states of matter - warsaw university of...
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JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
States of matter
Solids- defined shape and volume- long range order- harmonic interactions
Liquids Gases
- poorly compressible- local order- create free surface
- compressible- molecules in constant motion- fill volume
Fluids Shear force (parallel to the surface) causes the fluid to flow.
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Models of matter:history
Aristoteles (350 b.c) : Matter as continuous medium
Democritus (400 b.c.) : atom as indivisible particle. Matter is a combination of atoms.
John Dalton (1808)• Atom is uniform, invariable,and indivisible.• All atoms of a given element have identical chemical properties.• Atoms of one element are different than atoms of other element.• Chemical compounds are created by bonding of atoms in given constant proportions.
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Electron
Charging bodies and flow of charge is performed by charge carriers –electrons and ions.
Thomson experiment(1897 r.)
q/m = 1.7·1011 C/kg
The mass of particlecoming from cathoderadiation is about 2000 lower than that of ionizedhydrogen (proton)
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Properties of electron
Milikan experiment: estimation of electron charge
e = 1.602·10-19 C
m = 9.109·10-31 kg
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Models of atoms – Thomson and Rutherford
Thomson model – „cake with raisins”
Rutherford experiment –„hollow matter”
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Rutherford model
Mass and positive charge concentrated in the core
10-10 m10-15 m
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Bohr model
Problems of Rutherford model:- radiation (electron „falls” onto the core)- emission spectra are not continuous
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Bohr model
Balmer – lines in hydrogen spectrum
Rydberg RH =10 972 000 m−1
Lyman – ultraviolet spectrum
n=2,3,4...
Paschen, Brackett, Pfund, Humphrey series – infrared
n’=1,2,3... n>n’
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Assumptions of Bohr model
1. Electron moves in circular orbit around the core. The energy of electron is constant (it does not radiate energy)
2. Only such orbits are allowed, for which the orbital angular momentum of electron is equal the multiple of h/2π
3. Radiation or absorption of energy is possible only when the electronjumps from one orbit to another. The frequency of the correspondingradiation is expressed by equation ∆E = hν
π2hnLn = n- quantum number
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Hydrogen emission spectrum
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Bohr model: energy of electron
20
22
4 nn
ne
rZe
rum
πε=
π2hnrumL nnen ==
)()()( nEnEnE kp +=
( ) 2220
42 124
)(n
eZmnE e
hπε−=
n=1 ground staten=∞ ionized state
⎟⎠⎞
⎜⎝⎛ −⎟⎟
⎠
⎞⎜⎜⎝
⎛= 223
42
0
1144
11mnc
eme
hππελ MmRR
e+=
1µRadiation length
RH
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Basic physics: waves
Waves propagate in time and space.
Wave equation
⎟⎠⎞
⎜⎝⎛ −=Ψ
vxtf
2
22
2
2
xv
t ∂Ψ∂
=∂
Ψ∂Differential equation
Wavenumber
Frequency and angular frequency
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Old and new quantum theory
Faults of Bohr model:- gives only the wavelength, and not the intensity- gives correct wavelengths only for hydrogen, and hydrogen-like atoms
The new theory: based on de Broglie’s hypothesis on matter waves
The light can be treated as a wave, and as a particle (photon).The light transmits momentum and energy.Hence, the matter particle that has momentum represents wavelength!
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Explanation of Bohr model
The atom acts like a „resonance box” - electronorbit hosts a standing wave. The orbit length isdetermined by the electron wavelength.
π2hnrumL nnen == nλ=2πr
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Matter waves
Davisson-Germer experiment:Wave properties of electrons
Thomson experiment: diffraction of electronson thin polycrystalline foil
Stern experiment: diffraction of hydrogen andhelium atoms on crystals of lithium fluorideand sodium chloride
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Heisenberg uncertainty principle
Position and momentum cannot be estimated accurately at the same time.The particle can occupy a state with well defined energy for a long time. States with widespread energy are short-lived.
π4htE ≥∆⋅∆
π4hpx ≥∆⋅∆
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Heisenberg uncertainty principle
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Wave function
Wave function defines probability, that the particle can be found incertain space.
dxdxdxtxP 2*),( Ψ=ΨΨ= Probability density
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Schrödinger equation
Wavefunction are a solution of Schrödinger equation
Electron in a electrical field (stationary condition)
Gradient of the field
Potential of the field
Electron energy
The function, and its derivative cannot change abruptly on borders of different potentials – there is no „jump” in probability, just „smooth” changes.Consequence: the electrons can penetrate „forbidden” areas – just with small probability!
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Schrödinger equation – potential step
E<V0 I IIV0
V
0
Area I
Classical
QuantummEv 2
1 =Area I Electron does not penetrate area II
Area II
The electron penetrates area II...... but the probability decreases exponentially with distance.Eventually, the electron is always pushed away!
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
Potential step with finite length
The electron can pass through the barrier, despite „too low” energy.The probability decreases exponentially with barrier thickness.
( )⎟⎟⎠
⎞⎜⎜⎝
⎛ −−∝ l
EVmT
h
022exp
JONIKA I FOTOWOLTAIKA MICHAŁ MARZANTOWICZ
The model of atom: potential well
Inside the well:
The electron is a standing wave.