Blackbody A black body is an ideal system that absorbs all radiation incident on it
The electromagnetic radiation emitted by a black body is called blackbody radiation
Wien’s displacement lawλmaxT = 2.898 x 10-3 m.K
4
2I , Bπck Tλ Tλ
Stefan’s law4F T
Max Planck
In 1900 Planck developed a theory of blackbody radiation that leads to an equation for the intensity of the radiation (see in the class how to take limits).This equation can fit with experimental data
2
5
21
I ,Bhc λk T
πhcλ Tλ e
h = 6.626 x 10-34 J.sh is a fundamental constant of nature
Photoelectric EffectThe emitted electrons are called photoelectrons
0 max
hv w KEeV KE
Compton Effect
The graphs show the scattered x-ray for various angles
The shifted peak, λ’ is caused by the scattering of free electrons
Compton wavelength is
0002 43 nmCe
hλm c
.
1' cosoe
hλ λ θm c
Compton shift equation
Absorption Spectrum
Emission Spectra
Hα is red, λ = 656.3 nmHβ is green, λ = 486.1 nmHγ is blue, λ = 434.1 nmHδ is violet, λ = 410.2 nm
In 1885, Johann Balmer found an empirical equation that correctly predicted the four visible emission lines of hydrogen
H 2 2
1 1 12
Rλ n
RH is the Rydberg constantRH = 1.097 373 2 x 107 m-1
n is an integer, n = 3, 4, 5,…
Lyman series:
Paschen series:
Brackett series:
, , ,
H 2
1 11 2 3 4R nλ n
K
, , ,
H 2 2
1 1 1 4 5 63
R nλ n
K
, , ,
H 2 2
1 1 1 5 6 74
R nλ n
K
J. J. Thomson
Raisin cake
RutherfordFormal student of ThomsonAt Cambridge
Geiger Marsden
Rutherford worked with his students at the U of Machester
Arrival of the Quantum Hero, Niels Bohr
He knew that the work of Planck and Einstein on light radiation was very important, , not just clever German ideas.E hv
Until he discovered the Balmer series by mixing classical and quantum physics, also using two postulations: (see proof in the class)
1.
2.
( )2hL mvr n
i fhv E E
Louis de Broglie
He predicted the wave nature of electrons
postulated that because photons have both wave and particle characteristics, perhaps all forms of matter have both properties
h hλp mν The de Broglie wavelength of a particle
“Electron standing waves in an atom only certain Wavelengths will fit around a circle”
In his thesis, he started with Einstein’s Formula
2 ( ) ( ) ( )
( )forphotonE mc mc c p c p v
hv p vhp
Wavelength decreases as momentum increases
One of his committee (Paul Langevin) had forwardedhis thesis to Einstein
Electron DiffractionThe slit widths are small compared to the electron wavelength
Davisson-Germer Experiment
If particles have a wave nature, then they should exhibit diffraction effects
Bragg’s Law
• The phase speed of a wave in a wave packet is given by
– This is the rate of advance of a crest on a single wave• The group speed is given by
– This is the speed of the wave packet itself
phaseωv k
gdωv dk
Wave packet
Werner Heisenberg
x pE t
hh
Solve problems in the class and tutoring class
Erwin Schrodinger
The Schrödinger equation as it applies to a particle of mass m confined to moving along the x axis and interacting with its environment through a potential energy function U(x) is
This is called the time-independent Schrödinger equation
2 2
22d ψ Uψ Eψ
m dx
, , ,
22
2 1 2 38nhE n nmL
KA Particle in an infinite potential well
2h nhpλ L
2Lλn
The lowest allowed energy corresponds to the ground state
En = n2E1 are called excited states
E = 0 is not an allowed state, The particle can never be at rest
22
2 2
2 2d ψ mE mEψ k ψ where kdx
A Particle in a finite potential well
