The phenomenon of reflection,
refraction, interference and diffraction can be explained by considering
radiations as waves but quantum theory treat radiations as particles. It was
clear from the Young’s double slit experiment that light (radiations) is a form
of wave as it formed interference pattern on the screen. But with the help of
this concept of radiations being waves it was not possible to explain and solve
the problem of Black body Radiations which led to the formation of a new Theory
called Quantum Theory. Before discussing about Black Body Radiations let’s talk
about thermal radiations.
Radiations emitted by a body due to
its temperature is called thermal radiations. As the temperature of body
increases it emit radiations of specific wavelength. All
bodies emit and absorb these radiations. The spectrum of thermal radiations is
continuous with following characteristics:
- As the thermal radiations depend upon the temperature of the body. Higher the temperature greater will be the amount of radiations emitted.
- Wavelength of the radiations become shorter and shorter as the temperature increases.
Thermal
radiations not only depends upon the temperature of the body but also on the
material of the body. To understand and study these radiations we have to
introduce an ideal radiator. This ideal radiator is Black Body.
Black Body:
A black body is an ideal radiator
which absorbed all the radiations falling on it and emit all of them when
heated at a certain temperature. A black body is a good absorber as well as a
good emitter of radiations. But the problem is there is not a single body that
can absorb all the radiations and can emit all of them. So, we have to make one
that can be considered as a black body and can absorb almost all of the
radiation falling on it.
An ideal
radiator can be obtained by forming a cavity in the block of a metal with its
wall being held at uniform temperature. A small hole is drilled in the cavity
and inner walls of the cavity are coated with lamp black. Any radiations
entering the cavity has a very little chance to get out of it. When the cavity
(Black Body) is heated to a certain temperature it emit all the radiations. These
radiations emitted by a black body are called Black Body radiations / cavity Radiations
/ Temperature Radiations as it only depends upon the temperature of the walls
of the cavity. Let me define a few terms used for radiations emitted from a
black body.
- Emissive Power: The amount of energy radiated in vacuum per second per unit area of a surface. For any hot surface it is denoted by ‘e’ and for black body it is denoted by ‘E’.
- Monochromatic Emissive Power: the amount of energy radiated per second per unit area per unit wavelength of interval. It is denoted by ‘eλ’ for hot bodies and for black body it is denoted by ‘Eλ’.
- Absorptive Power: It is the ratio of the amount of energy absorbed by the body to the amount of energy falling on it and is denoted by ‘a’.
- Monochromatic Absorptive Power: It is the ratio to the amount of energy absorbed by the body to the amount of energy falling in a particular wavelength.
Energy Distribution in the spectrum
of a black body:
A black body is
the one which emits radiations which depends upon its temperature and does not
depend upon its surface nature. A spectrum of the radiations emitted by black
body can be obtained by spectrometer.
The black body radiations enclosed in the cavity exerts
pressure on the walls of the cavity just as the gas exerts pressure on the
walls of the vessel. But unlike molecules of gas all frequencies in black body
radiations move with same velocity (speed of light). Also pressure of the gas
can be varied without changing its temperature but pressure of the black body
radiations can be changed only by changing its temperature. The distribution of
energy among different wavelengths in black body spectrum was studied by Lummer
and Prigsheim. By plotting ‘Eλ’ as a function of wavelength , a
family of curves can be drawn for different temperatures of black body/ these
curves real the following interesting facts.
At
given temperature the energy is not uniformly distributed in the radiation
spectrum of the body.
For all wavelength, increase in
temperature cause an increase in the energy emission. The radiation intensity
increase with increase in the wavelength and at a certain wavelength λmax , it has a maximum value with further increase in wavelength, the
intensity decreases.
The
wavelength of the maximum intensity λmax
is inversely proportional to absolute
temperature ‘T’ of black body.
λmax x T = constant
The
value of the constant is 0.0029 mk. This equation is called WIEN DISPLACEMENT LAW.
The area under each curve represent
total energy radiated over all wavelengths at a particular temperature. It is
directly proportional to the Kelvin temperature.
E ∝ T4
E = σT4
This
equation is called STEPHEN-BOLTZMAN LAW.
Theoretical Explanation (Planks Law):
Wein’s and lord Rayleigh-jean
presented laws based upon classical mechanics and thermodynamics. Wein’s law
was agreed with the experimental data for shorter wavelengths and failed for
longer wavelength while on the other hand Rayleigh-jeans law was agreed with
experimental curves of longer wavelengths but it lead to infinity for shorter
wavelengths. The failure of Rayleigh-jeans law which was based on classical
theory presented a crises, because there was no flaw in the derivations. Max
Planks thought that the flaw must be in classical theory. He presented a new
assumption for the emission and absorption of radiations. These new assumption
led to a new field of though known as “Quantum Theory” that altered the whole
outlook of physics.
Planks suggested that the
electromagnetic radiations are not emitted continuously as required by the wave
theory but the oscillation atoms only absorb or re-emit energy in discrete
bundles called quanta. The assumptions are:
The atoms that make up the walls of the
cavity radiator behave like tiny electromagnetic oscillators, each with a
particular frequency of oscillation and each can absorb and emit radiations.
An oscillator cannot have any energy but
the only energy given by “E = nhf” where ‘n’ is the principle quantum number ‘h’
is the Planks constant and ‘f’ is the frequency.
The oscillators do not radiate energy
continuously, but only in bundle or quanta. These quanta of energy called
Photons are emitted when an oscillator changes its quantized energy state.
Using these assumptions, Plank
arrived at a formula for the distribution of energy in a black body radiation
spectrum.
The curve
representing this equation fits well with the experimental curve. Plank
received Nobel Prize in 1918 for his explanation of Black Body Radiations.