Quantum- element units of energy
Quantum optics: photoelectric effect laser emission blackbody radiation

1. Light Sources
 An object is a source of light.
 A direct source produces light, e.g. the sun, light bulb, fire.
 An indirect source does not produce light, e.g. an illuminated object.
 An extended object may be regarded as a set of point sources.

( a) Thermal source: sun, wax candle, kerosene lanterns, electric light bulb light--the consequence of the temperature
 kerosene lanterns : carbon freed by the combustion process
 electric light bulbs : a filament is heated . carbon filaments, metal filaments
Incandescent lamps: be heated to incandescenc e
 Refractory metals: a high melting point
 Tungsten: 3410

C ; evaporates,
 Some halogens( iodine), retard the process

How tungsten filaments works

(b) Fluorescent lamps

Fluorescent lamps
 High-pressure mercury lamps

High-pressure xenon lamps
(c) Stimulated emission: laser, LED

2. Blackbody Radiators
6.1 Light Sources
(a) Black body : is an ideal absorber , also a perfect emitter
 A good way of making a blackbody is to force reflected light to make lots of reflections: inside a bottle with a small opening
 The spectral distribution of that radiation is a function of temperature alone; the material as such plays no role

 Classical theory failed
 Ultraviolet catastrophe

Max Planck (1858-1947)
Solved the “ultraviolet catastrophe”
 Planck
’ s hypothesis: An object can only gain or lose energy by absorbing or emitting radiant energy in QUANTA .

Electromagnetic Radiation
 All waves have:
 frequency and wavelength symbol: n (
Greek letter
“ nu
”
) l (
Greek
“ lambda
”
)
 units:
“ cycles per sec
”
= Hertz
“ distance
”
(nm)
Note: Long wavelength
 small frequency
Short wavelength
 high frequency increasing frequency increasing wavelength

Energy of radiation is proportional to frequency.
E = h • n where h = Planck’s constant = 6.6262 x 10 -34 J•s
Light with large l
(small n
) has a small E.
Light with a short l
(large n
) has a large E.
(b) Photon: the oscillators emit energy, as discrete, elemental units of energy called quanta or photons




Light also behaves as a stream of particles, called photons .
Light has “ wave-particle duality ” , meaning that it behaves as waves and as particles.
This is a concept in quantum mechanics .

(c) Black-body radiation is electromagnetic radiation that is in thermal equilibrium at a temperature T with matter that can absorb and emit without favouring any particular wavelength
(d) Plank’s radiation law
M

C
1 l
5 e
C
2
1
/ l
T 
1

3. Wien's Displacement Law plot Planck's law for different temperatures increasing temperature
 more energy is emitted
 the peak emission shifts toward the shorter wavelengths
6.1 Light Sources l max

2 .
8978

10

3
T m K
The temperature and the wavelength of maximum intensity satisfy T l max
=constant

 Hole in a cavity is
 a perfect absorber
 a perfect emitter
 Called a Black Body

Wien’s law l max

2 .
898 mm

K
T

 What is the peak radiation emitted by an l object at 100 o C ?
max

2 .
898 mm
T

K

2 .
898 mm

K
373 K

7770 nm
 This is in the far infrared.
 What T required for middle of visible range?
T

2 .
898 mm l max

K

580 nm

5000 K

Blackbody Radiation: Experimental Results
 At 310 Kelvin (=37 o C = 98.6
o F), only get IR
Intensity
UV blue yellow red wavelength
IR

Blackbody Radiation:Experimental Results
 At much higher temperatures, get visible
 look at blue/red ratio to get temperature
Intensity
UV blue yellow red wavelength
IR

When we look at the visible spectra of the sun, we see that it’s intensity peaks at about 500 nm (green light). From the equation: l
= b/T (where b = 2.9 x 10 -3 m*K) we get: T = b/ l
= (2.9 x 10 -3 m*K) / 500 x 10 -9 m

6000 K .

6.1 Light Sources
4. Stefan-Boltzmann's Law
The total energy density inside a blackbody cavity is given by integration over all wavelengths
M
 
0

M
(  d l  
T
4
 
5 .
67

10

8 m
2
W

K
4
Note that Intensity increases with T
Temperature must be in Kelvin, where size of one Kelvin is same as size of one degree Celsius, but T=0K is absolute zero, and T=273K = 0 o C (freezing).

6.1 Light Sources
5. Klrchhoff's Law

Kirchhoff's law : an object that is a good radiator at a given wavelength is also a good absorber at the same wavelength
 Stefan-Boltzmann's law for gray bodies
M
  
T
4 factor

: the emissivity of the surface
•Recall that a good absorber is also a good emitter, and a poor absorber is a poor emitter. We use the symbol
 to indicate the blackness (

=0) or the whiteness (

=1) of an object.

Example
If you eat 2,000 calories per day, that is equivalent to about 100 joules per second or about 100 Watts which must be emitted.
Let’s see how much radiation you emit when the temperature is comfortable, say 75 o F=24 o C=297K, and pick a surface area, say 1.5m
2, that is at a temperature of 93 o F=34 o C=307K:
M emitted
=

AT 4 =
(5.67x10
-8 W/m 2 K 4 )*(.97)*(1.5m
2 )*(307K) 4 = 733
Watts emitted !

Example continued
But this is not the whole story: besides emitting radiation, we receive radiation from the outside:
M absorbed
=

AT 4 =
(5.67x10
-8 W/m 2 K 4 )*(.97)*(1.5m
2 )*(297K) 4 = 642
Watts absorbed !
Hence, the net power emitted by the body via radiation is: M net
= 733 Watts 642 Watts
Watts.
The peak of this radiation is at:
= 91
l peak
= b/T = 2.9x10
-3 m*K / 307K = is in the infrared (as expected).
9.5
 m which

 thermal detectors based on absorption and heating
If the absorbing material is black, they are independent of wavelength .
 quantum detectors .
based on photoelectric effect
Quantum detectors are of particular interest, both theoretical and practical; some of them are so sensitive they respond to individual quanta .

6.2 Detectors
1. Thermal Detectors slow to respond
 Golay cell a thin black membrane placed over a small, gas-filled chamber. Heat absorbed by the membrane causes the gas to expand, which in turn can be measured, either optically (by a movable mirror) or electrically (by a change in capacitance).
used in the infrared .

6.2 Detectors
 Thermocouple a junction between two dissimilar metals. As the junction is heated, the potential difference changes. In practice, two junctions are used in series, a hot junction exposed to the radiation, and a cold junction shielded from it. The two voltages are opposite to each other; thus the detector, which without this precaution would show the absolute temperature, now measures the temperature differential.
 thermopile contains several thermocouples and, therefore, is more sensitive .

6.2 Detectors
 bolometer contains a metal element whose electrical resistance changes as a function of temperature; if instead of the metal a semiconductor is used, it is called a thermistor .
Unlike a thermocouple, a bolometer or thermistor does not generate a voltage; they must be connected to a voltage source.

6.2 Detectors
2. Quantum Detectors
 the wavelength of the light plays an important role there is a certain threshold above which there is no effect at all, no matter what the intensity
 intense light and dim light cause same of an effect

Photoelectric effect demonstrates the particle nature of light
No e observed until light of a certain minimum E is used.
Number of e ejected does NOT depend on frequency, rather it depends on light intensity.

• Classical theory said that E of ejected electron should increase with increase in light intensity — not observed!


6.2 Detectors
Light
 plate M( photocathode ) when irradiated, releases electrons (called photoelectrons ) e-
A
 collector plate C( anode ) photoelectrons released by M are attracted by, and travel to C.
V
Variable power supply
As the potential V, read on an high-impedance voltmeter, is increased, the current, I, read on an ammeter, increases too, but only up to a given saturation level , because then all of the electrons emitted by M are collected by C.

6.2 Detectors if C is made negative , some photocurrent will still exist, provided the electrons ejected from M have enough kinetic energy to overcome the repulsive field at C. But as
C is made more negative, a point is reached where no electrons reach C and the current drops to zero. This occurs at the stopping potential , V
0
.
In short: A significant amount of photocurrent is present only if the collector, C, is made positive

When the frequency of the light is increased, the stopping potential also increases.

The electron photo-current can be stopped by a retarding potential .
Increasing the light intensity do not change the retarding potential .

6.2 Detectors

If more intense light falls on the photocathode, it will release more electrons but their energies, and their velocities, will remain the same.

The energy of the photoelectrons depends on the frequency of the light: blue light produces more energetic photo-electrons than red light.

The response of a quantum detector is all but instantaneous: there is no time lag, at least not more than 10 -8 s, between the receipt of the irradiation and the resulting current.

6.2 Detectors

The light is received in the form of discrete quanta .
 Part of the energy contained in a quantum is needed to make the electron escape from the surface; that part is called the work function , W.

Only the excess energy, beyond the work function, appears as kinetic energy of the electron. The maximum kinetic energy with which the electron can escape, therefore, is
KE max
= h n
- W
Einstein's photoelectric-effect equation .

h n
= W + KE
KE = h n
- W

Einstein suggested that the linear behaviour is simply a
Conservation of Energy.
 Energy of Light = Energy needed to get out + Kinetic
Energy of electron.

 Given that aluminum has a work function of
4.08 eV, what are the threshold frequency and the cutoff wavelength?
f c
 h
4.08 eV
 -15 
 15
10 Hz l c
 c f c l  c hc


4.08 eV

300 nm

6.2 Detectors
It is often convenient to measure energies on an atomic scale not in joule but in electron volt , eV.
1 eV = (1e)(1V) = 1.60 6

10 19 J l  hc
E

( 6 .
63

1
10
.
6

34
Js )( 3

10

19
J

10
8
/ eV m / s )

1240 nm eV
E

 Electron volts are useful size units of energy
1 eV = 1.6 x 10 -19 Coul × 1V = 1.6 x 10 -19 J .
 radio photon: hf = 6.63 x 10 -34 Js × 1 x 10 6 /s
= 6.63 x 10 -28 J = 4 x 10 -15 eV
 red photon : f = c/ l 
3 × 10 8 m/s / 7 x 10 -7 m
= 4.3 x 10 14 Hz, red photon energy = 1.78 eV
 blue : l
= 400 nm; photon energy = 3.11 eV .

6.2 Detectors
The work function determines the longest wavelength to which a detector can respond: the lower the work function, the longer the wavelength.
The lowest work functions are found among the alkali metals.
Photoelectric Properties Of Some Alkali Metals
Alkali Work function (eV) Threshold (nm)
Sodium 2.28 543
Potassium 2.25 551
Rubidium 2.13 582
Cesium 1.94 639

Determine the work function W wavelength nm stopping potential eV
200
4.11
300
2.05
KE=(hc)(1/ l
) － W
400
1.03
500
0.41

From the graph:
The plot is essentially KE vs 1/ l
, so that since
KE=hc/ l －
W
The intercept when (1/ l
)=0 give
W= － KE= － ( － 2eV)=2eV
To obtain Planck’s constant h, we need the slope S
Then h=S/c.
S=(4 － ( － 2))/(5 － 0) × 10 -3 =1.2 * 10 3 eV nm h = 1.2
×
10 3 ×
1.602
×
10 -19 ×
10 -9 /(3
×
10 8 ) J s
= 6.4
×
10 -34 J s cf (6.626
×
10 -34 J s)

In contrast to thermal detectors, quantum detectors respond to the number of quanta , rather than to the energy contained in them .

6.3 Practical Quantum Detectors

The simplest type is probably the vacuum phototube , an example of a photoemissive detector .
hv
+
-
-

Light strikes photocathode (-)

Photocathode emits photoelectrons

Photoelectrons accelerate toward anode (+)
 flow of electrons = current
 current proportional to # photons incident on photocathode e -

 quantum efficiency :the ratio of the number of photoelectrons released to the number of photons received.

Ordinarily, this efficiency is no higher than a few percent.

Several diodes are combined in series to form a photomultiplier , the efficiency becomes much higher.
•
Light strikes photocathode (-)
• Photocathode emits photoelectrons
•
Photoelectrons accelerate toward series of increasingly positive anodes (+) at which photoelectrons and secondary electrons are emitted (dynodes)
• Electrons accelerated toward collection anode

6.3 Practical Quantum Detectors

A photocell is the solid-state equivalent of the vacuum photodiode; most often it is a semiconductor .

A semiconductor conducts electricity better than an insulator but not as well as a conductor.

In an insulator , the electrons are tightly bound to their respective atoms.

In a metal , the electrons can move freely; hence, even a small voltage applied to the conductor will cause a current.

6.3 Practical Quantum Detectors
 photoconductive detectors : semiconductor, such as cadmium sulfide (CdS), gallium arsenide, and silicon, conduct electricity poorly only in the dark; when exposed to light, they conduct very well.

6.3 Practical Quantum Detectors
 photo-voltaic detectors : made from two semiconductors, one of them transparent to light, for instance a layer of CdS deposited on selenium. When light is incident on the junction, the electrons start moving, but only in one direction producing a current; in other words, the junction converts light energy into electrical energy.
used as solar cells and as exposure meters in photographic cameras.

6.3 Practical Quantum Detectors
 image tube: not only detects light but also preserves the spatial characteristics of an image.
•contain an array of photoconductors , one for each pixel. When exposed to light, the elements from a latent image that can be read by an electron beam scanning across them.
•the photoelectrons emitted by the cathode can be focused by an electron lens and made visible on a phosphor screen mounted in the same tube.

6.3 Practical Quantum Detectors
• image intensifier : the image is merely amplified .
• image converter the image is formed in the IR, the UV or the X-ray range and converted into the visible
• microchannel image intensifier the system is built around an array of many short fibers or capillaries , fused into a wafer.