Black body radiation.

Blackbody

radiation

Contents

Concept of Black body AndBlock body radiation

Stefan’s Law, Wien’s displacement lawTheories

1. Classical Theory2. Plank's Theory Bhor's Model and its limitations Photoelectric effect

Compton effect

introduction

The black body notion is important in studying thermal

radiation and electromagnetic radiation energy transfer in

all wavelength bands.

Black body as an ideal radiation absorber and it is used as

a standard for comparison with the radiation of real

physical bodies.

Its characteristics are sometimes are used in describing

and studying artificial electromagnetic radiation (in radio

and TV- broadcasting and communication).

Definition of black body

An ideal body which absorbs all the electromagnetic

radiation that strikes it so that all incident radiation is

completely absorbed.

Concept of black bodyWhy black body??

Because those bodies that absorb incident visible light well seem

black to the human eye.

Example: We can hardly characterize our sun which is indeed

almost a black body within a very wide band of electromagnetic

radiation wavelength as a black physical object in optics. It is namely

bright-white sunlight which represents the equilibrium black body

radiation.

Concept of black bodyApplication :

Optical band (surfaces approach an ideal black body in their

ability to absorb radiation) such as soot, silicon carbide,

platinum and golden niellos.

Earth surfaces (water surfaces, ice, land) absorb infrared

radiation well and in thermal IR band, these physical objects are

ideal black bodies.

Concept of black body

Concept of black body

Black body radiation /

Cavity radiation

The electromagnetic radiation that would be

radiated from an ideal black body

A good approximation of a black body is a small hole leading to the inside of a hollow object

The hole acts as a perfect absorber

The nature of the radiation leaving the cavity through the hole depends only on the temperature of the cavity

Blackbody Approximation

Intensity of Blackbody Radiation, Summary

• The intensity increases with increasing temperature

• The amount of radiation emitted increases with increasing temperature– The area under the curve

• The peak wavelength decreases with increasing temperature

Energy spectrum

EM Radiation : A kind of radiation including visible light, radio

waves, gamma rays, and X-rays, in which electric and magnetic fields

vary simultaneously.

Energy spectrum based on the EM spectrum.

EM Spectrum :  The distribution of electromagnetic radiation

according to energy (or equivalently, by virtue of the relations in the

previous section, according to frequency or wavelength).

Energy spectrumSpectrum of Electromagnetic Radiation

Region Wavelength(Angstroms)

Wavelength(centimeters)

Frequency(Hz)

Energy(eV)

Radio > 109 > 10 < 3 x 109 < 10-5

Microwave 109 - 106 10 - 0.01 3 x 109 - 3 x 1012 10-5 - 0.01

Infrared 106 - 7000 0.01 - 7 x 10-5 3 x 1012 - 4.3 x 1014 0.01 - 2

Visible 7000 - 4000 7 x 10-5 - 4 x 10-5 4.3 x 1014 - 7.5 x 1014 2 - 3

Ultraviolet 4000 - 10 4 x 10-5 - 10-7 7.5 x 1014 - 3 x 1017 3 - 103

X-Rays 10 - 0.1 10-7 - 10-9 3 x 1017 - 3 x 1019 103 - 105

Gamma Rays < 0.1 < 10-9 > 3 x 1019 > 105

RADIATION FROM ELECTRICALLY HEATED CARBON TUBE

Slit s1

Slit s2

To Bolometer

Fluorspar prism

Concave mirror M2

Concave mirror M1

Lummer and Pringsheim Experiment

At a particular temperature the distributed energy is not uniform among the various wavelengths of the radiation emitted by the black body.

For each temperature there is a wave length (λm) at which energy radiated is maximum (=Em ).

Increase in temperature Em increases but the corresponding (λm )decreases

The area under the curve for a particular temperature gives the total energy emitted by the black body per unit area per second for the complete spectrum .

Stefan’s law

Stefan’s Law or Stefan’s Boltzmann’s Law

The energy radiated by a blackbody radiator per second

per unit area is directly proportional to the fourth power of

the absolute temperature.

Stefan’s law

Stefan’s Law (1879, 1884) Josef Stefan deduced the rule in 1879 and Ludwig Boltzmann

provided a formal derivation in 1884.

Classical physics

Explain the growth in the height of the curve as the temperature

increase.

Energy emitted increase rapidly with an increase in temperature

which is proportional to the temperature raised to the fourth power.

Stefan’s lawFormula

Where

F= energy flux

T = Temperature

σ = Stefan Constant

F=σT4

wein’s displacement law

The black body radiation curve for

different temperature peaks at a wavelength

inversely proportional to the temperature.

Wein’s Displacement Law,

1893

wein’s displacement law

Formula

Unit constant, c : meter per Kelvin (m/K)

λmax = c = 2.898x10-3

T T

Rayleigh-Jeans Law This law explains blackbody radiation 𝑬𝝀 = 𝟖𝝅𝑲𝑻𝝀𝟒

𝑩𝒐𝒍𝒕𝒛𝒎𝒂𝒏𝒏′𝒔𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕= 𝟏.𝟑𝟖𝟎𝟔𝑿𝟏𝟎−𝟐𝟑 • At long wavelengths, the law

matched experimental results

fairly well

• At short wavelengths, there

was a major disagreement

between the Rayleigh-Jeans

law and experiment

clasical theory

This theory stats that “Black body radiation whose wavelength and colour that depends on the temperature of the object. The wavelength of energy emitted by an object depends on only its temperature, not its surface or composition.”

Classical theory could not explain the sharp decrease in the intensity of radiation emitted at shorter wavelengths.

Limitation of classical theory

Max PlanckIntroduced the concept of “quantum of theory ”In 1918 he was awarded the Nobel Prize for the discovery of the quantized nature of energy

Plank observed the Rayleigh-jeans and wein’s law and developed theory.

According to this theory

Radiant energy is emitted or absorbed discontinuously in the form of tiny bundles of energy known as quanta. This can be expressed by

Where,

Max Planck theory

A body can emit or absorb energy only in whole number multiplies of quantum number i.e 𝟏𝒉𝒗,𝟐𝒉𝒗,𝟑𝒉𝒗………,𝒏𝒉𝒗. Energy in fraction of a quantum cannot be lost or absorbed. This is known as quantization of energy.

Based on this theory plank obtained the following expression for energy density of black body radiation 𝑬𝝀= 𝟖𝝅𝒉𝒄𝝀𝟓 × 𝟏𝐞𝐱𝐩( 𝐡𝐜𝐊𝐓𝛌) − 𝟏 Where,

(h)= Planck’s constant, the

(c)= speed of light

(k)= Boltzmann constant and

(T)=absolute temperature

Max Planck theory

Photo electric effectPhoto electric effect is a process in which electrons are emitted when radiation of a certain frequency strikes the surface of a metal.

This was observed by Sir J.J Thomson in some his experiments. The electrons that are emitted are called photoelectrons.It was found that the emission of electron from a given metal depended on the frequency of the radiation and not on the intensity. Thus for every metal there exists a minimum frequency called the threshold frequency . Only radiation equal to this frequency or above it can cause emission of electron from the surface of metal.

Photo electric effectUV light

CLEAN METAL SURFACE

On the basis of quantum theory Einstein gave an expression

for the photo electric effect

ℎ𝜗= Ф+ 12𝑚𝑣2

where

Ф is threshold energy of the metal 12𝑚𝑣2 is kinetic energy

electrons in orbits

nucleus

Bohr’s Atomic model

Postulates of Bohr’s Theory1. In an atom, the electrons revolve around the nucleus in

certain definite circular paths called orbits, or shells.. Each shell or orbit corresponds to a definite energy. Therefore, these circular orbits are also known as energy levels or energy shells.

2. The electrons revolve rapidly around the nucleus in fixed circular paths called energy levels or shells. These can represented by number 1,2,3,4,…or by letters K,L,M,N…..

3. When an electron jumps from a higher energy level to a lower one, the amount of energy absorbed or emitted is given by the difference of energies associated with the two levels

The energy absorbed or lost is equal to the difference between the energies of the two energy levels, i.e.,

ΔE= Ehigher - Elower

Angular momentum of an electron moving

around the nucleus is quantised.

mvr = ( ℎ2𝜋)n

Where

m=mass

v= linear velocity of an electron and

r= radius of the electron.

Postulates of Bohr’s Theory

This model was applicable only for those atoms which have one electron.

Bohr theory explained only spherical orbits. This model failed to explain Zeeman Effect

and stark effect.Bohr model could not explain the uncertainty

principle of Heisenberg.Bohr model could not explain the wave nature

of electron. It explained only particle nature of electron.

Limitations of Bohr’s Model

Arthur Compton found that. “If monochromatic X-rays are allowed to fall on carbon or some other lighter elements, the scattered X-rays have wavelength larger than the incident rays. In other words, the scattered X-rays have low frequency than the incident rays. This causes decrease in the energy of incident ray.

Compton effect

Compton effect By applying law of conservation of energy and the law of momentum and assuming X-rays to consist of photons, having energy equal to ℎ𝜗 Compton shows that

∆λ = (2ℎ𝑚𝑐)sin2(𝜃2)

Where, ∆λ = Compton shift m = mass of the electron

C = velocity of light

𝜃 = angle between incident and scattered X-rays.

Reference Physical chemistry

(Puri Sharma)Physical chemistry

(R.L Madan) phy sical chemistry

(a.s negi S.C anand)

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