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Waves, Light & QuantaTim Freegarde
Web Gallery of Art; National Gallery, London
2
Davisson-Germer experiment
C Davisson & L H Germer, Phys Rev 30 705 (1927)
NICKEL TARGE
T
ELECTRON DIFFRACTION• electrons behave like
waves• electron wavelength
p
h
3
Diffracting atoms
E M Rasel et al, Phys Rev Lett 75 2633 (1995)nm811
-1m.s850v
Ar40
nm012.0Ar
rad32
m25.1
4
Diffracting molecules
S Gerlich et al, Nature Physics 3 711 (2007)
MOLECULE DIFFRACTION• molecules behave like
waves• molecule wavelength
p
h
5
Bohr model of the hydrogen atom
+
BOHR MODEL
• quantized angular momentum
• quantized energy levels
nmvr
• circular orbitsr
mv
r
e 2
20
2
4
hE
• de Broglie wavelength
p
h
• Hydrogen energy level measurements and calculations agree to 15 figures
Hz34074187413061466221 SSf
1m73527568.73197310 R
6
Quantum theoryPHOTONS
• energy quantized in units of
(h = Planck’s constant)
h
• momentum quantized in units of
hk
ch
• angular momentum quantized in units of
2
h
• blackbody radiation• photoelectric effect
• Compton scattering
PARTICLES
• frequency determined by energy
hE
• de Broglie wavelength determined by momentum
hkp • electron
diffraction
• angular momentum quantized in units of
2
h• atomic theory
7
Bohr model of the hydrogen atom
+
BOHR MODEL
• quantized angular momentum
• quantized energy levels
nmvr
• circular orbitsr
mv
r
e 2
20
2
4
hE
• de Broglie wavelength
p
h
• Hydrogen energy level measurements and calculations agree to 15 figures
Hz34074187413061466221 SSf
1m73527568.73197310 R
8
Bohr model of the hydrogen atom
• allowed energies 22
0
4 1
42 n
meE
220
3
4 1
8 nch
me
hc
E
2n
R Rydberg constant
en
erg y
0
hcR
4
hcR
n = 1
n = 3
n =
• emission wavelengths
22
111
ji
ji
nnR
hc
EE
hc
E
n = 2
1m73527568.73197310 R
9
Atomic line spectra
• allowed energies 22
0
4 1
42 n
meE
220
3
4 1
8 nch
me
hc
E
2n
R Rydberg constant• emission wavelengths
22
111
ji
ji
nnR
hc
EE
hc
E
en
erg y
0
hcR
4
hcR
n = 1
n = 3
n =
n = 2
1m73527568.73197310 R
10
Atomic line spectraen
erg y
0
hcR
4
hcR
n = 1
n = 3
n =
n = 2
Lyman
Balmer
Paschen
universe-review.ca
scope.pari.edu
1m73527568.73197310 R
11
Hydrogenic atoms
• allowed energies 22
0
42 1
42 n
meZE
2
2
20
3
4
8 n
Z
ch
me
hc
E
22
Zn
R Rydberg constant
en
erg y
0
hcR
4
hcR
n = 1
n = 3
n =
• emission wavelengths
22
2 111
ji
ji
nnRZ
hc
EE
hc
E
n = 2
1m73527568.73197310 R
12
Franck-Hertz experiment
• accelerate electrons through atomic vapour• periodic modulation of measured current
• inelastic collisions when electron energy equals atomic transition energy
singlet
triplet
Hg G Rapior et al., Am J Phys 74 423 (2006)
J Franck & G Hertz, Verh. Dtsch. Phys. Ges. 16 457 (1914)
13
Quantum theoryPHOTONS
• energy quantized in units of
(h = Planck’s constant)
h
• momentum quantized in units of
hk
ch
• angular momentum quantized in units of
2
h
• blackbody radiation• photoelectric effect
• Compton scattering
PARTICLES
• frequency determined by energy
hE
• de Broglie wavelength determined by momentum
hkp • electron
diffraction
• angular momentum quantized in units of
2
h• atomic theory
• discrete energy levels for bound particles
• atomic theory
• Stern-Gerlach
14
Quanta: absorption and emission of photons
ABSORPTION
en
erg y
0
hcR
4
hcR
n = 1
n = 3
n =
n = 2
absorption emission
EMISSIONSPONTANEOUS
ABSORPTIONEMISSION
STIMULATED
1121
d
dNB
t
N
1
2
1
2
1
1
2212
d
dNA
t
N
15
Quanta: absorption and emission of photons
ABSORPTIONEMISSION
SPONTANEOUS
ABSORPTIONEMISSION
STIMULATED
1121
d
dNB
t
N
1
2
1
2
1
1
2212
d
dNA
t
N
2212
d
dANNNB
t
N
EINSTEIN EQUATIONS
NNN 21
• spontaneous emission stimulated by vacuum field
• amplification of light if atomic population is inverted i.e. 12 NN
• thermal equilibrium blackbody
spectrum
• Einstein A and B coefficients
16
Waves, Light & Quanta: the LASER
by Stimulated Emission of Radiation
LIGHT AMPLIFICATION
• Theodore Maiman, 16 May 1960
beam splitter
flash tube
mirror
ruby
693.4 nm
light amplifier
optical resonator
17
Waves, Light & Quanta: the ruby LASER
beam splitter
flash tube
mirror
ruby
693.4 nm
light amplifier
optical resonator
en
erg y
absorption emission
Cr3+
• Cr3+ ions in sapphire (Al2O3) absorb blue and green from flash light
• internal transitions to metastable state
metastable
• spontaneous emission is amplified by passage through ruby
• repeatedly reflected/amplified near-axial light builds up to form coherent laser beam
18
Waves, Light & Quanta: beam characteristics
beam splitter
flash tube
mirror
ruby
693.4 nm
• as initial source recedes down unfolded cavity, emission approaches that from distant point source
• long pulse continuous wave (c.w.)
• narrow linewidth for long pulses ( )
1 t• noise from spontaneous emission gives lower limit to
linewidth• nonlinear processes have various effects in detail
• divergence determined by diffraction by limiting aperture
• Hecht section 13.1
• focusable
• monochromatic
• constructive interference between reflections for certain wavelengths