr (Ar)4s 2 3d 10 4p TÁMOP /2/A/KMR

49 Electron configurations 37. Rb (Kr)5s Sr (Kr)5s Y (Kr)5s 2 4d Zr (Kr)5s 2 4d The filling of atomic orbitals is not in numerical order... but by energy levels TÁMOP /2/A/KMR

50 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 TÁMOP /2/A/KMR

51 Aufbau principle filling of orbitals TÁMOP /2/A/KMR

52 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 TÁMOP /2/A/KMR

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