ANS:B - Planck's

Planck's law, formulated by the German physicist Max Planck in 1900, describes the spectral distribution of electromagnetic radiation emitted by a blackbody in thermal equilibrium. It played a crucial role in the development of quantum theory and the understanding of the nature of radiation. The equation for Planck's law is given by: B(λ,T)=λ52hc2​eλkB​Thc​−11​ Where:

• B(λ,T) is the spectral radiance (or spectral intensity) of the blackbody radiation at wavelength λ and temperature T.
• ℎh is Planck's constant (6.62607015×10−346.62607015×10−34 m² kg / s).
• c is the speed of light in vacuum (299,792,458299,792,458 m/s).
• λ is the wavelength of the radiation.
• kB​ is Boltzmann's constant (1.380649×10−231.380649×10−23 J/K).
• T is the temperature of the blackbody in Kelvin.

Planck's law describes how the spectral radiance of a blackbody radiation varies with wavelength and temperature. It shows that blackbody radiation is not continuous but rather consists of discrete packets of energy called photons. The distribution of these photons across different wavelengths depends on the temperature of the blackbody. Key features of Planck's law include:

1. Wavelength Dependence: The spectral radiance is inversely proportional to the fifth power of the wavelength (λ5). This means that shorter wavelengths (higher frequencies) have higher spectral radiance, with the distribution shifting towards the ultraviolet end of the spectrum as temperature increases.
2. Temperature Dependence: The exponential term in the denominator of the equation depends on the ratio of the photon energy to the thermal energy (given by kB​T). At low temperatures, this term becomes negligible, and Planck's law reduces to Wien's displacement law, which describes the peak wavelength of blackbody radiation. At high temperatures, the exponential term dominates, leading to a broader distribution of radiation across wavelengths.

Planck's law has significant implications in various fields, including astrophysics, cosmology, and thermal radiation engineering. It provides a fundamental understanding of how objects emit and absorb electromagnetic radiation based on their temperature and spectral characteristics.