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SEMMELWEIS
PÁZMÁNY PÉTER
UNIVERSITY
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.
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semmelweis-egyetem.hu
WORLD OF MOLECULES
(Molekulák világa)
PROPERTIES OF ATOMS
(Az atomok tulajdonságai)
KRISTÓF IVÁN
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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]
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Previously - Rutherford’s atom model (He)
http://http://en.wikipedia.org/wiki/File:Helium_atom_QM.svg
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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
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Previously – Periodic table of elements
http://en.wikipedia.org/wiki/Periodic_table
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Table of Contents
1.
2.
3.
4.
5.
6.
7.
8.
9.
Nucleus
Isotopes
Tables of isotopes
Radioactivity
Decay modes
Bohr-Sommerfeld model
Quantum numbers
Electron structure
Examples
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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
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Isotope
Same chemical element
• Atomic number (Z) is the same
Different number of neutrons (N)
Mass number (A) different!
A
e.g.: Carbon
12
6
C
13
6
C
14
6
C
Z
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Table of isotopes – table of nuclides
• 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
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Isotopes
stability
number of neutrons
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number of protons
http://en.wikipedia.org/wiki/File:Isotopes_and_half-life.svg
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Isotopes
Types of
decay
http://commons.wikimedia.org/wiki/File:Table_isotopes_en.svg
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Table of isotopes (half life representation)
National Nuclear Data Center, information extracted from the Chart of Nuclides database, http://www.nndc.bnl.gov/chart/
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Table of isotopes (decay mode representation)
National Nuclear Data Center, information extracted from the Chart of Nuclides database, http://www.nndc.bnl.gov/chart/
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Isotopes of Carbon
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Isotopes of Carbon
Carbon-12 (12C) is used as atomic mass unit:
1 atomic mass unit is 1/12th of 1 mole 12C.
Or
1 mole is the amount of atoms in 12grams of 12C.
It is the Avogadro number: 6.022×1023 mol-1
Different isotopes of the same chemical element
have different nuclear stabilities.
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Radioactivity
Main decay modes of unstable nuclei
• Alpha decay
• The release of 2 protons and 2 neutrons (i.e. a 4He
nucleus), A2=A1-4; Z2=Z1-2
• Beta decay
• Release of an electron from the nucleus, Z2=Z1+1
• Gamma decay
• High energy X-rays
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Main decay modes
http://en.wikipedia.org/wiki/File:Alfa_beta_gamma_radiation.svg
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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
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Decay modes on the table of nuclides
http://en.wikipedia.org/wiki/File:Radioactive_decay_modes.svg
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Radioactive decay chains
• half life: time required for half of the amount
to decay
t1/2
• Decay constant
λ
t1 2 =
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ln(2)
λ
N (t ) = N 0 ⋅ e
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− λ ⋅t
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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
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Decay chain of Uranium-238
from 238U (uranium)
to 206Pb (lead)
http://en.wikipedia.org/wiki/File:Decay_chain%284n%2B2,_Uranium_series%29.PNG
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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/
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http://en.wikipedia.org/wiki/Table_of_nuclides
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Electron configuration of atoms
http://en.wikipedia.org/wiki/File:Electron_Configuration_Table.jpg
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Bohr-Sommerfeld model
http://en.wikipedia.org/wiki/File:Bohr_atom_model_English.svg
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Bohr-Sommerfeld model
http://en.wikipedia.org/wiki/File:Sommerfeld_ellipses.svg
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Bohr-Sommerfeld model
• The electrons can only travel in special orbits
•
•
•
•
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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)
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Bohr-Sommerfeld model
• Angular momentum and wavelength
h
mv n rn = n
, where n = 1,2,…
2π
2π rn
h
h
λ= =
⇒
p mvn
n
• Radius of orbits
•
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h
2π rn = n
= nλ
mv n
The circumference of orbits are integer multiples
of the electron’s wavelength
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Bohr-Sommerfeld model
• 4 quantum numbers uniquely represent the
state of the electron inside an atom
•
•
•
•
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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)
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Bohr-Sommerfeld model
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
s=−
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1
1
or +
2
2
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Bohr-Sommerfeld model
value name of shell
Principal quantum number (n)
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number of electrons in shell
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
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Bohr-Sommerfeld model
value
Azimuthal quantum number (l)
name of subshell
number of electrons
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)
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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
•
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pairing of electrons is an unfavorable process
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Atomic orbitals
http://en.wikipedia.org/wiki/Atomic_orbital
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The electron structure of Hydrogen
1s1
n=1
l=0 (s orbital)
m=0
s =-1/2 or +1/2
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The electron structure of Helium
1s2
n=1 (closed shell)
l=0 (s orbital)
m=0
s =-1/2 and +1/2
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The electron structure of Carbon
1s2 2s2 2p2
example:
n=2
l=1 (p orbital)
m=0
s =-1/2 or +1/2
http://en.wikipedia.org/wiki/File:P2M0.png
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The electron structure of Nitrogen
1s2 2s2 2p3
example:
n=2
l=1 (p orbital)
m=1
s =-1/2 or +1/2
http://en.wikipedia.org/wiki/File:P2M1.png
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The electron structure of Oxygen
1s2 2s2 2p4
example:
n=2
l=1 (p orbital)
m=-1
s =-1/2 or +1/2
http://en.wikipedia.org/wiki/File:P2M-1.png
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The electron structure of Neon
1s2 2s2 2p6
n=2 (closed shell)
all atomic orbitals of shells
1 and 2 are filled
http://en.wikipedia.org/wiki/File:Neon-glow.jpg
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The electron structure of Radium
1s2 2s2 2p6 3s2 3p6 4s2 3d10
4p6 5s2 4d10 5p6 6s2 4f14
5d10 6p6 7s2
n=7
l=0 (s orbital)
m=0
s =-1/2 and +1/2
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http://en.wikipedia.org/wiki/File:S7M0.png
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Periodic table – electron configurations
http://en.wikipedia.org/wiki/Periodic_table_%28electron_configurations%29
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Electron configurations
1.
2.
3.
4.
5.
6.
7.
8.
9.
H 1s1
He 1s2
Li (He)2s1
Be (He)2s2
B (He)2s22p1
C (He)2s22p2
N (He)2s22p3
O (He)2s22p4
F (He)(2s)2(2p)5
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Electron configurations
10. Ne (He)2s22p6
11. Na (Ne)3s1
12. Mg (Ne)3s2
13. Al (Ne)3s23p1
14. Si (Ne)3s23p2
15. P (Ne)3s23p3
16. S (Ne)3s23p4
17. Cl (Ne)3s23p5
18. Ar (Ne)3s23p6
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Electron configurations
19.
20.
21.
22.
23.
24.
25.
26.
27.
K (Ar)4s1
Ca (Ar)4s2
Sc (Ar)4s23d1
Ti (Ar)4s23d2
V (Ar)4s23d3
Cr (Ar)4s13d5
Mn (Ar)4s23d5
Fe (Ar)4s23d6
Co (Ar)4s23d7
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Electron configurations
28. Ni (Ar)4s23d8
29. Cu (Ar)4s13d10
30. Zn (Ar)4s23d10
31. Ga (Ar)4s23d104p1
32. Ge (Ar)4s23d104p2
33. As (Ar)4s23d104p3
34. Se (Ar)4s23d104p4
35. Br (Ar)4s23d104p5
36. Kr (Ar)4s23d104p6
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Electron configurations
37. Rb (Kr)5s1
38. Sr (Kr)5s2
39. Y (Kr)5s24d1
40. Zr (Kr)5s24d2
41. ...
The filling of atomic orbitals is not in
numerical order... but by energy levels.
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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
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Aufbau principle – filling of orbitals
http://en.wikipedia.org/wiki/File:Klechkowski_rule_2.svg
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Next - Dual nature of electrons
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Dual nature of light
Particle nature of electron
Wave nature of electrons (de Broglie)
Particle-wave duality of electrons
Schrödinger equation
The wave functions of the electron in 1D
The wave functions of the electron in a harmonic oscillator
The wave functions of the electron in 3D
The wave functions of the electron in the Hydrogen atom
Short introduction to complex numbers
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