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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.

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