Skip to main content

Planck's radiation law.

Planck's radiation law;


Conclusion of Rayleigh-Jeans law;

According to Rayleigh-Jeans law as the frequency of radiation tends to infinity the spectral energy density must also tend to infinity. But in reality as the frequency increase spectral energy density decreases. Thus Rayleigh-Jeans law agrees with experimental results at low frequencies but strongly disagrees at high frequencies. This inconsistency between observations and the predictions of classical physics is commonly known as ultraviolet catastrophe.
UV catastrophe
Ultraviolet catastrophe.

 

Planck's law

Planck's hypothesis;

This failure of classical theory (Rayleigh-Jeans law) led Max Planck to develop a law known as Planck's law for the study of Blackbody radiation. He put forward the following assumptions (Planck's hypothesis) to derive the Blackbody radiation formula.
1) Blackbody radiation contain infinite number of harmonic oscillators. Each oscillator have its own natural frequency.
2) Blackbody does not emit or absorb radiation continuously but as an integral multiple of h𝛎, where h is Planck's constant and 𝛎 is the frequency of radiation. 
i.e E=nh𝛎 ; Where n is integer.
Thus according to Planck Blackbody emit radiation in the form of packets.

Derivation;

Planck's law derivation
Planck's law derivation~1


Planck's law derivation
Planck's law derivation~2



Questions on Planck's law                              

Q1) What is Ultraviolet catastrophe?
Ans)According to Rayleigh-Jeans law as the frequency of radiation tends to infinity the spectral energy density must also tend to infinity. But in reality as the frequency increase spectral energy density decreases. Thus Rayleigh-Jeans law agrees with experimental results at low frequencies but strongly disagrees at high frequencies. This inconsistency between observations and the predictions of classical physics is commonly known as ultraviolet catastrophe.

Q2) What assumptions are made by Planck to derive the Blackbody radiation formula?
Ans) The failure of classical theory (Rayleigh-Jeans law) led Max Planck to develop a law known as Planck's law for the study of Blackbody radiation. He put forward the following assumptions (Planck's hypothesis) to derive the Blackbody radiation formula.
1) Blackbody radiation contain infinite number of harmonic oscillators. Each oscillator have its own natural frequency.
2) Blackbody does not emit or absorb radiation continuously but as an integral multiple of h𝛎, where h is Planck's constant and 𝛎 is the frequency of radiation. 
i.e E=nh𝛎 ; Where n is integer.
Thus according to Planck Blackbody emit radiation in the form of packets.

Q3) State whether the statement is true or false; In Planck's law there is no more Ultraviolet catastrophe?
Ans) The following Statement is true;
In Planck's law there is no more Ultraviolet catastrophe.

Comments

Post a Comment

Popular posts from this blog

Mass defect, packing fraction and binding energy.

 Mass defect, packing fraction and binding energy: It was assumed that mass of the nucleus is equal to the mass of its constituents (i.e protons and neutrons). But experimentally it was found that the actual mass of the nucleus is less than the theoretical mass. Thus, the difference between the theoretical mass and experimental mass is called mass defect i.e ∆m={[Zmₚ + (A-Z)mₙ] - M} Where mₚ= mass of proton              mₙ= mass of neutron               M= actual mass of nucleus                Z= atomic number                A= mass number The ratio of mass defect and mass number (A) is called packing fraction (f) f = ∆m/A Thus packing fraction is the mass defect available per nucleon. The packing fraction explains the stability of the nucleus. The packing fraction may be positive, negative or zero. The positive value of packing fraction indicates that the nuclei is unstable while the negative value of packing fraction indicates that a fraction of nucleus mass has been converted into e
Post a Comment
Read more

Different kinds of beta decay.

 Different kinds of beta decay 1) Negative beta decay process: When there is excess number of neutrons in the nucleus, the neutron is converted into proton with the emission of electron and antineutrino particle and this process is called negative beta decay process. Negative beta decay. 2) Positive beta decay process: When there is excess number of protons in the nucleus, the proton is converted into neutron with the emission of positron and neutrino particle and this process is called positive beta decay process. Positive beta decay. 3) Electron Capture: When there is excess number of protons in the nucleus, sometimes the nucleus will absorbed the nearby electrons in the nearest electron orbital emitting neutron and a neutrino and this process is called electron capture. Electron capture. 4) Inverse beta decay: Inverse beta decay. Thus such kind of reaction in which neutrinos are absorbed to create some sort of beta decay is called inverse beta decay. Inverse beta decay confirm the e
Post a Comment
Read more

LS coupling and jj coupling.

 Total angular momentum: The total angular momentum of an electron is the sum of the orbital angular momentum and spin angular momentum of the electron i.e Coupling Scheme Since an atom consist of large number of electrons having different orbital and spin momenta, Coupling scheme is necessary to obtain the resultant orbit and spin momenta of atom as a whole. There are two types of coupling scheme namely 1) LS Coupling 2) JJ Coupling. 1)LS Coupling: In this coupling the 'l' vectors of all electrons combine to form resultant 'L' vector and all the 's' vectors of these electrons combine to form resultant 'S' vector. Then the 'L' vector and 'S' vector undergoes vector addition to give resultant 'J' vector which represents the total angular momentum of an atom. Symbolically LS coupling is represented as This type of coupling is governed by the following principles: 1) All the three vectors (L,S and J vectors) are quantized. 2)L is an
Post a Comment
Read more