Transcript Quantum (Todownload)

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
Stefan’s law
F  T 4
Wien’s displacement law
λmaxT = 2.898 x 10-3 m.K
I  λ,T  
2πck BT
λ4
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
Max Planck
2πhc 2
I  λ,T   5 hc λk T
B
λ e
 1
h = 6.626 x 10-34 J.s
h is a fundamental constant of nature
Photoelectric Effect
The emitted electrons are called photoelectrons
hv  w  KE
eV0  KEmax
Compton Effect
The shifted peak, λ’ is caused by
the scattering of free electrons
The graphs show the scattered
x-ray for various angles
h
λ'  λo 
1  cos θ 
mec
Compton shift equation
Compton wavelength is
h
λC 
 0.002 43 nm
me c
Emission Spectra
Absorption Spectrum
In 1885, Johann Balmer found an empirical equation that correctly predicted
the four visible emission lines of hydrogen
1
 1
 RH 
2
λ
 2
Hα is red, λ = 656.3
nm
Hβ is green, λ = 486.1
nm
Hγ is blue, λ = 434.1
nm
Hδ 1
is violet,
 λ = 410.2

nmn 2 

RH is the Rydberg constant
RH = 1.097 373 2 x 107 m-1
n is an integer, n = 3, 4, 5,…
Lyman series:
1
1

 RH  1 2  n  2, 3 , 4 ,K
λ
 n 
Paschen series:
1
 1 1
 RH  2  2  n  4 , 5 , 6 ,K
λ
3 n 
Brackett series:
1
 1 1
 RH  2  2  n  5 , 6 , 7 ,K
λ
4 n 
Rutherford
J. J. Thomson
Formal student of Thomson
At Cambridge
Geiger
Raisin cake
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, E  hv, not just clever German ideas.
Until he discovered the Balmer series by mixing
classical and quantum physics, also using two
postulations: (see proof in the class)
h
1. L  mvr  n( )
2
2. hv  Ei  E f
postulated that because
photons have both wave and
particle characteristics,
perhaps all forms of matter have
both properties
Louis de Broglie
He predicted the wave nature of electrons
h
h
λ 
p 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
E  mc 2  (mc)c  ( p forphoton )c  p (v )
hv  p (v )
h

p
Wavelength decreases as momentum increases
One of his committee (Paul Langevin) had forwarded
his thesis to Einstein
Electron Diffraction
The 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
Wave packet
• The phase speed of a wave in a wave packet is
given by
v phase  ω
k
– This is the rate of advance of a crest on a single wave
• The group speed is given by
v g  dω
dk
– This is the speed of the wave packet itself
xp  h
Et  h
Werner Heisenberg
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
2
d 2ψ

 Uψ  Eψ
2
2m dx
This is called the time-independent
Schrödinger equation
A Particle in an infinite potential well
 h2  2
En  
n
2 
 8mL 
n  1, 2, 3,K
2L
λ
n
h nh
p 
λ 2L
d 2ψ
2mE
2mE
2
  2 ψ  k ψ where k 
2
dx
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
A Particle in a finite potential well