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What is the basic equation of thermal radiation from which all other equations of radiation can be derived?
- a)Stefan-Boltzmann equation
- b)Planck’s equation
- c)Wien’s equation
- d)Rayleigh-Jeans formula
Correct answer is option 'B'. Can you explain this answer?
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The basic equation of thermal radiation is Planck's equation. It is the fundamental equation for describing the spectral distribution of electromagnetic radiation emitted by a black body at a given temperature. This equation is the starting point for deriving all other equations of radiation.
Planck's Equation:
Planck's equation is given by:
$$B(\nu, T) = \frac{2h\nu^3}{c^2}\frac{1}{e^{\frac{h\nu}{kT}}-1}$$
where
- $B(\nu, T)$ is the spectral radiance of the black body at frequency $\nu$ and temperature $T$.
- $h$ is Planck's constant.
- $c$ is the speed of light.
- $k$ is Boltzmann's constant.
Derivation:
Planck derived this equation in 1900 by assuming that the energy of the electromagnetic field was quantized, that is, it could only have certain discrete values. He used this assumption to derive an expression for the energy density of the radiation, and from this, he derived an expression for the spectral radiance.
Applications:
Planck's equation is used in many areas of physics, including astrophysics, cosmology, and materials science. It is used to calculate the spectral distribution of electromagnetic radiation emitted by a black body at a given temperature. This equation is also used to calculate the temperature of a black body based on the spectral radiance of the radiation it emits.
Conclusion:
In conclusion, Planck's equation is the basic equation of thermal radiation from which all other equations of radiation can be derived. It is a fundamental equation in physics and is used in many areas of research.
Planck's Equation:
Planck's equation is given by:
$$B(\nu, T) = \frac{2h\nu^3}{c^2}\frac{1}{e^{\frac{h\nu}{kT}}-1}$$
where
- $B(\nu, T)$ is the spectral radiance of the black body at frequency $\nu$ and temperature $T$.
- $h$ is Planck's constant.
- $c$ is the speed of light.
- $k$ is Boltzmann's constant.
Derivation:
Planck derived this equation in 1900 by assuming that the energy of the electromagnetic field was quantized, that is, it could only have certain discrete values. He used this assumption to derive an expression for the energy density of the radiation, and from this, he derived an expression for the spectral radiance.
Applications:
Planck's equation is used in many areas of physics, including astrophysics, cosmology, and materials science. It is used to calculate the spectral distribution of electromagnetic radiation emitted by a black body at a given temperature. This equation is also used to calculate the temperature of a black body based on the spectral radiance of the radiation it emits.
Conclusion:
In conclusion, Planck's equation is the basic equation of thermal radiation from which all other equations of radiation can be derived. It is a fundamental equation in physics and is used in many areas of research.
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What is the basic equation of thermal radiation from which all other equations of radiation can be derived?a)Stefan-Boltzmann equationb)Planck’s equationc)Wien’s equationd)Rayleigh-Jeans formulaCorrect answer is option 'B'. Can you explain this answer?
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