number of neutrons

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.

PÁZMÁNY PÉTER CATHOLIC UNIVERSITY SEMMELWEIS

UNIVERSITY

WORLD OF MOLECULES

PROPERTIES OF ATOMS

(Molekulák világa)

(Az atomok tulajdonságai)

KRISTÓF IVÁN

semmelweis-egyetem.hu

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

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]

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Previously - Rutherford’s atom model (He)

http://http://en.wikipedia.org/wiki/File:Helium_atom_QM.svg

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Previously - Elementary particles

http://en.wikipedia.org/wiki/File:Standard_Model_of_Elementary_Particles.svg

Elementary particles

• Fermions

• Quarks

• Leptons

• Bosons

• Gauge bosons

Fundamental interactions

• strong nuclear force

• weak nuclear force

• electromagnetic force

• gravitational force

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

http://en.wikipedia.org/wiki/Periodic_table

Previously – Periodic table of elements

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

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

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

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Nucleus

Same chemical element

• Atomic number (Z) is the same

Different number of neutrons (N) Mass number (A) different!

e.g.: Carbon

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Isotope

C

C

C ¹³ ₆ ¹⁴ ₆

12 6

A

Z

• 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

• Checker board for following radioactive decay chains

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Table of isotopes – table of nuclides

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Isotopes

http://en.wikipedia.org/wiki/File:Isotopes_and_half-life.svg

number of protons

number of neutrons

stability

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Isotopes

http://commons.wikimedia.org/wiki/File:Table_isotopes_en.svg

Types of

decay

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Table of isotopes (half life representation)

National Nuclear Data Center, information extracted from the Chart of Nuclides database, http://www.nndc.bnl.gov/chart/

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Table of isotopes (decay mode representation)

National Nuclear Data Center, information extracted from the Chart of Nuclides database, http://www.nndc.bnl.gov/chart/

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

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.

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Isotopes of Carbon

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

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Radioactivity

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Main decay modes

http://en.wikipedia.org/wiki/File:Alfa_beta_gamma_radiation.svg

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

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Radioactivity

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Decay modes on the table of nuclides

http://en.wikipedia.org/wiki/File:Radioactive_decay_modes.svg

• half life: time required for half of the amount to decay

t _1/2

• Decay constant λ

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Radioactive decay chains

λ

) 2 ln(

2

1 =

t N ( t ) = N ₀ ⋅ e ^{− λ ⋅ t}

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

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Radioactive decay chains

World of Molecules: Properties of atoms

from ²³⁸ U (uranium) to ²⁰⁶ Pb (lead)

semmelweis-egyetem.hu

Decay chain of Uranium-238

http://en.wikipedia.org/wiki/File:Decay_chain%284n%2B2,_Uranium_series%29.PNG

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Table of isotopes (decay mode representation)

National Nuclear Data Center, information extracted from the Chart of Nuclides database, http://www.nndc.bnl.gov/chart/

Z

N

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

http://en.wikipedia.org/wiki/Table_of_nuclides

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Electron configuration of atoms

http://en.wikipedia.org/wiki/File:Electron_Configuration_Table.jpg

Bohr-Sommerfeld model

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

http://en.wikipedia.org/wiki/File:Bohr_atom_model_English.svg

Bohr-Sommerfeld model

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

http://en.wikipedia.org/wiki/File:Sommerfeld_ellipses.svg

Bohr-Sommerfeld model

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

• 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)

Bohr-Sommerfeld model

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

• Angular momentum and wavelength

• Radius of orbits

• The circumference of orbits are integer multiples of the electron’s wavelength

, … 2 , 1 where

2 ,

h =

= n n

r m

v π

n r mv

h p

n n

λ = ^h = ⇒ ² π

λ

π n

n m r

n

n = =

v

2 h

Bohr-Sommerfeld model

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

• 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)

Bohr-Sommerfeld model

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

name symbol meaning Value

Principal quantum number

n Shell (distance from nucleus) n=1,2,3...,6 Azimuthal quantum

number

l Subshell (shape of orbital) l=0,1, ..., n-1 Magnetic quantum

number

m energy shift (orientation of the subshell's shape)

m=-l, ...,0, ..., l Spin quantum number s Spin of the electron

2 or 1 2

1 +

−

=

s

Bohr-Sommerfeld model

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

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

Bohr-Sommerfeld model

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

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)

Bohr-Sommerfeld model

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

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

Atomic orbitals

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

http://en.wikipedia.org/wiki/Atomic_orbital

World of Molecules: Properties of atoms

1s ¹ n=1

l=0 (s orbital) m=0

s =-1/2 or +1/2

The electron structure of Hydrogen

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

1s ²

n=1 (closed shell) l=0 (s orbital)

m=0

s =-1/2 and +1/2

The electron structure of Helium

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

1s ² 2s ² 2p ² example:

n=2

l=1 (p orbital) m=0

s =-1/2 or +1/2

The electron structure of Carbon

semmelweis-egyetem.hu

http://en.wikipedia.org/wiki/File:P2M0.png

World of Molecules: Properties of atoms

1s ² 2s ² 2p ³ example:

n=2

l=1 (p orbital) m=1

s =-1/2 or +1/2

The electron structure of Nitrogen

semmelweis-egyetem.hu

http://en.wikipedia.org/wiki/File:P2M1.png

World of Molecules: Properties of atoms

1s ² 2s ² 2p ⁴ example:

n=2

l=1 (p orbital) m=-1

s =-1/2 or +1/2

The electron structure of Oxygen

semmelweis-egyetem.hu

http://en.wikipedia.org/wiki/File:P2M-1.png

World of Molecules: Properties of atoms

1s ² 2s ² 2p ⁶

n=2 (closed shell)

all atomic orbitals of shells 1 and 2 are filled

The electron structure of Neon

semmelweis-egyetem.hu

http://en.wikipedia.org/wiki/File:Neon-glow.jpg

World of Molecules: Properties of atoms

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

The electron structure of Radium

semmelweis-egyetem.hu

http://en.wikipedia.org/wiki/File:S7M0.png

Periodic table – electron configurations

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

http://en.wikipedia.org/wiki/Periodic_table_%28electron_configurations%29

World of Molecules: Properties of atoms

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

Electron configurations

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Electron configurations

semmelweis-egyetem.hu

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

World of Molecules: Properties of atoms

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

Electron configurations

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Electron configurations

semmelweis-egyetem.hu

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

World of Molecules: Properties of atoms

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.

Electron configurations

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

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

Aufbau principle

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

Aufbau principle – filling of orbitals

semmelweis-egyetem.hu

http://en.wikipedia.org/wiki/File:Klechkowski_rule_2.svg

semmelweis-egyetem.hu

World of Molecules: Properties of atoms

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