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