Lecture 2.0
Bonds Between Atoms
Famous Physicists’ Lecture
Electronic Structure in Atoms
• Max Planck
– Electron (1897) has duality,
• Wave E=hc/λ = h,
– λ =wavelength of electron
–  =frequency
• Particle of mass, me
Bohr Atom
• Only specific orbits = Atomic Orbitals
– Circumference of orbit = n*λ
•
n 2h 2 o
n2
Rn 
 0.0529nm
2
 me Ze
Z
– for Hydrogen, Z=1, R1=0.0529 nm
•
Z 2mee4
Z2
En   2 2 2  13.6eV 2
8 0 h n
n
– Z= number of protons
Electronic Structure in Atoms
• Ionization energy = transition from n
 Z2 Z2 
En  13.6eV  2  2 
 n 
• Emission Radiation (Light and X-rays)
– transition nanb gives off Photon with
energy
 Z 2 Z 2  hc
En  13.6eV  2  2  
 nb na  
• Bonding in Molecules – Ionic and Covalent
Louis Victor Pierre Raymond duc de Broglie
EN Not correct due to charge screening and QM
Emission Line Spectra
 Z 2 Z 2  hc
En  13.6eV  2  2  
 nb nb  
Energy Level Diagrams, Hydrogen
-0.85 eV
-1.51 eV
4
3
2
1
L
K
-3.40 eV
-13.6 eV
Periodic Table of Element
• Chemical Properties
Heisenberg Uncertainty
Principle
• (me v) x  h/(2π)
• Cannot specify both momentum (or
velocity) and location of an electron at
same time
• Electrons are smeared in space
• Probability of finding an electron at a
location is best way to describe and
electron
Schrodinger Wave Equation
(time independent)
 2

   ( E  V )  0
2me
• Wave Function, ψ=f(r,θ,φ)
2 2
• Probability of finding an electron= 4  r dr
• | ψ|2 = ψ* ψ i.e. complex conjugate
Pauli’s Exclusion Principle
-Only one electron in each location
accounting for spin
n
1
l
0
ml
0
2
0
0
2
1
-1
2
1
0
2
1
+1
Principle Q# Orbital Q#
Magnetic Q#
ms
-½
½
-½
½
-½
½
-½
½
-½
½
Spin Q#
Zeeman Effect = Splitting or
emission lines if in B field
e
E  ml
B
2me
H field
Shape of Orbitals
Bonding in Molecules
• Ionic - electrons stolen
• Covalent - electrons shared
– Metal
– hybridization, sp, sp2, sp3
• Molecular Orbitals for shared electrons =
covalent bonds
Atoms in Solids
•
•
•
•
Ionic Bonding, NaCl
Covalent Bonding
Metals
Hetero Atoms = Ceramics, e.g. MgO
Electrostatic forces in Ionic
Solids
E
e2
40 r
F 
e2
40 r 2
• Many Atoms at various separations
– Maudelin Constant, Md
Elattice   M d
e2
40ao
– NaCl, ao=0.281 nm and Elatttice=8.95 eV.
Repulsive Force at small r
• Total Force = Coulomb Force + Repulsive Force
F  FCoulomb  Frepel
e2
Ba 010
Aa02 Ba 010

 10   2  10
2
40r
r
r
r
Metallic Bonding
• Electrons Free to move among all atoms
– Electron Gas
• Determines
– Electrical Conduction
– Thermal Conduction
In Covalent Crystalline Solids,
what happens to the atomic
orbitals?
Molecular Orbitals
• New Energy
– Bonding
– Anti Bonding
1s •
•
• •
1s
• New Shapes to Orbitals if hybridization
Bonds Between Molecules
• Hydrogen Bonding
• Van der Waals Forces
– Dipole-Dipole interactions
• Dipole Moment = Charge * separation
– Permanent
– Instantaneous
Melting Point
Molecular Solids
Metals
Ionic Solids
Covalent Solids
Strength of
Inter-Molecular
Bonds
Melting Point
Melting Point