Laws of Radiation - Lecture 5

Wien Law :
wavelength (lmax) of the most intense radiation emitted by a black-body only depends on its temperature (T) according to the following formula
lmax = a/T

a=2897 micron K
lmax is in micron
T is in K

Stefan-Boltzman Law :
total amount of radiation (F) emitted per unit time from a unit area (say 1 m**2) of a black body only depends on its temperature (T) according to the following formula
F= b T**4

where b=5.67E-8 W /m**2/K**4
W= Watt= J/s ;
J=Joule=kg m**2/s**2 ; unit of energy

The sun emits radiation approximately like a black-body;
The sun's temperature is about 6000 K;
In agreement with Wien Law , most of the solar radiation is
in the range of visible light (0.4 < l <0.7 microns)
lmax = 2897/6000 = 0.5 micron ;
SOLAR Radiation

Everything on earth typically has temperature between 250 and 320 K;
the equivalent black-body radiation of such materials is
therefore mostly in the 5 to 20 micron range
lmax = 2897/300 = 10 micron ;
TERRESTRIAL Radiation

General law of radiation : Planck Law
A mathematical result describing
how the radiation intensity emitted by a black body depends upon
the wavelength of the radiation (l) and its temperature (T).

F(black body) = F( l , T)

Sketch of F( l , T)

Max Planck's (1901) basic idea :
energy of radiation only exists in discrete amount & not in any arbitrary amount ;
Concept of quantum ;
Led to the development of "Quantum Theory" of physics in 1920s
The concept of quantum applies to all fundamental properties of matter in atomic scale.
Two major aspects of atomic physics of general interests & far-reaching implications :
(1) Duality in the identity of atomic objects such as light, electron .
i.e. In some experiment setups, they appear to have properties of Waves &
in other setups, they appear to have properties of Particles .
(2) Uncertainty Principle : e.g. Can't measure all properties of an object with arbitrary precision at the same time.


How can we quantify and interpret "optical" phenomenoa involving absorption/emission by real materials ?
Notions of emissivity, e and absorptivity , a
Writing F for rate of emission and A for rate of absorption, we define for each wavelength :

F(object) = e F(black body)
A(object) = a A(black body)

For each wavelength,
0 < e < 1
0 < a < 1
Emissivity and absorptivity of a material have different values at different wavelengths :
e(l), a(l)
They can be measured with high accuracy
e.g. Snow :
e(l) ~0 for the visible light,
e(l) ~1 for infrared light
So snow emits very little visible light, but a lot of infrared light
Such information for the common materials have been established.


Kirchhoff Law :
Emissivity = absorptivity at each wavelength for all materials.
e(l) = a(l)
Therefore, a good absorber is also a good emitter of radiation.
So snow also absorbs very little visible light, but a lot of infrared light
That is why we can see coming down on a dimly lighted ski-slope

A related quantity is reflectivity, also called :
Albedo (A) is the % of radiation reflected by a material
A=1-a
Snow, 75 to 95 %
cloud (thick), 60 to 90 %
cloud, (thin) 30 to 50 %
sand, 15 to 45 %
water, 10 %
forest, 3 to 10 %
The earth as a whole, 30 %

Thus, 70% of incoming solar radiation affects the atmosphere & surface of earth
About 20% is absorbed by atmosphere
About 50% is absorbed by the surface
Thus, air is warmed from below
We will discuss the details later

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